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responsesR 0.1.0 (Release date: 2020-10-17)

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responsesR 1.0.0 (Release date: 2024-03-28)

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  • This version now only imports mvtnorm, along with the standard R -packages stats and graphics, which are typically included in R -releases.
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responsesR 1.1.0 (Release date: 2024-06-06)

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responsesR 1.1.1 (Release date: 2024-06-06)

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- - - - - - - - - - - - - - - diff --git a/NEWS.md b/NEWS.md index 0a24ae6..3776035 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,33 +1,30 @@ -# latent2likert 0.1.0 (Release date: 2020-10-17) - +## Version 0.1.0 +- Release date: 2020-10-17 - Initial release (development version). - Tested on platforms: x86_64-pc-linux-gnu (64-bit) and x86_64-w64-mingw32 (64-bit). -# latent2likert 1.0.0 (Release date: 2024-03-28) - -- The option to generate correlated Likert scale items was added to the function `rLikert()`. -- New function `estimate_parameters()` was added that allows for the estimation of parameters from existing survey data to replicate it more accurately. -- Issues related to the dependencies have been resolved. -- This version now only imports the standard R packages mvtnorm, stats, and graphics packages stats and graphics, which are typically included in R releases. -- The package sn is necessary only when generating correlated responses based on skew normal distribution. -- Added user prompts for installing the sn package when necessary. - -# latent2likert 1.1.0 (Release date: 2024-06-06) - -- A minor update of functions and vignettes. - -# latent2likert 1.1.1 (Release date: 2024-06-06) - -- The package was renamed from responsesR to latent2likert. -- To capture the essence of converting latent variables into Likert scale responses. -- Improvements of package website and documentation. - -# latent2likert 1.2.1 (Release date: 2024-06-12) - -- Refactored code for improved modularity and maintainability. -- Modularized core functions for better readability. +## Version 1.0.0 +- Release date: 2024-03-28 +- Added the option to generate correlated Likert scale items in the `rlikert()` function. +- Added the `estimate_params()` function for estimating parameters from existing survey data. +- Resolved dependency issues. +- Reduced dependency to only standard R packages: mvtnorm, stats, and graphics. +- The sn package is now required only for generating correlated responses using a skew normal distribution. +- Added user prompts to install the sn package when needed. + +## Version 1.1.0 +- Release date: 2024-06-06 +- Minor updates to functions and vignettes. + +## Version 1.1.1 +- Release date: 2024-06-06 +- Renamed the package from `responsesR` to `latent2likert` to better reflect its purpose of converting latent variables into Likert scale responses. +- Improved the package website and documentation. +- **Note:** The codebase is under development, and finer details may change. + +## Version 1.2.1 +- Release date: 2024-06-12 +- Refactored code for enhanced modularity and maintainability. +- Modularized core functions for improved readability. - Improved the structure and organization of the codebase. -- Improved error handling of different cases for correlations input. -- Updated the `estimate_parameters()` function for estimating latent parameters from survey data. -- The codebase is currently in development, finer details may change. - +- Enhanced error handling for various correlation input scenarios. diff --git a/R/discretization.R b/R/discretization.R index db49749..d2dc5ae 100644 --- a/R/discretization.R +++ b/R/discretization.R @@ -18,14 +18,15 @@ #' @examples #' discretize_density(density_fn = stats::dnorm, n_levels = 5) #' discretize_density(density_fn = function(x) { -#' 2 * stats::dnorm(x) * stats::pnorm(0.5 * x)}, n_levels = 4) -#' @details -#' The function addresses the problem of transforming a continuous random -#' variable \eqn{X} into a discrete random variable \eqn{Y} with minimal +#' 2 * stats::dnorm(x) * stats::pnorm(0.5 * x) +#' }, n_levels = 4) +#' @details +#' The function addresses the problem of transforming a continuous random +#' variable \eqn{X} into a discrete random variable \eqn{Y} with minimal #' distortion. Distortion is measured as mean-squared error (MSE): #' \deqn{ -#' \text{E}\left[ (X - Y)^2 \right] = -#' \sum_{k=1}^{K} \int_{x_{k-1}}^{x_{k}} f_{X}(x) +#' \text{E}\left[ (X - Y)^2 \right] = +#' \sum_{k=1}^{K} \int_{x_{k-1}}^{x_{k}} f_{X}(x) #' \left( x - r_{k} \right)^2 \, dx #' } #' where: @@ -38,41 +39,41 @@ #' } #' This problem is solved using the following iterative procedure: #' \describe{ -#' \item{\eqn{1.}}{Start with an arbitrary initial set of representation +#' \item{\eqn{1.}}{Start with an arbitrary initial set of representation #' points: \eqn{r_{1} < r_{2} < \dots < r_{K}}.} -#' \item{\eqn{2.}}{Repeat the following steps until the improvement in MSE +#' \item{\eqn{2.}}{Repeat the following steps until the improvement in MSE #' falls below given \eqn{\varepsilon}.} #' \item{\eqn{3.}}{Calculate endpoints as \eqn{x_{k} = (r_{k+1} + r_{k})/2} -#' for each \eqn{k = 1, \dots, K-1} and set \eqn{x_{0}} and \eqn{x_{K}} to +#' for each \eqn{k = 1, \dots, K-1} and set \eqn{x_{0}} and \eqn{x_{K}} to #' \eqn{-\infty} and \eqn{\infty}, respectively.} -#' \item{\eqn{4.}}{Update representation points by setting \eqn{r_{k}} +#' \item{\eqn{4.}}{Update representation points by setting \eqn{r_{k}} #' equal to the conditional mean of \eqn{X} given \eqn{X \in (x_{k-1}, x_{k})} #' for each \eqn{k = 1, \dots, K}.} #' } -#' +#' #' With each execution of step \eqn{(3)} and step \eqn{(4)}, the MSE decreases -#' or remains the same. As MSE is nonnegative, it approaches a limit. -#' The algorithm terminates when the improvement in MSE is less than a given -#' \eqn{\varepsilon > 0}, ensuring convergence after a finite number +#' or remains the same. As MSE is nonnegative, it approaches a limit. +#' The algorithm terminates when the improvement in MSE is less than a given +#' \eqn{\varepsilon > 0}, ensuring convergence after a finite number #' of iterations. -#' -#' This procedure is known as Lloyd-Max's algorithm, initially used for scalar -#' quantization and closely related to the k-means algorithm. Local convergence -#' has been proven for log-concave density functions by Kieffer. Many common -#' probability distributions are log-concave including the normal and skew +#' +#' This procedure is known as Lloyd-Max's algorithm, initially used for scalar +#' quantization and closely related to the k-means algorithm. Local convergence +#' has been proven for log-concave density functions by Kieffer. Many common +#' probability distributions are log-concave including the normal and skew #' normal distribution, as shown by Azzalini. #' #' @references -#' Azzalini, A. (1985). -#' A class of distributions which includes the normal ones. +#' Azzalini, A. (1985). +#' A class of distributions which includes the normal ones. #' \emph{Scandinavian Journal of Statistics} \bold{12(2)}, 171–178. -#' +#' #' Kieffer, J. (1983). -#' Uniqueness of locally optimal quantizer for log-concave density and convex +#' Uniqueness of locally optimal quantizer for log-concave density and convex #' error function. #' \emph{IEEE Transactions on Information Theory} \bold{29}, 42–47. -#' -#' Lloyd, S. (1982). +#' +#' Lloyd, S. (1982). #' Least squares quantization in PCM. #' \emph{IEEE Transactions on Information Theory} \bold{28 (2)}, 129–137. #' @@ -134,7 +135,7 @@ update_epresentatives <- function(density_fn, midp) { #' Compute Distortion #' -#' Computes the distortion (mean-squared error) given the midpoints and +#' Computes the distortion (mean-squared error) given the midpoints and #' representation points. #' #' @param density_fn probability density function. @@ -148,7 +149,8 @@ compute_distortion <- function(density_fn, midp, repr) { endp <- c(-Inf, midp, Inf) mse <- vapply(seq_len(n_levels), function(k) { stats::integrate(function(x) { - density_fn(x) * (x - repr[k])^2}, endp[k], endp[k + 1])[[1]] + density_fn(x) * (x - repr[k])^2 + }, endp[k], endp[k + 1])[[1]] }, numeric(1)) return(sum(mse)) } @@ -166,7 +168,8 @@ calc_probs <- function(density_fn, endp) { n_levels <- length(endp) - 1 prob <- vapply(seq_len(n_levels), function(k) { stats::integrate(function(x) { - density_fn(x)}, endp[k], endp[k + 1])[[1]] + density_fn(x) + }, endp[k], endp[k + 1])[[1]] }, numeric(1)) return(prob) } diff --git a/R/estimation.R b/R/estimation.R index 0716265..74ca600 100644 --- a/R/estimation.R +++ b/R/estimation.R @@ -46,7 +46,7 @@ #' * Estimates the probabilities \eqn{p_{k}} for each item. #' * Computes the estimates of \eqn{\xi} and \eqn{\omega} for each item. #' * Combines the estimated parameters for all items into a table. -#' +#' #' @seealso \code{\link{discretize_density}} for details on calculating #' the endpoints, and \code{\link{part_bfi}} for example of the survey data. #' @export @@ -78,26 +78,26 @@ estimate_params <- function(data, n_levels, skew = 0) { } #' Estimate mean and standard deviation -#' -#' Estimates the mean and standard deviation of a latent variable given the +#' +#' Estimates the mean and standard deviation of a latent variable given the #' discrete probabilities of its observed Likert scale responses. -#' +#' #' @param prob vector of probabilities for each response category. #' @param n_levels number of response categories for the Likert scale item. #' @param skew marginal skewness of the latent variable, defaults to 0. #' @param eps tolerance for convergence, defaults to 1e-6. #' @param maxit maximum number of iterations, defaults to 100. -#' -#' @return A numeric vector with two elements: the estimated mean and +#' +#' @return A numeric vector with two elements: the estimated mean and #' standard deviation. -#' +#' #' @details #' This function uses an iterative algorithm to solve the system of non-linear -#' equations that describe the relationship between the continuous latent +#' equations that describe the relationship between the continuous latent #' variable and the observed discrete probability distribution of Likert scale #' responses. The algorithm ensures stability by reparameterizing the system #' and applying constraints to prevent stepping into invalid regions. -#' +#' #' @noRd estimate_mean_and_sd <- function(prob, n_levels, skew = 0, eps = 1e-6, maxit = 100) { @@ -134,14 +134,14 @@ estimate_mean_and_sd <- function(prob, n_levels, skew = 0, #' Initialize CDF and PDF Functions #' -#' Initializes the cumulative distribution function (CDF) and probability +#' Initializes the cumulative distribution function (CDF) and probability #' density function (PDF) based on the skewness parameter. #' #' @param skew numeric value representing the skewness of the distribution. -#' -#' @return A list containing the CDF and PDF functions appropriate for the +#' +#' @return A list containing the CDF and PDF functions appropriate for the #' given skewness. -#' +#' #' @noRd initialize_distributions <- function(skew) { if (abs(skew) > 0) { @@ -163,15 +163,15 @@ initialize_distributions <- function(skew) { #' #' @param x numeric vector of current estimates for the location and scaling #' parameters. -#' @param endp numeric vector of endpoints defining the boundaries of the +#' @param endp numeric vector of endpoints defining the boundaries of the #' response categories. #' @param prob numeric vector of probabilities for each response category. #' @param cdf_X function representing the cumulative distribution function #' (CDF) of the latent variable. -#' +#' #' @return A matrix of differences between the CDF evaluated at the endpoints #' and the observed probabilities. -#' +#' #' @noRd fn <- function(x, endp, prob, cdf_X) { u <- x[1] @@ -184,16 +184,16 @@ fn <- function(x, endp, prob, cdf_X) { #' #' Computes the Jacobian matrix used in the iterative root-finding process. #' -#' @param x numeric vector of current estimates for the location and scaling +#' @param x numeric vector of current estimates for the location and scaling #' parameters. -#' @param endp numeric vector of endpoints defining the boundaries of the +#' @param endp numeric vector of endpoints defining the boundaries of the #' response categories. #' @param pdf_X function representing the probability density function (PDF) #' of the latent variable. -#' +#' #' @return A matrix representing the Jacobian of the system of equations with #' respect to the parameters. -#' +#' #' @noRd jac <- function(x, endp, pdf_X) { u <- x[1] @@ -209,38 +209,3 @@ jac <- function(x, endp, pdf_X) { return(cbind(du, dv)) } - -#' Plot Contour -#' -#' Plots the contour of the objective function values over a grid -#' of parameter values. It visualizes the norm of the function \code{fn} -#' for different values of \code{u} (mean) and \code{v} (1/standard deviation) -#' and overlays the trace of parameter updates during the optimization process. -#' -#' @param fn objective function to be minimized. -#' @param endp endpoints of intervals that partition the continuous domain. -#' @param prob discrete probability distribution. -#' @param cdf_X cumulative distribution function of the latent variable. -#' @param trace matrix of parameter updates. -#' @noRd -plot_contour <- function(fn, endp, prob, cdf_X, trace) { - xlen <- 50 - ylen <- 50 - xgrid <- seq(-3, 3, length.out = xlen) # Range for mean (mu) - ygrid <- seq(0.1, 3, length.out = ylen) # Range for 1/sd - zvals <- matrix(NA, ncol = xlen, nrow = ylen) - for (i in seq_len(xlen)) { - for (j in seq_len(ylen)) { - zvals[i, j] <- norm(fn( - matrix(c(xgrid[i], ygrid[j])), - endp, prob, cdf_X - ), "2") - } - } - graphics::contour( - x = xgrid, y = ygrid, z = zvals, - col = "gray42", xlab = "u = mu", ylab = "v = 1/sd" - ) - graphics::grid(col = "lightgray", lty = "dotted") - graphics::points(trace[1, ], trace[2, ], pch = 20, col = "blue") -} diff --git a/R/part_bfi.R b/R/part_bfi.R index 5b168c9..1bfc362 100644 --- a/R/part_bfi.R +++ b/R/part_bfi.R @@ -23,7 +23,7 @@ #' \item{A5}{Make people feel at ease.} #' \item{gender}{Gender of the respondent.} #' } -#' @source {International Personality Item Pool (ipip.ori.org)} +#' @source {International Personality Item Pool ({https://ipip.ori.org})} #' @source {https://search.r-project.org/CRAN/refmans/psychTools/html/bfi.html} #' @references #' Revelle, W. (2024). diff --git a/R/simulation.R b/R/simulation.R index 56430db..6d0d9d9 100644 --- a/R/simulation.R +++ b/R/simulation.R @@ -1,12 +1,12 @@ #' Simulate Likert Scale Item Responses -#' -#' Simulates Likert scale item responses based on a specified number +#' +#' Simulates Likert scale item responses based on a specified number #' of response categories and the centered parameters of the latent variable. -#' -#' @param n_levels Integer. The number of response categories for the Likert scale item. -#' @param cp Named vector. The centered parameters of the latent variable, including -#' mean (`mu`), standard deviation (`sd`), and skewness (`skew`). -#' Skewness must be between -0.95 and 0.95. +#' +#' @param n_levels number of response categories for the Likert scale item. +#' @param cp centered parameters of the latent variable. +#' Named vector including mean (`mu`), standard deviation (`sd`), +#' and skewness (`skew`). Skewness must be between -0.95 and 0.95. #' @return A named vector of probabilities for each response category. #' @examples #' cp <- c(mu = 0, sd = 1, skew = 0.5) @@ -14,10 +14,10 @@ #' cp2 <- c(mu = 1, sd = 2, skew = -0.3) #' simulate_likert(n_levels = 7, cp = cp2) #' @details -#' The simulation process uses the following model detailed by Boari and Nai-Ruscone. -#' Let \eqn{X} be the continuous variable of interest, measured using Likert scale -#' questions with \eqn{K} response categories. The observed discrete variable \eqn{Y} is -#' defined as follows: +#' The simulation process uses the following model detailed by +#' Boari and Nai-Ruscone. Let \eqn{X} be the continuous variable of interest, +#' measured using Likert scale questions with \eqn{K} response categories. The +#' observed discrete variable \eqn{Y} is defined as follows: #' \deqn{ #' Y = k, \quad \text{ if } \ \ x_{k - 1} < X \leq x_{k} #' \quad \text{ for } \ \ k = 1, \dots, K @@ -27,26 +27,28 @@ #' \deqn{ #' -\infty = x_{0} < x_{1} < \dots < x_{K - 1} < x_{K} = \infty. #' } -#' The endpoints dictate the transformation of the density \eqn{f_{X}} of \eqn{X} -#' into a discrete probability distribution: +#' The endpoints dictate the transformation of the density +#' \eqn{f_{X}} of \eqn{X} into a discrete probability distribution: #' \deqn{ #' \text{Pr}(Y = k) = \int_{x_{k - 1}}^{x_{k}} f_{X}(x) \, dx #' \quad \text{ for } \ \ k = 1, \dots, K. #' } -#' +#' #' The continuous latent variable is modeled using a skew normal distribution. #' The function \code{simulate_likert} performs the following steps: #' * Ensures the centered parameters are within the acceptable range. #' * Converts the centered parameters to direct parameters. #' * Defines the density function for the skew normal distribution. -#' * Computes the probabilities for each response category using optimal endpoints. +#' * Computes the probabilities for each response category +#' using optimal endpoints. #' #' @references #' Boari, G. and Nai Ruscone, M. (2015). -#' A procedure simulating Likert scale item responses. -#' \emph{Electronic Journal of Applied Statistical Analysis} \bold{8(3)}, 288–297. -#' \doi{10.1285/i20705948v8n3p288} -#' +#' A procedure simulating Likert scale item responses. +#' \emph{Electronic Journal of Applied Statistical Analysis} \bold{8(3)}, +#' 288–297. +#' \doi{10.1285/i20705948v8n3p288} +#' #' @seealso \code{\link{discretize_density}} for details on how to calculate #' the optimal endpoints. #' @export @@ -156,12 +158,12 @@ rlikert <- function(size, n_items, n_levels, #' Calculate Optimal Endpoints #' -#' Returns the optimal endpoints of intervals that transform +#' Returns the optimal endpoints of intervals that transform #' a neutral density into discrete probability distribution. -#' +#' #' @param n_levels integer. Number of response categories. #' @param skew numeric. Skewness parameter of the latent variable. -#' +#' #' @return A numeric vector of optimal endpoints. #' @noRd calc_endpoints <- function(n_levels, skew) { @@ -184,7 +186,7 @@ calc_endpoints <- function(n_levels, skew) { #' @param mean numeric. Mean of the latent variable. #' @param sd numeric. Standard deviation of the latent variable. #' @param skew numeric. Skewness parameter of the latent variable. -#' +#' #' @return A numeric vector of simulated responses. #' @noRd generate_responses <- function(size, n_levels, mean, sd, skew) { @@ -198,7 +200,7 @@ generate_responses <- function(size, n_levels, mean, sd, skew) { #' Determines the type of correlation input provided. #' #' @param corr numeric or character or matrix. Correlation input. -#' +#' #' @return An integer representing the correlation case. #' @noRd handle_corr_case <- function(corr) { @@ -226,7 +228,7 @@ handle_corr_case <- function(corr) { #' @param corr numeric or matrix. Correlation input. #' @param corr_case integer. Correlation case identifier. #' @param n_items integer. Number of Likert scale items. -#' +#' #' @return A numeric matrix representing the correlation matrix. #' @noRd generate_corr_matrix <- function(corr, corr_case, n_items) { @@ -252,7 +254,7 @@ generate_corr_matrix <- function(corr, corr_case, n_items) { #' @param mean means of the latent variables. Numeric vector. #' @param sigma covariance matrix of the latent variables. #' @param skew skewness parameters of the latent variables. Numeric vector. -#' +#' #' @return A matrix of generated latent variables. #' @noRd generate_latent_variables <- function(size, mean, sigma, skew) { diff --git a/R/utilities.R b/R/utilities.R index 042c502..c112103 100644 --- a/R/utilities.R +++ b/R/utilities.R @@ -1,40 +1,84 @@ #' Plot Transformation #' -#' Plots the densities of latent variables in the first row -#' and transformed discrete probability distributions below. +#' Plots the densities of latent variables and the corresponding +#' transformed discrete probability distributions. #' #' @param n_items number of Likert scale items (questions). -#' @param n_levels number of response categories for each Likert item. Integer or vector of integers. -#' @param mean means of the latent variables. Numeric or vector of numerics. Defaults to 0. -#' @param sd standard deviations of the latent variables. Numeric or vector of numerics. Defaults to 1. -#' @param skew marginal skewness of the latent variables. Numeric or vector of numerics. Defaults to 0. -#' @return a plot showing the densities of latent variables and the corresponding discrete probability distributions. +#' @param n_levels number of response categories for each Likert item. +#' Integer or vector of integers. +#' @param mean means of the latent variables. +#' Numeric or vector of numerics. Defaults to 0. +#' @param sd standard deviations of the latent variables. +#' Numeric or vector of numerics. Defaults to 1. +#' @param skew marginal skewness of the latent variables. +#' Numeric or vector of numerics. Defaults to 0. +#' @return NULL. The function produces a plot. #' @examples #' plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)) -#' plot_likert_transform(n_items = 3, n_levels = 5, mean=c(0, 1, 2)) -#' plot_likert_transform(n_items = 3, n_levels = 5, sd=c(0.8, 1, 1.2)) -#' plot_likert_transform(n_items = 3, n_levels = 5, skew=c(-0.5, 0, 0.5)) +#' plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, 1, 2)) +#' plot_likert_transform(n_items = 3, n_levels = 5, sd = c(0.8, 1, 1.2)) +#' plot_likert_transform(n_items = 3, n_levels = 5, skew = c(-0.5, 0, 0.5)) #' @export -plot_likert_transform <- function(n_items, n_levels, mean=0, sd=1, skew=0) { +plot_likert_transform <- function( + n_items, n_levels, + mean = 0, sd = 1, skew = 0) { n_levels <- rep(n_levels, length.out = n_items) mean <- rep(mean, length.out = n_items) sd <- rep(sd, length.out = n_items) skew <- rep(skew, length.out = n_items) - graphics::layout(matrix(seq_len(n_items * 2), nrow=2, ncol=n_items)) + graphics::layout(matrix(seq_len(n_items * 2), nrow = 2, ncol = n_items)) x <- seq(-3, 3, length = 1000) for (i in seq_len(n_items)) { # Draw the densities of latent variables cp <- c("mu" = mean[i], "sd" = sd[i], "skew" = skew[i]) dp <- convert_params(cp) y <- density_sn(x, dp[["xi"]], dp[["omega"]], dp[["alpha"]]) - graphics::plot(x, y, type="l", lwd = 2, xlab = "", ylab = "", main="") + graphics::plot(x, y, type = "l", lwd = 2, xlab = "", ylab = "", main = "") graphics::title(paste("X", i, sep = "")) - + # Draw the corresponding discrete probability distributions prob <- simulate_likert(n_levels[i], cp) graphics::barplot(prob) graphics::title(paste("Y", i, sep = "")) } + invisible(NULL) +} + +#' Plot Contour +#' +#' Plots the contour of the objective function values over a grid +#' of parameter values. It visualizes the norm of the function \code{fn} +#' for different values of \code{u} (mean) and \code{v} (1/standard deviation) +#' and overlays the trace of parameter updates during the estimation process. +#' +#' @param fn objective function to be minimized. +#' @param endp endpoints of intervals that partition the continuous domain. +#' @param prob discrete probability distribution. +#' @param cdf_X cumulative distribution function of the latent variable. +#' @param trace matrix of parameter updates. +#' @return NULL. The function produces a plot. +#' @noRd +plot_contour <- function(fn, endp, prob, cdf_X, trace) { + xlen <- 50 + ylen <- 50 + xgrid <- seq(-3, 3, length.out = xlen) # Range for mean (mu) + ygrid <- seq(0.1, 3, length.out = ylen) # Range for 1/sd + zvals <- matrix(NA, ncol = xlen, nrow = ylen) + for (i in seq_len(xlen)) { + for (j in seq_len(ylen)) { + zvals[i, j] <- norm(fn( + matrix(c(xgrid[i], ygrid[j])), + endp, prob, cdf_X + ), "2") + } + } + graphics::contour( + x = xgrid, y = ygrid, z = zvals, + col = "gray42", xlab = "u = mu", ylab = "v = 1/sd" + ) + graphics::grid(col = "lightgray", lty = "dotted") + graphics::points(trace[1, ], trace[2, ], pch = 20, col = "blue") + invisible(NULL) } #' Calculate Response Proportions @@ -65,8 +109,8 @@ response_prop <- function(data, n_levels) { #' Pad Missing Levels #' -#' Helper function that takes a vector of proportions or probabilities -#' across possible responses and pads the missing levels with zeros up +#' Helper function that takes a vector of proportions or probabilities +#' across possible responses and pads the missing levels with zeros up #' to the specified number of response categories. #' #' @param pr proportions or probabilities across possible responses. @@ -92,7 +136,7 @@ pad_levels <- function(pr, n_levels) { #' @noRd validate_skewness <- function(skew) { if (skew > 0.95 || skew < -0.95) { - stop("The value of skewness must be in the range -0.95 to 0.95: + stop("The value of skewness must be in the range -0.95 to 0.95: `skew >= -0.95` and `skew <= 0.95`.") } } @@ -105,9 +149,11 @@ validate_skewness <- function(skew) { #' @noRd check_package <- function(pkg) { if (!requireNamespace(pkg, quietly = TRUE)) { - stop(sprintf('Package "%s" must be installed. - Please run:\n\n\tinstall.packages("%s")\n\n', - pkg, pkg), call. = FALSE) + stop(sprintf( + 'Package "%s" must be installed. + Please run:\n\n\tinstall.packages("%s")\n\n', + pkg, pkg + ), call. = FALSE) } } @@ -129,7 +175,7 @@ density_sn <- function(x, xi = 0, omega = 1, alpha = 0) { #' Convert Centered Parameters #' -#' Converts centered parameters to direct parameters used in the +#' Converts centered parameters to direct parameters used in the #' skew normal density. #' #' @param cp numeric vector. Centered parameters c(mu, sd, skew). diff --git a/README.Rmd b/README.Rmd index ed4bbca..a2d2b0c 100644 --- a/README.Rmd +++ b/README.Rmd @@ -17,12 +17,12 @@ knitr::opts_chunk$set( [![R-CMD-check](https://github.com/markolalovic/latent2likert/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/markolalovic/latent2likert/actions/workflows/R-CMD-check.yaml) -[![codecov](https://codecov.io/gh/markolalovic/latent2likert/branch/main/graph/badge.svg?token=HZTG6RUB2J)](https://codecov.io/gh/markolalovic/latent2likert) +[![codecov](https://codecov.io/gh/markolalovic/latent2likert/branch/main/graph/badge.svg?token=HZTG6RUB2J)](https://app.codecov.io/gh/markolalovic/latent2likert) ## Overview -The R package **latent2likert** is designed to effectively simulate the discretization process inherent to Likert scales while minimizing distortion. It converts continuous latent variables into ordinal categories to generate Likert scale item responses. This is particularly useful for accurately modeling and analyzing survey data that use Likert scales, especially when applying statistical techniques that require metric data. +The **latent2likert** package is designed to effectively simulate the discretization process inherent to Likert scales while minimizing distortion. It converts continuous latent variables into ordinal categories to generate Likert scale item responses. This is particularly useful for accurately modeling and analyzing survey data that use Likert scales, especially when applying statistical techniques that require metric data. ## Installation @@ -35,8 +35,7 @@ devtools::install_github("markolalovic/latent2likert") ## Dependencies -To keep the package lightweight, **latent2likert** only imports [mvtnorm](https://cran.r-project.org/package=mvtnorm), along with the standard R packages stats and graphics, which are typically included in R releases. An additional suggested dependency is the [sn package](https://cran.r-project.org/package=sn), which is required only for generating random responses from correlated Likert items based on a multivariate skew normal distribution. The package prompts the user to install this dependency during interactive sessions if needed. - +To keep the package lightweight, **latent2likert** only imports [mvtnorm](https://cran.r-project.org/package=mvtnorm), along with the standard R packages stats and graphics, which are typically included in R releases. An additional suggested dependency is the package [sn](https://cran.r-project.org/package=sn), which is required only for generating random responses from correlated Likert items based on a multivariate skew normal distribution. The package prompts the user to install this dependency during interactive sessions if needed. ## Features @@ -133,6 +132,6 @@ Note that, depending on the value of the skewness parameter, the normal latent d To simulate Likert item responses, the `draw_likert` function from the [fabricatr](https://CRAN.R-project.org/package=fabricatr) package can be used to recode a latent variable into a Likert response variable by specifying intervals that subdivide the continuous range. The **latent2likert** package, however, offers an advantage by automatically calculating optimal intervals that minimize distortion between the latent variable and the Likert response variable for both normal and skew normal latent distributions, eliminating the need to manually specify the intervals. -There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete probability distribution and sampling from it using the sample function in R or the `likert` function from the [wakefield](https://CRAN.R-project.org/package=wakefield) package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use [LikertMakeR](https://CRAN.R-project.org/package=LikertMakeR) or [SimCorMultRes](https://CRAN.R-project.org/package=SimCorMultRes) to generate correlated multinomial responses. +There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete probability distribution and sampling from it using the `sample` function in R or the `likert` function from the [wakefield](https://CRAN.R-project.org/package=wakefield) package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use [LikertMakeR](https://CRAN.R-project.org/package=LikertMakeR) or [SimCorMultRes](https://CRAN.R-project.org/package=SimCorMultRes) to generate correlated multinomial responses. Additionally, you can define a data generating process. For those familiar with item response theory, the [mirt](https://CRAN.R-project.org/package=mirt) package allows users to specify discrimination and difficulty parameters for each response category. diff --git a/README.html b/README.html index fd71523..b92648a 100644 --- a/README.html +++ b/README.html @@ -607,24 +607,24 @@

latent2likert Package logo

-

R-CMD-check - +

R-CMD-check + - + - + - - + + codecov codecov - 96% - 96% + 98% + 98% @@ -632,13 +632,13 @@

latent2likert

Overview

-

The R package latent2likert is designed to -effectively simulate the discretization process inherent to Likert -scales while minimizing distortion. It converts continuous latent -variables into ordinal categories to generate Likert scale item -responses. This is particularly useful for accurately modeling and -analyzing survey data that use Likert scales, especially when applying -statistical techniques that require metric data.

+

The latent2likert package is designed to effectively +simulate the discretization process inherent to Likert scales while +minimizing distortion. It converts continuous latent variables into +ordinal categories to generate Likert scale item responses. This is +particularly useful for accurately modeling and analyzing survey data +that use Likert scales, especially when applying statistical techniques +that require metric data.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
@@ -647,7 +647,8 @@ 
Dependencies

 
To keep the package lightweight, latent2likert only
 imports mvtnorm, along
 with the standard R packages stats and graphics, which are typically
-included in R releases. An additional suggested dependency is the sn package, which is
+included in R releases. An additional suggested dependency is the
+package sn, which is
 required only for generating random responses from correlated Likert
 items based on a multivariate skew normal distribution. The package
 prompts the user to install this dependency during interactive sessions
@@ -673,7 +674,7 @@ 
Using rlikert

 Likert scale, use:

 
library(latent2likert)
 rlikert(size = 10, n_items = 1, n_levels = 5)
-#>  [1] 4 2 3 2 1 3 2 3 2 3

+#>  [1] 2 5 2 3 3 1 2 2 1 5

To generate responses to multiple items with specified parameters:

rlikert(size = 10,
@@ -683,16 +684,16 @@ 
Using rlikert

         sd   = c(0.8, 1, 1),
         corr = 0.5)
 #>       Y1 Y2 Y3
-#>  [1,]  3  2  6
-#>  [2,]  2  2  5
-#>  [3,]  2  2  3
-#>  [4,]  3  1  3
-#>  [5,]  3  1  5
-#>  [6,]  3  3  6
-#>  [7,]  4  3  3
-#>  [8,]  3  3  6
-#>  [9,]  2  3  3
-#> [10,]  3  2  3
+#> [1,] 4 3 5 +#> [2,] 3 2 3 +#> [3,] 3 3 3 +#> [4,] 2 3 4 +#> [5,] 2 3 4 +#> [6,] 3 2 4 +#> [7,] 3 1 3 +#> [8,] 2 1 3 +#> [9,] 2 1 6 +#> [10,] 3 1 3

You can also provide a correlation matrix:

corr <- matrix(c(1.00, -0.63, -0.39, 
                  -0.63, 1.00, 0.41, 
@@ -708,17 +709,17 @@ 
Using rlikert

 and these estimates are typically lower:

 
cor(data)
 #>            Y1         Y2         Y3
-#> Y1  1.0000000 -0.5634259 -0.3760927
-#> Y2 -0.5634259  1.0000000  0.4362989
-#> Y3 -0.3760927  0.4362989  1.0000000

+#> Y1  1.0000000 -0.5277858 -0.3678057
+#> Y2 -0.5277858  1.0000000  0.3983187
+#> Y3 -0.3678057  0.3983187  1.0000000

Using estimate_params

Given the data, you can estimate the values of latent parameters using:

estimate_params(data, n_levels = c(4, 5, 6), skew = 0)
 #>          items
-#> estimates            Y1            Y2            Y3
-#>      mean -0.0415071755 -0.9654381812  0.0004640853
-#>      sd    0.8131470573  0.9995025670  1.0275232490
+#> estimates Y1 Y2 Y3 +#> mean 0.08270757 -1.10356623 0.01029328 +#> sd 0.79986937 1.06032921 1.01115089

Transformation

To visualize the transformation, you can use plot_likert_transform(). It plots the densities of latent @@ -764,8 +765,9 @@

manually specify the intervals.

There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete -probability distribution and sampling from it using the sample function -in R or the likert function from the wakefield +probability distribution and sampling from it using the +sample function in R or the likert function +from the wakefield package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use LikertMakeR diff --git a/README.md b/README.md index 68ff6cc..44573f3 100644 --- a/README.md +++ b/README.md @@ -6,12 +6,12 @@ [![R-CMD-check](https://github.com/markolalovic/latent2likert/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/markolalovic/latent2likert/actions/workflows/R-CMD-check.yaml) -[![codecov](https://codecov.io/gh/markolalovic/latent2likert/branch/main/graph/badge.svg?token=HZTG6RUB2J)](https://codecov.io/gh/markolalovic/latent2likert) +[![codecov](https://codecov.io/gh/markolalovic/latent2likert/branch/main/graph/badge.svg?token=HZTG6RUB2J)](https://app.codecov.io/gh/markolalovic/latent2likert) ## Overview -The R package **latent2likert** is designed to effectively simulate the +The **latent2likert** package is designed to effectively simulate the discretization process inherent to Likert scales while minimizing distortion. It converts continuous latent variables into ordinal categories to generate Likert scale item responses. This is particularly @@ -33,9 +33,9 @@ devtools::install_github("markolalovic/latent2likert") To keep the package lightweight, **latent2likert** only imports [mvtnorm](https://cran.r-project.org/package=mvtnorm), along with the standard R packages stats and graphics, which are typically included in -R releases. An additional suggested dependency is the [sn -package](https://cran.r-project.org/package=sn), which is required only -for generating random responses from correlated Likert items based on a +R releases. An additional suggested dependency is the package +[sn](https://cran.r-project.org/package=sn), which is required only for +generating random responses from correlated Likert items based on a multivariate skew normal distribution. The package prompts the user to install this dependency during interactive sessions if needed. @@ -64,7 +64,7 @@ scale, use: ``` r library(latent2likert) rlikert(size = 10, n_items = 1, n_levels = 5) -#> [1] 4 2 3 2 1 3 2 3 2 3 +#> [1] 2 5 2 3 3 1 2 2 1 5 ``` To generate responses to multiple items with specified parameters: @@ -77,16 +77,16 @@ rlikert(size = 10, sd = c(0.8, 1, 1), corr = 0.5) #> Y1 Y2 Y3 -#> [1,] 3 2 6 -#> [2,] 2 2 5 -#> [3,] 2 2 3 -#> [4,] 3 1 3 -#> [5,] 3 1 5 -#> [6,] 3 3 6 -#> [7,] 4 3 3 -#> [8,] 3 3 6 -#> [9,] 2 3 3 -#> [10,] 3 2 3 +#> [1,] 4 3 5 +#> [2,] 3 2 3 +#> [3,] 3 3 3 +#> [4,] 2 3 4 +#> [5,] 2 3 4 +#> [6,] 3 2 4 +#> [7,] 3 1 3 +#> [8,] 2 1 3 +#> [9,] 2 1 6 +#> [10,] 3 1 3 ``` You can also provide a correlation matrix: @@ -110,9 +110,9 @@ these estimates are typically lower: ``` r cor(data) #> Y1 Y2 Y3 -#> Y1 1.0000000 -0.5634259 -0.3760927 -#> Y2 -0.5634259 1.0000000 0.4362989 -#> Y3 -0.3760927 0.4362989 1.0000000 +#> Y1 1.0000000 -0.5277858 -0.3678057 +#> Y2 -0.5277858 1.0000000 0.3983187 +#> Y3 -0.3678057 0.3983187 1.0000000 ``` ## Using `estimate_params` @@ -122,9 +122,9 @@ Given the data, you can estimate the values of latent parameters using: ``` r estimate_params(data, n_levels = c(4, 5, 6), skew = 0) #> items -#> estimates Y1 Y2 Y3 -#> mean -0.0415071755 -0.9654381812 0.0004640853 -#> sd 0.8131470573 0.9995025670 1.0275232490 +#> estimates Y1 Y2 Y3 +#> mean 0.08270757 -1.10356623 0.01029328 +#> sd 0.79986937 1.06032921 1.01115089 ``` ## Transformation @@ -180,8 +180,8 @@ specify the intervals. There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete -probability distribution and sampling from it using the sample function -in R or the `likert` function from the +probability distribution and sampling from it using the `sample` +function in R or the `likert` function from the [wakefield](https://CRAN.R-project.org/package=wakefield) package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use diff --git a/dev/prepare_data.R b/dev/prepare_data.R index 9b0ccdc..1b7d124 100644 --- a/dev/prepare_data.R +++ b/dev/prepare_data.R @@ -20,8 +20,5 @@ for (var in vars) { } str(part_bfi) -# Save it to `./data` directory -#save(part_bfi, file="./data/part_bfi.rda") - -# Save and add `LazyData: true` in DESCRIPTION +# Save the data set usethis::use_data(part_bfi) diff --git a/docs/articles/using_latent2likert.html b/docs/articles/using_latent2likert.html index 094e02a..2629e0c 100644 --- a/docs/articles/using_latent2likert.html +++ b/docs/articles/using_latent2likert.html @@ -82,7 +82,7 @@

Marko Lalovic

-

Last Updated: 2024-06-21

+

Last Updated: 2024-06-22

Source: vignettes/using_latent2likert.Rmd
using_latent2likert.Rmd
@@ -91,8 +91,11 @@

Last Updated: 2024-06-21

-

Introduction +

Using latent2likert

+
+

Introduction +

In social sciences, variables of interest are often conceptualized as latent variables — hidden continuous variables measured through Likert scale questions, typically categorized as Strongly disagree, Disagree, @@ -105,9 +108,9 @@

Introduction -

Simulating Survey Data -

+
+

Simulating Survey Data +

The following hypothetical survey simulation is loosely based on an actual comparative study on teaching and learning R in a pair of introductory statistics labs (McNamara 2024).

@@ -129,24 +132,31 @@

Simulating Survey Data 
-library(latent2likert) # load the package
-set.seed(12345) # to ensure reproducible results
+library(latent2likert) # Load the package
+set.seed(12345) # Ensure reproducible results
 
-course_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1)
-course_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1)
+# Generate responses for Course A and Course B +responses_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1) +responses_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1)

To summarize the results, create a data frame from all responses:

 n_levels <- 4
 n_groups <- 2
-cats <- c("Poor", "Fair", "Good", "Excellent")
-data <- data.frame(
+categories <- c("Poor", "Fair", "Good", "Excellent")
+
+# Create a data frame to summarize the responses
+response_data <- data.frame(
   Course = rep(c("A", "B"), each = n_levels),
-  Response = factor(rep(cats, n_groups), levels = cats),
-  Proportion = c(response_prop(course_A, n_levels),
-                 response_prop(course_B, n_levels))
+  Response = factor(rep(categories, n_groups), levels = categories),
+  Proportion = c(
+    response_prop(responses_A, n_levels),
+    response_prop(responses_B, n_levels)
+  )
 )
-data <- data[data$Prop > 0, ]
-data
+
+# Filter out rows with zero proportions
+response_data <- response_data[response_data$Proportion > 0, ]
+response_data
 #>   Course  Response Proportion
 #> 1      A      Poor       0.30
 #> 2      A      Fair       0.20
@@ -158,9 +168,9 @@ 
Simulating Survey DataThe results can then be visualized using a grouped bar chart:

 
Grouped bar chart
-
-

Pre and Post Comparison -

+
+

Pre and Post Comparison +

Now suppose that the survey also asked the participants to rate their skills on a 5-point Likert scale, ranging from 1 (very poor) to 5 (very good) in:

@@ -189,23 +199,35 @@

Pre and Post Comparisonpost_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(0, 0, 0))

Create a data frame from all responses to summarize the results:

-pre_post <- list(pre_A, post_A, pre_B, post_B)
-n_items <- 6 # for 3 questions before and after
-n_levels <- 5 # for a 5-point Likert scale
+# Combine pre and post responses into a list
+pre_post <- list(pre_A, post_A, pre_B, post_B)
+
+# Number of items and response levels
+n_items <- 3
+n_levels <- 5
+
+# Define skills assessed
 skills <- c("Programming", "Searching online", "Solving problems")
-questions <- rep(as.vector(sapply(skills, 
-                                  function(skill) rep(skill, n_levels))), 4)
+
+# Generate repeated skill labels for questions
+questions <- rep(rep(skills, each = n_levels), 4)
 questions <- factor(questions, levels = skills)
-data <- data.frame (
-  Course = c(rep("Course A", n_items * n_levels), 
-             rep("Course B", n_items * n_levels)),
+
+# Create a data frame to summarize the responses
+response_data <- data.frame(
+  Course = rep(c("Course A", "Course B"), each = 2 * n_items * n_levels),
   Question = questions,
-  Time = as.factor(rep(c(rep("before", 3*n_levels), 
-                         rep("after", 3*n_levels)), 2)),
-  Response = rep(rep(seq_len(n_levels), 3), length(pre_post)),
-  Proportion = as.vector(sapply(pre_post, function(d) { 
-    as.vector(t(response_prop(d, n_levels))) })))
-head(data)
+  Time = as.factor(rep(c(
+    rep("before", n_items * n_levels),
+    rep("after", n_items * n_levels)
+  ), 2)),
+  Response = rep(seq_len(n_levels), 2 * n_items * 2),
+  Proportion = as.vector(sapply(pre_post, function(d) {
+    as.vector(t(response_prop(d, n_levels)))
+  }))
+)
+
+head(response_data)
 #>     Course         Question   Time Response Proportion
 #> 1 Course A      Programming before        1        0.5
 #> 2 Course A      Programming before        2        0.2
@@ -216,14 +238,15 @@ 
Pre and Post ComparisonAnd visualize the results with a stacked bar chart:

 
Stacked bar chart
-
-

Recreating Scale Scores -

-

We will use part of bfi +

+

Recreating Scale Scores +

+

We will use part of the bfi data set from (Revelle -2024). In particular only the first 5 items corresponding to -agreeableness. To investigate the differences in agreeableness between -men and women we will also use the gender attribute.

+2024). Specifically, we’ll focus on the first 5 items +corresponding to agreeableness. To investigate the differences in +agreeableness between men and women, we’ll also use the gender +attribute.

Load the data:

 data(part_bfi)
@@ -238,38 +261,42 @@ 
Recreating Scale ScoresSeparate the items into two groups according to their gender:

 
 vars <- c("A1", "A2", "A3", "A4", "A5")
-items_M <- part_bfi[part_bfi$gender == 0, vars]
-items_F <- part_bfi[part_bfi$gender == 1, vars]

-
To reproduce the items, start by estimating the parameters of the
-latent variables, assuming they are normal and providing the number of
-possible response categories ‘n_levels = 6’:

+items_male <- part_bfi[part_bfi$gender == 0, vars]
+items_female <- part_bfi[part_bfi$gender == 1, vars]
+

Estimate the parameters of the latent variables, assuming they are +normal and providing the number of possible response categories +n_levels = 6:

-params_M <- estimate_params(data = items_M, n_levels = 6)
-params_F <- estimate_params(data = items_F, n_levels = 6)
-

Then, generate new responses to the items using the estimated -parameters and estimated correlations:

+params_male <- estimate_params(data = items_male, n_levels = 6) +params_female <- estimate_params(data = items_female, n_levels = 6)
+

Generate new responses to the items using the estimated parameters +and estimated correlations:

-set.seed(12345) # to ensure reproducible results
+set.seed(12345) # Ensure reproducible results
 
-new_items_M <- rlikert(size = nrow(items_M), 
-                       n_items = 5,
-                       n_levels = 6,
-                       mean = params_M["mean", ], 
-                       sd = params_M["sd", ],
-                       corr = cor(items_M))
+new_items_male <- rlikert(
+  size = nrow(items_male),
+  n_items = 5,
+  n_levels = 6,
+  mean = params_male["mean", ],
+  sd = params_male["sd", ],
+  corr = cor(items_male)
+)
 
-new_items_F <- rlikert(size = nrow(items_F), 
-                       n_items = 5,
-                       n_levels = 6,
-                       mean = params_F["mean", ], 
-                       sd = params_F["sd", ],
-                       corr = cor(items_F))
-

The next step would be to create agreeableness scale scores for both -groups of participants, by taking the average of these 5 items.

+new_items_female <- rlikert( + size = nrow(items_female), + n_items = 5, + n_levels = 6, + mean = params_female["mean", ], + sd = params_female["sd", ], + corr = cor(items_female) +)
+

Create agreeableness scale scores for both groups of participants by +taking the average of these 5 items:

 # Combine new items and gender in new data frame
-new_data <- data.frame(rbind(new_items_M, new_items_F))
-new_data$gender <- c(rep(0, nrow(items_M)), rep(1, nrow(items_F)))
+new_data <- data.frame(rbind(new_items_male, new_items_female))
+new_data$gender <- c(rep(0, nrow(items_male)), rep(1, nrow(items_female)))
 head(new_data)
 #>   Y1 Y2 Y3 Y4 Y5 gender
 #> 1  3  5  5  4  5      0
@@ -280,19 +307,19 @@ 
Recreating Scale Scores#> 6  5  4  5  6  5      0
 
-# We also need to reverse the first item because it has negative correlations
+# Reverse the first item because it has negative correlations
 part_bfi$A1 <- (min(part_bfi$A1) + max(part_bfi$A1)) - part_bfi$A1
 new_data$Y1 <- (min(new_data$Y1) + max(new_data$Y1)) - new_data$Y1
 
 # Create agreeableness scale scores
 part_bfi$agreeable <- rowMeans(part_bfi[, vars])
 new_data$agreeable <- rowMeans(new_data[, c("Y1", "Y2", "Y3", "Y4", "Y5")])
-

And visualize the results with a grouped boxplot:

+

The results can be visualized with a grouped boxplot:

Scales
-
-

References -

+
+

References +

McNamara, Amelia. 2024. “Teaching Modeling in Introductory @@ -304,6 +331,7 @@

Referenceshttps://CRAN.R-project.org/package=psych.

+
diff --git a/docs/index.html b/docs/index.html index f301fd3..11e7c9a 100644 --- a/docs/index.html +++ b/docs/index.html @@ -84,7 +84,7 @@

Overview

-

The R package latent2likert is designed to effectively simulate the discretization process inherent to Likert scales while minimizing distortion. It converts continuous latent variables into ordinal categories to generate Likert scale item responses. This is particularly useful for accurately modeling and analyzing survey data that use Likert scales, especially when applying statistical techniques that require metric data.

+

The latent2likert package is designed to effectively simulate the discretization process inherent to Likert scales while minimizing distortion. It converts continuous latent variables into ordinal categories to generate Likert scale item responses. This is particularly useful for accurately modeling and analyzing survey data that use Likert scales, especially when applying statistical techniques that require metric data.

Installation @@ -97,7 +97,7 @@

Installation

Dependencies

-

To keep the package lightweight, latent2likert only imports mvtnorm, along with the standard R packages stats and graphics, which are typically included in R releases. An additional suggested dependency is the sn package, which is required only for generating random responses from correlated Likert items based on a multivariate skew normal distribution. The package prompts the user to install this dependency during interactive sessions if needed.

+

To keep the package lightweight, latent2likert only imports mvtnorm, along with the standard R packages stats and graphics, which are typically included in R releases. An additional suggested dependency is the package sn, which is required only for generating random responses from correlated Likert items based on a multivariate skew normal distribution. The package prompts the user to install this dependency during interactive sessions if needed.

Features @@ -123,7 +123,7 @@

Using rlikert 
 library(latent2likert)
 rlikert(size = 10, n_items = 1, n_levels = 5)
-#>  [1] 4 2 3 2 1 3 2 3 2 3
+#> [1] 2 5 2 3 3 1 2 2 1 5

To generate responses to multiple items with specified parameters:

 rlikert(size = 10,
@@ -133,16 +133,16 @@ 
Using rlikert
         sd   = c(0.8, 1, 1),
         corr = 0.5)
 #>       Y1 Y2 Y3
-#>  [1,]  3  2  6
-#>  [2,]  2  2  5
-#>  [3,]  2  2  3
-#>  [4,]  3  1  3
-#>  [5,]  3  1  5
-#>  [6,]  3  3  6
-#>  [7,]  4  3  3
-#>  [8,]  3  3  6
-#>  [9,]  2  3  3
-#> [10,]  3  2  3
+#> [1,] 4 3 5 +#> [2,] 3 2 3 +#> [3,] 3 3 3 +#> [4,] 2 3 4 +#> [5,] 2 3 4 +#> [6,] 3 2 4 +#> [7,] 3 1 3 +#> [8,] 2 1 3 +#> [9,] 2 1 6 +#> [10,] 3 1 3

You can also provide a correlation matrix:

 corr <- matrix(c(1.00, -0.63, -0.39, 
@@ -158,9 +158,9 @@ 
Using rlikert
 
 cor(data)
 #>            Y1         Y2         Y3
-#> Y1  1.0000000 -0.5634259 -0.3760927
-#> Y2 -0.5634259  1.0000000  0.4362989
-#> Y3 -0.3760927  0.4362989  1.0000000

+#> Y1  1.0000000 -0.5277858 -0.3678057
+#> Y2 -0.5277858  1.0000000  0.3983187
+#> Y3 -0.3678057  0.3983187  1.0000000

Using estimate_params @@ -170,9 +170,9 @@

Using estimate_params 
 estimate_params(data, n_levels = c(4, 5, 6), skew = 0)
 #>          items
-#> estimates            Y1            Y2            Y3
-#>      mean -0.0415071755 -0.9654381812  0.0004640853
-#>      sd    0.8131470573  0.9995025670  1.0275232490
+#> estimates Y1 Y2 Y3 +#> mean 0.08270757 -1.10356623 0.01029328 +#> sd 0.79986937 1.06032921 1.01115089

Transformation @@ -203,7 +203,7 @@

Further ReadingRelated R Packages

To simulate Likert item responses, the draw_likert function from the fabricatr package can be used to recode a latent variable into a Likert response variable by specifying intervals that subdivide the continuous range. The latent2likert package, however, offers an advantage by automatically calculating optimal intervals that minimize distortion between the latent variable and the Likert response variable for both normal and skew normal latent distributions, eliminating the need to manually specify the intervals.

-

There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete probability distribution and sampling from it using the sample function in R or the likert function from the wakefield package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use LikertMakeR or SimCorMultRes to generate correlated multinomial responses.

+

There are also several alternative approaches that do not rely on latent distributions. One method involves directly defining a discrete probability distribution and sampling from it using the sample function in R or the likert function from the wakefield package. Another approach is to specify the means, standard deviations, and correlations among Likert response variables. For this, you can use LikertMakeR or SimCorMultRes to generate correlated multinomial responses.

Additionally, you can define a data generating process. For those familiar with item response theory, the mirt package allows users to specify discrimination and difficulty parameters for each response category.

@@ -242,7 +242,7 @@

Developers

Dev status

diff --git a/docs/news/index.html b/docs/news/index.html index b6e58e3..3ca2e13 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -51,37 +51,41 @@
-

latent2likert 0.1.0 (Release date: 2020-10-17)

-
-

latent2likert 1.0.0 (Release date: 2024-03-28)

-
-

latent2likert 1.1.0 (Release date: 2024-06-06)

-
-

latent2likert 1.1.1 (Release date: 2024-06-06)

-
-

latent2likert 1.2.1 (Release date: 2024-06-12)

-
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index 93b4516..3c858b2 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -3,7 +3,7 @@ pkgdown: 2.0.9 pkgdown_sha: ~ articles: using_latent2likert: using_latent2likert.html -last_built: 2024-06-20T22:53Z +last_built: 2024-06-22T13:27Z urls: reference: https://markolalovic.github.io/latent2likert/reference article: https://markolalovic.github.io/latent2likert/articles diff --git a/docs/reference/discretize_density.html b/docs/reference/discretize_density.html index 830e694..f152551 100644 --- a/docs/reference/discretize_density.html +++ b/docs/reference/discretize_density.html @@ -104,8 +104,8 @@

Details
\(f_{X}\)
@@ -182,7 +182,8 @@

Examples#> [1] 0.07994185 #> discretize_density(density_fn = function(x) { - 2 * stats::dnorm(x) * stats::pnorm(0.5 * x)}, n_levels = 4) + 2 * stats::dnorm(x) * stats::pnorm(0.5 * x) +}, n_levels = 4) #> $prob #> [1] 0.1647781 0.3380772 0.3359810 0.1611637 #> diff --git a/docs/reference/figures/courses-grouped.png b/docs/reference/figures/courses-grouped.png deleted file mode 100644 index db5f60c97f42acf36c3405c65342ad2896b70e2d..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 67037 zcmeFZhdY-2A3v5~f|Jdg_BTNxZwh>+|LYI6XI!el|MeRF^XF+1S*rhe`2ocVX0rcz z^_|!LK+^wt^|t8F+Q0ti)w3tJ>23L+SE(u7v;OBr67QWNs{i}ywZCK7{`b{WSN{L6 zOG5JhvATXns`gm2K2zlkt;9pDN;_M&?>%;1NJuELdpeBUz;JzK!9B-EXvK@)W>ogg z)StVypMsHr;d6<@+%_XY$N88OS04q+`ABwjX6ioSdexP#oIxiY$)CH&Y1@DILN@Qu zE=U}&@Ys>#xL_=zR_eGQDag#q%NuNxZ_<(eXFD*zT3d6LPx*59&K;Q?yUq8HyF|LH{Z1w8R=v2E?A9D7MtS%!)Aa~JC*E5bT3?wLwi3S+ zm^V3Ty7K#nk5SbN+61MPnx3AB_B3_zTPaHH6X{#7+kJaadW1`7Tji%u{?DJ2H@v(U 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Course B - - Course A - - Course B - - - Course B - 100 - 50 - 0 - 50 - 100 - before - after - Percentage - - - - - - - - - - - - Very poor - Poor - Fair - Good - Very good - Course A - Course A - Programming - - Searching - online - - - Solving - problems - - before - after - before - 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100644 --- a/docs/reference/part_bfi.html +++ b/docs/reference/part_bfi.html @@ -106,7 +106,7 @@

Format<

Source

-

International Personality Item Pool (ipip.ori.org)

+

International Personality Item Pool (https://ipip.ori.org)

https://search.r-project.org/CRAN/refmans/psychTools/html/bfi.html

diff --git a/docs/reference/plot_likert_transform.html b/docs/reference/plot_likert_transform.html index f3a1bd2..b094485 100644 --- a/docs/reference/plot_likert_transform.html +++ b/docs/reference/plot_likert_transform.html @@ -1,7 +1,7 @@ -Plot Transformation — plot_likert_transform • latent2likertPlot Transformation — plot_likert_transform • latent2likert @@ -54,8 +54,8 @@
-

Plots the densities of latent variables in the first row -and transformed discrete probability distributions below.

+

Plots the densities of latent variables and the corresponding +transformed discrete probability distributions.

@@ -70,37 +70,41 @@

Arguments

Value

-

a plot showing the densities of latent variables and the corresponding discrete probability distributions.

+

NULL. The function produces a plot.

Examples

plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5))
 
-plot_likert_transform(n_items = 3, n_levels = 5, mean=c(0, 1, 2))
+plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, 1, 2))
 
-plot_likert_transform(n_items = 3, n_levels = 5, sd=c(0.8, 1, 1.2))
+plot_likert_transform(n_items = 3, n_levels = 5, sd = c(0.8, 1, 1.2))
 
-plot_likert_transform(n_items = 3, n_levels = 5, skew=c(-0.5, 0, 0.5))
+plot_likert_transform(n_items = 3, n_levels = 5, skew = c(-0.5, 0, 0.5))
diff --git a/docs/reference/simulate_likert.html b/docs/reference/simulate_likert.html index 6c94ae8..f5c8248 100644 --- a/docs/reference/simulate_likert.html +++ b/docs/reference/simulate_likert.html @@ -66,13 +66,13 @@

Usage

Arguments

n_levels
-

Integer. The number of response categories for the Likert scale item.

+

number of response categories for the Likert scale item.

cp
-

Named vector. The centered parameters of the latent variable, including -mean (mu), standard deviation (sd), and skewness (skew). -Skewness must be between -0.95 and 0.95.

+

centered parameters of the latent variable. +Named vector including mean (mu), standard deviation (sd), +and skewness (skew). Skewness must be between -0.95 and 0.95.

@@ -83,10 +83,10 @@

Value

Details

-

The simulation process uses the following model proposed by Boari and Nai-Ruscone. -Let \(X\) be the continuous variable of interest, measured using Likert scale -questions with \(K\) response categories. The observed discrete variable \(Y\) is -defined as follows: +

The simulation process uses the following model detailed by +Boari and Nai-Ruscone. Let \(X\) be the continuous variable of interest, +measured using Likert scale questions with \(K\) response categories. The +observed discrete variable \(Y\) is defined as follows: $$ Y = k, \quad \text{ if } \ \ x_{k - 1} < X \leq x_{k} \quad \text{ for } \ \ k = 1, \dots, K @@ -96,8 +96,8 @@

DetailsDetailssimulate_likert performs the following steps:

  • Ensures the centered parameters are within the acceptable range.

  • Converts the centered parameters to direct parameters.

  • Defines the density function for the skew normal distribution.

    • -

  • Computes the probabilities for each response category using optimal endpoints.

    • +

  • Computes the probabilities for each response category +using optimal endpoints.

References

Boari, G. and Nai Ruscone, M. (2015). -A procedure simulating likert scale item responses. -Electronic journal of applied statistical analysis 8(3), 288–297. +A procedure simulating Likert scale item responses. +Electronic Journal of Applied Statistical Analysis 8(3), +288–297. doi:10.1285/i20705948v8n3p288

diff --git a/docs/search.json b/docs/search.json index 9fb0fa5..379f2de 100644 --- a/docs/search.json +++ b/docs/search.json @@ -1 +1 @@ -[{"path":"https://markolalovic.github.io/latent2likert/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 Marko Lalovic Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Using latent2likert","text":"social sciences, variables interest often conceptualized latent variables — hidden continuous variables measured Likert scale questions, typically categorized Strongly disagree, Disagree, Neutral, Agree, Strongly agree. Researchers frequently aim uncover latent variables using various statistical techniques. Accurate modeling survey data essential comparative analysis simulation. latent2likert package addresses need providing effective algorithm simulate Likert response variables hypothetical latent variables. vignette provides two practical workflow examples demonstrating use latent2likert package.","code":""},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"simulating-survey-data","dir":"Articles","previous_headings":"","what":"Simulating Survey Data","title":"Using latent2likert","text":"following hypothetical survey simulation loosely based actual comparative study teaching learning R pair introductory statistics labs (McNamara 2024). Imagine situation 10 participants Course 20 participants Course B completed survey. Suppose initial question : “rate experience course?” four possible answers: Poor, Fair, Good, Excellent. Let’s assume participants Course neutral regarding question, participants Course B positive experience average. choosing appropriate parameters latent distributions setting number categories n_levels = 4, can generate hypothetical responses (standard deviation sd = 1 skewness skew = 0, default): summarize results, create data frame responses: results can visualized using grouped bar chart:","code":"library(latent2likert) # load the package set.seed(12345) # to ensure reproducible results course_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1) course_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1) n_levels <- 4 n_groups <- 2 cats <- c(\"Poor\", \"Fair\", \"Good\", \"Excellent\") data <- data.frame( Course = rep(c(\"A\", \"B\"), each = n_levels), Response = factor(rep(cats, n_groups), levels = cats), Proportion = c(response_prop(course_A, n_levels), response_prop(course_B, n_levels)) ) data <- data[data$Prop > 0, ] data #> Course Response Proportion #> 1 A Poor 0.30 #> 2 A Fair 0.20 #> 3 A Good 0.20 #> 4 A Excellent 0.30 #> 6 B Fair 0.10 #> 7 B Good 0.25 #> 8 B Excellent 0.65"},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"pre-and-post-comparison","dir":"Articles","previous_headings":"","what":"Pre and Post Comparison","title":"Using latent2likert","text":"Now suppose survey also asked participants rate skills 5-point Likert scale, ranging 1 (poor) 5 (good) : Programming, Searching Online, Solving Problems. survey completed participants taking course pre post-comparison. Suppose participants’ assessments : Programming skills average increased, Searching Online stayed , Solving Problems increased Course , decreased participants Course B. Let’s simulate survey data scenario: Create data frame responses summarize results: visualize results stacked bar chart:","code":"# Pre- and post-assessments of skills for Course A pre_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(-1, 0, 1)) post_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(0, 0, 2)) # Pre- and post-assessments of skills for Course B pre_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(-1, 0, 1)) post_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(0, 0, 0)) pre_post <- list(pre_A, post_A, pre_B, post_B) n_items <- 6 # for 3 questions before and after n_levels <- 5 # for a 5-point Likert scale skills <- c(\"Programming\", \"Searching online\", \"Solving problems\") questions <- rep(as.vector(sapply(skills, function(skill) rep(skill, n_levels))), 4) questions <- factor(questions, levels = skills) data <- data.frame ( Course = c(rep(\"Course A\", n_items * n_levels), rep(\"Course B\", n_items * n_levels)), Question = questions, Time = as.factor(rep(c(rep(\"before\", 3*n_levels), rep(\"after\", 3*n_levels)), 2)), Response = rep(rep(seq_len(n_levels), 3), length(pre_post)), Proportion = as.vector(sapply(pre_post, function(d) { as.vector(t(response_prop(d, n_levels))) }))) head(data) #> Course Question Time Response Proportion #> 1 Course A Programming before 1 0.5 #> 2 Course A Programming before 2 0.2 #> 3 Course A Programming before 3 0.3 #> 4 Course A Programming before 4 0.0 #> 5 Course A Programming before 5 0.0 #> 6 Course A Searching online before 1 0.1"},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"recreating-scale-scores","dir":"Articles","previous_headings":"","what":"Recreating Scale Scores","title":"Using latent2likert","text":"use part bfi data set (Revelle 2024). particular first 5 items corresponding agreeableness. investigate differences agreeableness men women also use gender attribute. Load data: Separate items two groups according gender: reproduce items, start estimating parameters latent variables, assuming normal providing number possible response categories ‘n_levels = 6’: , generate new responses items using estimated parameters estimated correlations: next step create agreeableness scale scores groups participants, taking average 5 items. visualize results grouped boxplot:","code":"data(part_bfi) head(part_bfi) #> A1 A2 A3 A4 A5 gender #> 61617 2 4 3 4 4 0 #> 61618 2 4 5 2 5 1 #> 61620 5 4 5 4 4 1 #> 61621 4 4 6 5 5 1 #> 61622 2 3 3 4 5 0 #> 61623 6 6 5 6 5 1 vars <- c(\"A1\", \"A2\", \"A3\", \"A4\", \"A5\") items_M <- part_bfi[part_bfi$gender == 0, vars] items_F <- part_bfi[part_bfi$gender == 1, vars] params_M <- estimate_params(data = items_M, n_levels = 6) params_F <- estimate_params(data = items_F, n_levels = 6) set.seed(12345) # to ensure reproducible results new_items_M <- rlikert(size = nrow(items_M), n_items = 5, n_levels = 6, mean = params_M[\"mean\", ], sd = params_M[\"sd\", ], corr = cor(items_M)) new_items_F <- rlikert(size = nrow(items_F), n_items = 5, n_levels = 6, mean = params_F[\"mean\", ], sd = params_F[\"sd\", ], corr = cor(items_F)) # Combine new items and gender in new data frame new_data <- data.frame(rbind(new_items_M, new_items_F)) new_data$gender <- c(rep(0, nrow(items_M)), rep(1, nrow(items_F))) head(new_data) #> Y1 Y2 Y3 Y4 Y5 gender #> 1 3 5 5 4 5 0 #> 2 1 5 4 4 4 0 #> 3 2 6 5 6 4 0 #> 4 4 4 4 6 5 0 #> 5 4 5 3 2 2 0 #> 6 5 4 5 6 5 0 # We also need to reverse the first item because it has negative correlations part_bfi$A1 <- (min(part_bfi$A1) + max(part_bfi$A1)) - part_bfi$A1 new_data$Y1 <- (min(new_data$Y1) + max(new_data$Y1)) - new_data$Y1 # Create agreeableness scale scores part_bfi$agreeable <- rowMeans(part_bfi[, vars]) new_data$agreeable <- rowMeans(new_data[, c(\"Y1\", \"Y2\", \"Y3\", \"Y4\", \"Y5\")])"},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Marko Lalovic. Author, maintainer.","code":""},{"path":"https://markolalovic.github.io/latent2likert/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Lalovic M (2024). latent2likert: Converting Latent Variables Likert Scale Responses. R package version 1.2.1, https://lalovic.io/latent2likert/.","code":"@Manual{, title = {latent2likert: Converting Latent Variables into Likert Scale Responses}, author = {Marko Lalovic}, year = {2024}, note = {R package version 1.2.1}, url = {https://lalovic.io/latent2likert/}, }"},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"overview","dir":"","previous_headings":"","what":"Overview","title":"Converting Latent Variables into Likert Scale Responses","text":"R package latent2likert designed effectively simulate discretization process inherent Likert scales minimizing distortion. converts continuous latent variables ordinal categories generate Likert scale item responses. particularly useful accurately modeling analyzing survey data use Likert scales, especially applying statistical techniques require metric data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Converting Latent Variables into Likert Scale Responses","text":"can install development version GitHub :","code":"# install.packages(\"devtools\") devtools::install_github(\"markolalovic/latent2likert\")"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"dependencies","dir":"","previous_headings":"","what":"Dependencies","title":"Converting Latent Variables into Likert Scale Responses","text":"keep package lightweight, latent2likert imports mvtnorm, along standard R packages stats graphics, typically included R releases. additional suggested dependency sn package, required generating random responses correlated Likert items based multivariate skew normal distribution. package prompts user install dependency interactive sessions needed.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"features","dir":"","previous_headings":"","what":"Features","title":"Converting Latent Variables into Likert Scale Responses","text":"rlikert: Generates random responses Likert scale questions based specified means standard deviations latent variables, optional settings skewness correlations. estimate_params: Estimates latent parameters existing survey data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"structure","dir":"","previous_headings":"","what":"Structure","title":"Converting Latent Variables into Likert Scale Responses","text":"Overview inputs outputs.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"using-rlikert","dir":"","previous_headings":"","what":"Using rlikert","title":"Converting Latent Variables into Likert Scale Responses","text":"generate sample random responses one item 5-point Likert scale, use: generate responses multiple items specified parameters: can also provide correlation matrix: Note correlations among Likert response variables estimates actual correlations latent variables, estimates typically lower:","code":"library(latent2likert) rlikert(size = 10, n_items = 1, n_levels = 5) #> [1] 4 2 3 2 1 3 2 3 2 3 rlikert(size = 10, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = 0.5) #> Y1 Y2 Y3 #> [1,] 3 2 6 #> [2,] 2 2 5 #> [3,] 2 2 3 #> [4,] 3 1 3 #> [5,] 3 1 5 #> [6,] 3 3 6 #> [7,] 4 3 3 #> [8,] 3 3 6 #> [9,] 2 3 3 #> [10,] 3 2 3 corr <- matrix(c(1.00, -0.63, -0.39, -0.63, 1.00, 0.41, -0.39, 0.41, 1.00), nrow=3) data <- rlikert(size = 10^3, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = corr) cor(data) #> Y1 Y2 Y3 #> Y1 1.0000000 -0.5634259 -0.3760927 #> Y2 -0.5634259 1.0000000 0.4362989 #> Y3 -0.3760927 0.4362989 1.0000000"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"using-estimate_params","dir":"","previous_headings":"","what":"Using estimate_params","title":"Converting Latent Variables into Likert Scale Responses","text":"Given data, can estimate values latent parameters using:","code":"estimate_params(data, n_levels = c(4, 5, 6), skew = 0) #> items #> estimates Y1 Y2 Y3 #> mean -0.0415071755 -0.9654381812 0.0004640853 #> sd 0.8131470573 0.9995025670 1.0275232490"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"transformation","dir":"","previous_headings":"","what":"Transformation","title":"Converting Latent Variables into Likert Scale Responses","text":"visualize transformation, can use plot_likert_transform(). plots densities latent variables first row transformed discrete probability distributions : Transformation latent variables Likert response variables. Note , depending value skewness parameter, normal latent distribution used skew = 0, otherwise skew normal distribution used. value skewness restricted range -0.95 0.95, skew >= -0.95 skew <= 0.95.","code":"plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, -1, 0), sd = c(0.8, 1, 1), skew = c(0, 0, 0.5))"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"further-reading","dir":"","previous_headings":"","what":"Further Reading","title":"Converting Latent Variables into Likert Scale Responses","text":"detailed information practical examples, please refer package vignette. implemented algorithms described functions reference.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"related-r-packages","dir":"","previous_headings":"","what":"Related R Packages","title":"Converting Latent Variables into Likert Scale Responses","text":"simulate Likert item responses, draw_likert function fabricatr package can used recode latent variable Likert response variable specifying intervals subdivide continuous range. latent2likert package, however, offers advantage automatically calculating optimal intervals minimize distortion latent variable Likert response variable normal skew normal latent distributions, eliminating need manually specify intervals. also several alternative approaches rely latent distributions. One method involves directly defining discrete probability distribution sampling using sample function R likert function wakefield package. Another approach specify means, standard deviations, correlations among Likert response variables. , can use LikertMakeR SimCorMultRes generate correlated multinomial responses. Additionally, can define data generating process. familiar item response theory, mirt package allows users specify discrimination difficulty parameters response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":null,"dir":"Reference","previous_headings":"","what":"Discretize Density — discretize_density","title":"Discretize Density — discretize_density","text":"Transforms density function continuous random variable discrete probability distribution minimal distortion using Lloyd-Max algorithm.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Discretize Density — discretize_density","text":"","code":"discretize_density(density_fn, n_levels, eps = 1e-06)"},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Discretize Density — discretize_density","text":"density_fn probability density function. n_levels cardinality set possible outcomes. eps convergence threshold algorithm.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Discretize Density — discretize_density","text":"list containing: prob discrete probability distribution. endp endpoints intervals partition continuous domain. repr representation points intervals. dist distortion measured mean-squared error (MSE).","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Discretize Density — discretize_density","text":"function addresses problem transforming continuous random variable \\(X\\) discrete random variable \\(Y\\) minimal distortion. Distortion measured mean-squared error (MSE): $$ \\text{E}\\left[ (X - Y)^2 \\right] = \\sum_{k=1}^{K} \\int_{x_{k-1}}^{x_{k}} f_{X}(x) \\left( x - r_{k} \\right)^2 \\, dx $$ : \\(f_{X}\\) probability density function \\(X\\), \\(K\\) number possible outcomes \\(Y\\), \\(x_{k}\\) endpoints intervals partition domain \\(X\\), \\(r_{k}\\) representation points intervals. problem solved using following iterative procedure: \\(1.\\) Start arbitrary initial set representation points: \\(r_{1} < r_{2} < \\dots < r_{K}\\). \\(2.\\) Repeat following steps improvement MSE falls given \\(\\varepsilon\\). \\(3.\\) Calculate endpoints \\(x_{k} = (r_{k+1} + r_{k})/2\\) \\(k = 1, \\dots, K-1\\) set \\(x_{0}\\) \\(x_{K}\\) \\(-\\infty\\) \\(\\infty\\), respectively. \\(4.\\) Update representation points setting \\(r_{k}\\) equal conditional mean \\(X\\) given \\(X \\(x_{k-1}, x_{k})\\) \\(k = 1, \\dots, K\\). execution step \\((3)\\) step \\((4)\\), MSE decreases remains . MSE nonnegative, approaches limit. algorithm terminates improvement MSE less given \\(\\varepsilon > 0\\), ensuring convergence finite number iterations. procedure known Lloyd-Max's algorithm, initially used scalar quantization closely related k-means algorithm. Local convergence proven log-concave density functions Kieffer. Many common probability distributions log-concave including normal skew normal distribution, shown Azzalini.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Discretize Density — discretize_density","text":"Azzalini, . (1985). class distributions includes normal ones. Scandinavian Journal Statistics 12(2), 171–178. Kieffer, J. (1983). Uniqueness locally optimal quantizer log-concave density convex error function. IEEE Transactions Information Theory 29, 42–47. Lloyd, S. (1982). Least squares quantization PCM. IEEE Transactions Information Theory 28 (2), 129–137.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Discretize Density — discretize_density","text":"","code":"discretize_density(density_fn = stats::dnorm, n_levels = 5) #> $prob #> [1] 0.1063142 0.2444957 0.2983803 0.2444957 0.1063142 #> #> $endp #> [1] -Inf -1.2463707 -0.3831349 0.3831349 1.2463707 Inf #> #> $repr #> [1] -1.7264716 -0.7662698 0.0000000 0.7662698 1.7264716 #> #> $dist #> [1] 0.07994185 #> discretize_density(density_fn = function(x) { 2 * stats::dnorm(x) * stats::pnorm(0.5 * x)}, n_levels = 4) #> $prob #> [1] 0.1647781 0.3380772 0.3359810 0.1611637 #> #> $endp #> [1] -Inf -0.5537368 0.3597728 1.2808536 Inf #> #> $repr #> [1] -1.04423728 -0.06323628 0.78278182 1.77892538 #> #> $dist #> [1] 0.1026681 #>"},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate Latent Parameters — estimate_params","title":"Estimate Latent Parameters — estimate_params","text":"Estimates location scaling parameters latent variables existing survey data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate Latent Parameters — estimate_params","text":"","code":"estimate_params(data, n_levels, skew = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate Latent Parameters — estimate_params","text":"data survey data columns representing individual items. Apart , data can almost class \"data.frame\" \"matrix\" \"array\". n_levels number response categories, vector number. skew marginal skewness latent variables, defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate Latent Parameters — estimate_params","text":"table estimated parameters latent variable.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Estimate Latent Parameters — estimate_params","text":"relationship continuous random variable \\(X\\) discrete probability distribution \\(p_k\\), \\(k = 1, \\dots, K\\), can described system non-linear equations: $$ p_{k} = F_{X}\\left( \\frac{x_{k - 1} - \\xi}{\\omega} \\right) - F_{X}\\left( \\frac{x_{k} - \\xi}{\\omega} \\right) \\quad \\text{} \\ k = 1, \\dots, K $$ : \\(F_{X}\\) cumulative distribution function \\(X\\), \\(K\\) number possible response categories, \\(x_{k}\\) endpoints defining boundaries response categories, \\(p_{k}\\) probability \\(k\\)-th response category, \\(\\xi\\) location parameter \\(X\\), \\(\\omega\\) scaling parameter \\(X\\). endpoints \\(x_{k}\\) calculated discretizing random variable \\(Z\\) mean 0 standard deviation 1 follows distribution \\(X\\). solving system non-linear equations iteratively, can find parameters best fit observed discrete probability distribution \\(p_{k}\\). function estimate_params: Computes proportion table responses item. Estimates probabilities \\(p_{k}\\) item. Computes estimates \\(\\xi\\) \\(\\omega\\) item. Combines estimated parameters items table.","code":""},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate Latent Parameters — estimate_params","text":"","code":"data(part_bfi) vars <- c(\"A1\", \"A2\", \"A3\", \"A4\", \"A5\") estimate_params(data = part_bfi[, vars], n_levels = 6) #> items #> estimates A1 A2 A3 A4 A5 #> mean -0.9759824 1.0830781 0.9776057 1.1723519 0.9006478 #> sd 1.1798137 0.7968668 0.8432599 1.3825407 0.8648150"},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":null,"dir":"Reference","previous_headings":"","what":"Agreeableness and Gender Data — part_bfi","title":"Agreeableness and Gender Data — part_bfi","text":"dataset cleaned version small part bfi dataset psychTools package. contains responses first 5 items agreeableness scale International Personality Item Pool (IPIP) gender attribute. includes responses 2800 subjects. item answered six point Likert scale ranging 1 (inaccurate), 6 (accurate). Gender coded 0 male 1 female. Missing values addressed using mode imputation.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Agreeableness and Gender Data — part_bfi","text":"","code":"data(part_bfi)"},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Agreeableness and Gender Data — part_bfi","text":"object class \"data.frame\" 2800 observations following 6 variables: A1 indifferent feelings others. A2 Inquire others' well-. A3 Know comfort others. A4 Love children. A5 Make people feel ease. gender Gender respondent.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Agreeableness and Gender Data — part_bfi","text":"International Personality Item Pool (ipip.ori.org) https://search.r-project.org/CRAN/refmans/psychTools/html/bfi.html","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Agreeableness and Gender Data — part_bfi","text":"Revelle, W. (2024). Psych: Procedures Psychological, Psychometric, Personality Research. Evanston, Illinois: Northwestern University. https://CRAN.R-project.org/package=psych","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Agreeableness and Gender Data — part_bfi","text":"","code":"data(part_bfi) head(part_bfi) #> A1 A2 A3 A4 A5 gender #> 61617 2 4 3 4 4 0 #> 61618 2 4 5 2 5 1 #> 61620 5 4 5 4 4 1 #> 61621 4 4 6 5 5 1 #> 61622 2 3 3 4 5 0 #> 61623 6 6 5 6 5 1"},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot Transformation — plot_likert_transform","title":"Plot Transformation — plot_likert_transform","text":"Plots densities latent variables first row transformed discrete probability distributions .","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot Transformation — plot_likert_transform","text":"","code":"plot_likert_transform(n_items, n_levels, mean = 0, sd = 1, skew = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot Transformation — plot_likert_transform","text":"n_items number Likert scale items (questions). n_levels number response categories Likert item. Integer vector integers. mean means latent variables. Numeric vector numerics. Defaults 0. sd standard deviations latent variables. Numeric vector numerics. Defaults 1. skew marginal skewness latent variables. Numeric vector numerics. Defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot Transformation — plot_likert_transform","text":"plot showing densities latent variables corresponding discrete probability distributions.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot Transformation — plot_likert_transform","text":"","code":"plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)) plot_likert_transform(n_items = 3, n_levels = 5, mean=c(0, 1, 2)) plot_likert_transform(n_items = 3, n_levels = 5, sd=c(0.8, 1, 1.2)) plot_likert_transform(n_items = 3, n_levels = 5, skew=c(-0.5, 0, 0.5))"},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Response Proportions — response_prop","title":"Calculate Response Proportions — response_prop","text":"Returns table proportions possible response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Response Proportions — response_prop","text":"","code":"response_prop(data, n_levels)"},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Response Proportions — response_prop","text":"data numeric vector matrix responses. n_levels number response categories.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Response Proportions — response_prop","text":"table response category proportions.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate Response Proportions — response_prop","text":"","code":"data <- c(1, 2, 2, 3, 3, 3) response_prop(data, n_levels = 3) #> 1 2 3 #> 0.1666667 0.3333333 0.5000000 data_matrix <- matrix(c(1, 2, 2, 3, 3, 3), ncol = 2) response_prop(data_matrix, n_levels = 3) #> Response #> Item 1 2 3 #> [1,] 0.3333333 0.6666667 0 #> [2,] 0.0000000 0.0000000 1"},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate Random Responses — rlikert","title":"Generate Random Responses — rlikert","text":"Generates array random responses Likert-type questions based specified latent variables.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate Random Responses — rlikert","text":"","code":"rlikert(size, n_items, n_levels, mean = 0, sd = 1, skew = 0, corr = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate Random Responses — rlikert","text":"size number observations. n_items number Likert scale items (number questions). n_levels number response categories item. Integer vector integers. mean means latent variables. Numeric vector numerics. Defaults 0. sd standard deviations latent variables. Numeric vector numerics. Defaults 1. skew marginal skewness latent variables. Numeric vector numerics. Defaults 0. corr correlations latent variables. Can single numeric value representing correlation pairs, actual correlation matrix. Defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate Random Responses — rlikert","text":"matrix random responses dimensions size n_items. column names Y1, Y2, ..., Yn n number items. entry matrix represents Likert scale response, ranging 1 n_levels.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate Random Responses — rlikert","text":"","code":"# Generate responses for a single item with 5 levels rlikert(size = 10, n_items = 1, n_levels = 5) #> [1] 3 5 4 3 3 2 2 3 4 4 # Generate responses for three items with different levels and parameters rlikert( size = 10, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = 0.5 ) #> Y1 Y2 Y3 #> [1,] 3 1 3 #> [2,] 2 1 3 #> [3,] 3 4 2 #> [4,] 2 1 2 #> [5,] 2 2 2 #> [6,] 3 2 2 #> [7,] 3 4 4 #> [8,] 2 1 2 #> [9,] 2 2 4 #> [10,] 3 4 4 # Generate responses with a correlation matrix corr <- matrix(c( 1.00, -0.63, -0.39, -0.63, 1.00, 0.41, -0.39, 0.41, 1.00 ), nrow = 3) data <- rlikert( size = 1000, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = corr )"},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate Likert Scale Item Responses — simulate_likert","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"Simulates Likert scale item responses based specified number response categories centered parameters latent variable.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"","code":"simulate_likert(n_levels, cp)"},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"n_levels Integer. number response categories Likert scale item. cp Named vector. centered parameters latent variable, including mean (mu), standard deviation (sd), skewness (skew). Skewness must -0.95 0.95.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"named vector probabilities response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"simulation process uses following model proposed Boari Nai-Ruscone. Let \\(X\\) continuous variable interest, measured using Likert scale questions \\(K\\) response categories. observed discrete variable \\(Y\\) defined follows: $$ Y = k, \\quad \\text{ } \\ \\ x_{k - 1} < X \\leq x_{k} \\quad \\text{ } \\ \\ k = 1, \\dots, K $$ \\(x_{k}\\), \\(k = 0, \\dots, K\\) endpoints defined domain \\(X\\) : $$ -\\infty = x_{0} < x_{1} < \\dots < x_{K - 1} < x_{K} = \\infty. $$ endpoints dictate transformation density \\(f_{X}\\) \\(X\\) discrete probability distribution: $$ \\text{Pr}(Y = k) = \\int_{x_{k - 1}}^{x_{k}} f_{X}(x) \\, dx \\quad \\text{ } \\ \\ k = 1, \\dots, K. $$ continuous latent variable modeled using skew normal distribution. function simulate_likert performs following steps: Ensures centered parameters within acceptable range. Converts centered parameters direct parameters. Defines density function skew normal distribution. Computes probabilities response category using optimal endpoints.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"Boari, G. Nai Ruscone, M. (2015). procedure simulating likert scale item responses. Electronic journal applied statistical analysis 8(3), 288–297. doi:10.1285/i20705948v8n3p288","code":""},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"","code":"cp <- c(mu = 0, sd = 1, skew = 0.5) simulate_likert(n_levels = 5, cp = cp) #> 1 2 3 4 5 #> 0.15995244 0.29511214 0.28435807 0.18964493 0.07093241 cp2 <- c(mu = 1, sd = 2, skew = -0.3) simulate_likert(n_levels = 7, cp = cp2) #> 1 2 3 4 5 6 7 #> 0.08311645 0.07169556 0.07928979 0.08940184 0.10477572 0.13413804 0.43758260"},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"latent2likert-010-release-date-2020-10-17","dir":"Changelog","previous_headings":"","what":"latent2likert 0.1.0 (Release date: 2020-10-17)","title":"latent2likert 0.1.0 (Release date: 2020-10-17)","text":"Initial release (development version). Tested platforms: x86_64-pc-linux-gnu (64-bit) x86_64-w64-mingw32 (64-bit).","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"latent2likert-100-release-date-2024-03-28","dir":"Changelog","previous_headings":"","what":"latent2likert 1.0.0 (Release date: 2024-03-28)","title":"latent2likert 1.0.0 (Release date: 2024-03-28)","text":"option generate correlated Likert scale items added function rLikert(). New function estimate_parameters() added allows estimation parameters existing survey data replicate accurately. Issues related dependencies resolved. version now imports standard R packages mvtnorm, stats, graphics packages stats graphics, typically included R releases. package sn necessary generating correlated responses based skew normal distribution. Added user prompts installing sn package necessary.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"latent2likert-110-release-date-2024-06-06","dir":"Changelog","previous_headings":"","what":"latent2likert 1.1.0 (Release date: 2024-06-06)","title":"latent2likert 1.1.0 (Release date: 2024-06-06)","text":"minor update functions vignettes.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"latent2likert-111-release-date-2024-06-06","dir":"Changelog","previous_headings":"","what":"latent2likert 1.1.1 (Release date: 2024-06-06)","title":"latent2likert 1.1.1 (Release date: 2024-06-06)","text":"package renamed responsesR latent2likert. capture essence converting latent variables Likert scale responses. Improvements package website documentation.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"latent2likert-121-release-date-2024-06-12","dir":"Changelog","previous_headings":"","what":"latent2likert 1.2.1 (Release date: 2024-06-12)","title":"latent2likert 1.2.1 (Release date: 2024-06-12)","text":"Refactored code improved modularity maintainability. Modularized core functions better readability. Improved structure organization codebase. Improved error handling different cases correlations input. Updated estimate_parameters() function estimating latent parameters survey data. codebase currently development, finer details may change.","code":""}] +[{"path":"https://markolalovic.github.io/latent2likert/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 Marko Lalovic Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"introduction","dir":"Articles","previous_headings":"Using latent2likert","what":"Introduction","title":"Using latent2likert","text":"social sciences, variables interest often conceptualized latent variables — hidden continuous variables measured Likert scale questions, typically categorized Strongly disagree, Disagree, Neutral, Agree, Strongly agree. Researchers frequently aim uncover latent variables using various statistical techniques. Accurate modeling survey data essential comparative analysis simulation. latent2likert package addresses need providing effective algorithm simulate Likert response variables hypothetical latent variables. vignette provides two practical workflow examples demonstrating use latent2likert package.","code":""},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"simulating-survey-data","dir":"Articles","previous_headings":"Using latent2likert","what":"Simulating Survey Data","title":"Using latent2likert","text":"following hypothetical survey simulation loosely based actual comparative study teaching learning R pair introductory statistics labs (McNamara 2024). Imagine situation 10 participants Course 20 participants Course B completed survey. Suppose initial question : “rate experience course?” four possible answers: Poor, Fair, Good, Excellent. Let’s assume participants Course neutral regarding question, participants Course B positive experience average. choosing appropriate parameters latent distributions setting number categories n_levels = 4, can generate hypothetical responses (standard deviation sd = 1 skewness skew = 0, default): summarize results, create data frame responses: results can visualized using grouped bar chart:","code":"library(latent2likert) # Load the package set.seed(12345) # Ensure reproducible results # Generate responses for Course A and Course B responses_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1) responses_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1) n_levels <- 4 n_groups <- 2 categories <- c(\"Poor\", \"Fair\", \"Good\", \"Excellent\") # Create a data frame to summarize the responses response_data <- data.frame( Course = rep(c(\"A\", \"B\"), each = n_levels), Response = factor(rep(categories, n_groups), levels = categories), Proportion = c( response_prop(responses_A, n_levels), response_prop(responses_B, n_levels) ) ) # Filter out rows with zero proportions response_data <- response_data[response_data$Proportion > 0, ] response_data #> Course Response Proportion #> 1 A Poor 0.30 #> 2 A Fair 0.20 #> 3 A Good 0.20 #> 4 A Excellent 0.30 #> 6 B Fair 0.10 #> 7 B Good 0.25 #> 8 B Excellent 0.65"},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"pre-and-post-comparison","dir":"Articles","previous_headings":"Using latent2likert","what":"Pre and Post Comparison","title":"Using latent2likert","text":"Now suppose survey also asked participants rate skills 5-point Likert scale, ranging 1 (poor) 5 (good) : Programming, Searching Online, Solving Problems. survey completed participants taking course pre post-comparison. Suppose participants’ assessments : Programming skills average increased, Searching Online stayed , Solving Problems increased Course , decreased participants Course B. Let’s simulate survey data scenario: Create data frame responses summarize results: visualize results stacked bar chart:","code":"# Pre- and post-assessments of skills for Course A pre_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(-1, 0, 1)) post_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(0, 0, 2)) # Pre- and post-assessments of skills for Course B pre_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(-1, 0, 1)) post_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(0, 0, 0)) # Combine pre and post responses into a list pre_post <- list(pre_A, post_A, pre_B, post_B) # Number of items and response levels n_items <- 3 n_levels <- 5 # Define skills assessed skills <- c(\"Programming\", \"Searching online\", \"Solving problems\") # Generate repeated skill labels for questions questions <- rep(rep(skills, each = n_levels), 4) questions <- factor(questions, levels = skills) # Create a data frame to summarize the responses response_data <- data.frame( Course = rep(c(\"Course A\", \"Course B\"), each = 2 * n_items * n_levels), Question = questions, Time = as.factor(rep(c( rep(\"before\", n_items * n_levels), rep(\"after\", n_items * n_levels) ), 2)), Response = rep(seq_len(n_levels), 2 * n_items * 2), Proportion = as.vector(sapply(pre_post, function(d) { as.vector(t(response_prop(d, n_levels))) })) ) head(response_data) #> Course Question Time Response Proportion #> 1 Course A Programming before 1 0.5 #> 2 Course A Programming before 2 0.2 #> 3 Course A Programming before 3 0.3 #> 4 Course A Programming before 4 0.0 #> 5 Course A Programming before 5 0.0 #> 6 Course A Searching online before 1 0.1"},{"path":"https://markolalovic.github.io/latent2likert/articles/using_latent2likert.html","id":"recreating-scale-scores","dir":"Articles","previous_headings":"Using latent2likert","what":"Recreating Scale Scores","title":"Using latent2likert","text":"use part bfi data set (Revelle 2024). Specifically, ’ll focus first 5 items corresponding agreeableness. investigate differences agreeableness men women, ’ll also use gender attribute. Load data: Separate items two groups according gender: Estimate parameters latent variables, assuming normal providing number possible response categories n_levels = 6: Generate new responses items using estimated parameters estimated correlations: Create agreeableness scale scores groups participants taking average 5 items: results can visualized grouped boxplot:","code":"data(part_bfi) head(part_bfi) #> A1 A2 A3 A4 A5 gender #> 61617 2 4 3 4 4 0 #> 61618 2 4 5 2 5 1 #> 61620 5 4 5 4 4 1 #> 61621 4 4 6 5 5 1 #> 61622 2 3 3 4 5 0 #> 61623 6 6 5 6 5 1 vars <- c(\"A1\", \"A2\", \"A3\", \"A4\", \"A5\") items_male <- part_bfi[part_bfi$gender == 0, vars] items_female <- part_bfi[part_bfi$gender == 1, vars] params_male <- estimate_params(data = items_male, n_levels = 6) params_female <- estimate_params(data = items_female, n_levels = 6) set.seed(12345) # Ensure reproducible results new_items_male <- rlikert( size = nrow(items_male), n_items = 5, n_levels = 6, mean = params_male[\"mean\", ], sd = params_male[\"sd\", ], corr = cor(items_male) ) new_items_female <- rlikert( size = nrow(items_female), n_items = 5, n_levels = 6, mean = params_female[\"mean\", ], sd = params_female[\"sd\", ], corr = cor(items_female) ) # Combine new items and gender in new data frame new_data <- data.frame(rbind(new_items_male, new_items_female)) new_data$gender <- c(rep(0, nrow(items_male)), rep(1, nrow(items_female))) head(new_data) #> Y1 Y2 Y3 Y4 Y5 gender #> 1 3 5 5 4 5 0 #> 2 1 5 4 4 4 0 #> 3 2 6 5 6 4 0 #> 4 4 4 4 6 5 0 #> 5 4 5 3 2 2 0 #> 6 5 4 5 6 5 0 # Reverse the first item because it has negative correlations part_bfi$A1 <- (min(part_bfi$A1) + max(part_bfi$A1)) - part_bfi$A1 new_data$Y1 <- (min(new_data$Y1) + max(new_data$Y1)) - new_data$Y1 # Create agreeableness scale scores part_bfi$agreeable <- rowMeans(part_bfi[, vars]) new_data$agreeable <- rowMeans(new_data[, c(\"Y1\", \"Y2\", \"Y3\", \"Y4\", \"Y5\")])"},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Marko Lalovic. Author, maintainer.","code":""},{"path":"https://markolalovic.github.io/latent2likert/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Lalovic M (2024). latent2likert: Converting Latent Variables Likert Scale Responses. R package version 1.2.1, https://lalovic.io/latent2likert/.","code":"@Manual{, title = {latent2likert: Converting Latent Variables into Likert Scale Responses}, author = {Marko Lalovic}, year = {2024}, note = {R package version 1.2.1}, url = {https://lalovic.io/latent2likert/}, }"},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"overview","dir":"","previous_headings":"","what":"Overview","title":"Converting Latent Variables into Likert Scale Responses","text":"latent2likert package designed effectively simulate discretization process inherent Likert scales minimizing distortion. converts continuous latent variables ordinal categories generate Likert scale item responses. particularly useful accurately modeling analyzing survey data use Likert scales, especially applying statistical techniques require metric data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Converting Latent Variables into Likert Scale Responses","text":"can install development version GitHub :","code":"# install.packages(\"devtools\") devtools::install_github(\"markolalovic/latent2likert\")"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"dependencies","dir":"","previous_headings":"","what":"Dependencies","title":"Converting Latent Variables into Likert Scale Responses","text":"keep package lightweight, latent2likert imports mvtnorm, along standard R packages stats graphics, typically included R releases. additional suggested dependency package sn, required generating random responses correlated Likert items based multivariate skew normal distribution. package prompts user install dependency interactive sessions needed.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"features","dir":"","previous_headings":"","what":"Features","title":"Converting Latent Variables into Likert Scale Responses","text":"rlikert: Generates random responses Likert scale questions based specified means standard deviations latent variables, optional settings skewness correlations. estimate_params: Estimates latent parameters existing survey data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"structure","dir":"","previous_headings":"","what":"Structure","title":"Converting Latent Variables into Likert Scale Responses","text":"Overview inputs outputs.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"using-rlikert","dir":"","previous_headings":"","what":"Using rlikert","title":"Converting Latent Variables into Likert Scale Responses","text":"generate sample random responses one item 5-point Likert scale, use: generate responses multiple items specified parameters: can also provide correlation matrix: Note correlations among Likert response variables estimates actual correlations latent variables, estimates typically lower:","code":"library(latent2likert) rlikert(size = 10, n_items = 1, n_levels = 5) #> [1] 2 5 2 3 3 1 2 2 1 5 rlikert(size = 10, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = 0.5) #> Y1 Y2 Y3 #> [1,] 4 3 5 #> [2,] 3 2 3 #> [3,] 3 3 3 #> [4,] 2 3 4 #> [5,] 2 3 4 #> [6,] 3 2 4 #> [7,] 3 1 3 #> [8,] 2 1 3 #> [9,] 2 1 6 #> [10,] 3 1 3 corr <- matrix(c(1.00, -0.63, -0.39, -0.63, 1.00, 0.41, -0.39, 0.41, 1.00), nrow=3) data <- rlikert(size = 10^3, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = corr) cor(data) #> Y1 Y2 Y3 #> Y1 1.0000000 -0.5277858 -0.3678057 #> Y2 -0.5277858 1.0000000 0.3983187 #> Y3 -0.3678057 0.3983187 1.0000000"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"using-estimate_params","dir":"","previous_headings":"","what":"Using estimate_params","title":"Converting Latent Variables into Likert Scale Responses","text":"Given data, can estimate values latent parameters using:","code":"estimate_params(data, n_levels = c(4, 5, 6), skew = 0) #> items #> estimates Y1 Y2 Y3 #> mean 0.08270757 -1.10356623 0.01029328 #> sd 0.79986937 1.06032921 1.01115089"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"transformation","dir":"","previous_headings":"","what":"Transformation","title":"Converting Latent Variables into Likert Scale Responses","text":"visualize transformation, can use plot_likert_transform(). plots densities latent variables first row transformed discrete probability distributions : Transformation latent variables Likert response variables. Note , depending value skewness parameter, normal latent distribution used skew = 0, otherwise skew normal distribution used. value skewness restricted range -0.95 0.95, skew >= -0.95 skew <= 0.95.","code":"plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, -1, 0), sd = c(0.8, 1, 1), skew = c(0, 0, 0.5))"},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"further-reading","dir":"","previous_headings":"","what":"Further Reading","title":"Converting Latent Variables into Likert Scale Responses","text":"detailed information practical examples, please refer package vignette. implemented algorithms described functions reference.","code":""},{"path":"https://markolalovic.github.io/latent2likert/index.html","id":"related-r-packages","dir":"","previous_headings":"","what":"Related R Packages","title":"Converting Latent Variables into Likert Scale Responses","text":"simulate Likert item responses, draw_likert function fabricatr package can used recode latent variable Likert response variable specifying intervals subdivide continuous range. latent2likert package, however, offers advantage automatically calculating optimal intervals minimize distortion latent variable Likert response variable normal skew normal latent distributions, eliminating need manually specify intervals. also several alternative approaches rely latent distributions. One method involves directly defining discrete probability distribution sampling using sample function R likert function wakefield package. Another approach specify means, standard deviations, correlations among Likert response variables. , can use LikertMakeR SimCorMultRes generate correlated multinomial responses. Additionally, can define data generating process. familiar item response theory, mirt package allows users specify discrimination difficulty parameters response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":null,"dir":"Reference","previous_headings":"","what":"Discretize Density — discretize_density","title":"Discretize Density — discretize_density","text":"Transforms density function continuous random variable discrete probability distribution minimal distortion using Lloyd-Max algorithm.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Discretize Density — discretize_density","text":"","code":"discretize_density(density_fn, n_levels, eps = 1e-06)"},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Discretize Density — discretize_density","text":"density_fn probability density function. n_levels cardinality set possible outcomes. eps convergence threshold algorithm.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Discretize Density — discretize_density","text":"list containing: prob discrete probability distribution. endp endpoints intervals partition continuous domain. repr representation points intervals. dist distortion measured mean-squared error (MSE).","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Discretize Density — discretize_density","text":"function addresses problem transforming continuous random variable \\(X\\) discrete random variable \\(Y\\) minimal distortion. Distortion measured mean-squared error (MSE): $$ \\text{E}\\left[ (X - Y)^2 \\right] = \\sum_{k=1}^{K} \\int_{x_{k-1}}^{x_{k}} f_{X}(x) \\left( x - r_{k} \\right)^2 \\, dx $$ : \\(f_{X}\\) probability density function \\(X\\), \\(K\\) number possible outcomes \\(Y\\), \\(x_{k}\\) endpoints intervals partition domain \\(X\\), \\(r_{k}\\) representation points intervals. problem solved using following iterative procedure: \\(1.\\) Start arbitrary initial set representation points: \\(r_{1} < r_{2} < \\dots < r_{K}\\). \\(2.\\) Repeat following steps improvement MSE falls given \\(\\varepsilon\\). \\(3.\\) Calculate endpoints \\(x_{k} = (r_{k+1} + r_{k})/2\\) \\(k = 1, \\dots, K-1\\) set \\(x_{0}\\) \\(x_{K}\\) \\(-\\infty\\) \\(\\infty\\), respectively. \\(4.\\) Update representation points setting \\(r_{k}\\) equal conditional mean \\(X\\) given \\(X \\(x_{k-1}, x_{k})\\) \\(k = 1, \\dots, K\\). execution step \\((3)\\) step \\((4)\\), MSE decreases remains . MSE nonnegative, approaches limit. algorithm terminates improvement MSE less given \\(\\varepsilon > 0\\), ensuring convergence finite number iterations. procedure known Lloyd-Max's algorithm, initially used scalar quantization closely related k-means algorithm. Local convergence proven log-concave density functions Kieffer. Many common probability distributions log-concave including normal skew normal distribution, shown Azzalini.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Discretize Density — discretize_density","text":"Azzalini, . (1985). class distributions includes normal ones. Scandinavian Journal Statistics 12(2), 171–178. Kieffer, J. (1983). Uniqueness locally optimal quantizer log-concave density convex error function. IEEE Transactions Information Theory 29, 42–47. Lloyd, S. (1982). Least squares quantization PCM. IEEE Transactions Information Theory 28 (2), 129–137.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/discretize_density.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Discretize Density — discretize_density","text":"","code":"discretize_density(density_fn = stats::dnorm, n_levels = 5) #> $prob #> [1] 0.1063142 0.2444957 0.2983803 0.2444957 0.1063142 #> #> $endp #> [1] -Inf -1.2463707 -0.3831349 0.3831349 1.2463707 Inf #> #> $repr #> [1] -1.7264716 -0.7662698 0.0000000 0.7662698 1.7264716 #> #> $dist #> [1] 0.07994185 #> discretize_density(density_fn = function(x) { 2 * stats::dnorm(x) * stats::pnorm(0.5 * x) }, n_levels = 4) #> $prob #> [1] 0.1647781 0.3380772 0.3359810 0.1611637 #> #> $endp #> [1] -Inf -0.5537368 0.3597728 1.2808536 Inf #> #> $repr #> [1] -1.04423728 -0.06323628 0.78278182 1.77892538 #> #> $dist #> [1] 0.1026681 #>"},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate Latent Parameters — estimate_params","title":"Estimate Latent Parameters — estimate_params","text":"Estimates location scaling parameters latent variables existing survey data.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate Latent Parameters — estimate_params","text":"","code":"estimate_params(data, n_levels, skew = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate Latent Parameters — estimate_params","text":"data survey data columns representing individual items. Apart , data can almost class \"data.frame\" \"matrix\" \"array\". n_levels number response categories, vector number. skew marginal skewness latent variables, defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate Latent Parameters — estimate_params","text":"table estimated parameters latent variable.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Estimate Latent Parameters — estimate_params","text":"relationship continuous random variable \\(X\\) discrete probability distribution \\(p_k\\), \\(k = 1, \\dots, K\\), can described system non-linear equations: $$ p_{k} = F_{X}\\left( \\frac{x_{k - 1} - \\xi}{\\omega} \\right) - F_{X}\\left( \\frac{x_{k} - \\xi}{\\omega} \\right) \\quad \\text{} \\ k = 1, \\dots, K $$ : \\(F_{X}\\) cumulative distribution function \\(X\\), \\(K\\) number possible response categories, \\(x_{k}\\) endpoints defining boundaries response categories, \\(p_{k}\\) probability \\(k\\)-th response category, \\(\\xi\\) location parameter \\(X\\), \\(\\omega\\) scaling parameter \\(X\\). endpoints \\(x_{k}\\) calculated discretizing random variable \\(Z\\) mean 0 standard deviation 1 follows distribution \\(X\\). solving system non-linear equations iteratively, can find parameters best fit observed discrete probability distribution \\(p_{k}\\). function estimate_params: Computes proportion table responses item. Estimates probabilities \\(p_{k}\\) item. Computes estimates \\(\\xi\\) \\(\\omega\\) item. Combines estimated parameters items table.","code":""},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/reference/estimate_params.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate Latent Parameters — estimate_params","text":"","code":"data(part_bfi) vars <- c(\"A1\", \"A2\", \"A3\", \"A4\", \"A5\") estimate_params(data = part_bfi[, vars], n_levels = 6) #> items #> estimates A1 A2 A3 A4 A5 #> mean -0.9759824 1.0830781 0.9776057 1.1723519 0.9006478 #> sd 1.1798137 0.7968668 0.8432599 1.3825407 0.8648150"},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":null,"dir":"Reference","previous_headings":"","what":"Agreeableness and Gender Data — part_bfi","title":"Agreeableness and Gender Data — part_bfi","text":"dataset cleaned version small part bfi dataset psychTools package. contains responses first 5 items agreeableness scale International Personality Item Pool (IPIP) gender attribute. includes responses 2800 subjects. item answered six point Likert scale ranging 1 (inaccurate), 6 (accurate). Gender coded 0 male 1 female. Missing values addressed using mode imputation.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Agreeableness and Gender Data — part_bfi","text":"","code":"data(part_bfi)"},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Agreeableness and Gender Data — part_bfi","text":"object class \"data.frame\" 2800 observations following 6 variables: A1 indifferent feelings others. A2 Inquire others' well-. A3 Know comfort others. A4 Love children. A5 Make people feel ease. gender Gender respondent.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Agreeableness and Gender Data — part_bfi","text":"International Personality Item Pool (https://ipip.ori.org) https://search.r-project.org/CRAN/refmans/psychTools/html/bfi.html","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Agreeableness and Gender Data — part_bfi","text":"Revelle, W. (2024). Psych: Procedures Psychological, Psychometric, Personality Research. Evanston, Illinois: Northwestern University. https://CRAN.R-project.org/package=psych","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/part_bfi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Agreeableness and Gender Data — part_bfi","text":"","code":"data(part_bfi) head(part_bfi) #> A1 A2 A3 A4 A5 gender #> 61617 2 4 3 4 4 0 #> 61618 2 4 5 2 5 1 #> 61620 5 4 5 4 4 1 #> 61621 4 4 6 5 5 1 #> 61622 2 3 3 4 5 0 #> 61623 6 6 5 6 5 1"},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot Transformation — plot_likert_transform","title":"Plot Transformation — plot_likert_transform","text":"Plots densities latent variables corresponding transformed discrete probability distributions.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot Transformation — plot_likert_transform","text":"","code":"plot_likert_transform(n_items, n_levels, mean = 0, sd = 1, skew = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot Transformation — plot_likert_transform","text":"n_items number Likert scale items (questions). n_levels number response categories Likert item. Integer vector integers. mean means latent variables. Numeric vector numerics. Defaults 0. sd standard deviations latent variables. Numeric vector numerics. Defaults 1. skew marginal skewness latent variables. Numeric vector numerics. Defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot Transformation — plot_likert_transform","text":"NULL. function produces plot.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/plot_likert_transform.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot Transformation — plot_likert_transform","text":"","code":"plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)) plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, 1, 2)) plot_likert_transform(n_items = 3, n_levels = 5, sd = c(0.8, 1, 1.2)) plot_likert_transform(n_items = 3, n_levels = 5, skew = c(-0.5, 0, 0.5))"},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Response Proportions — response_prop","title":"Calculate Response Proportions — response_prop","text":"Returns table proportions possible response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Response Proportions — response_prop","text":"","code":"response_prop(data, n_levels)"},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Response Proportions — response_prop","text":"data numeric vector matrix responses. n_levels number response categories.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Response Proportions — response_prop","text":"table response category proportions.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/response_prop.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate Response Proportions — response_prop","text":"","code":"data <- c(1, 2, 2, 3, 3, 3) response_prop(data, n_levels = 3) #> 1 2 3 #> 0.1666667 0.3333333 0.5000000 data_matrix <- matrix(c(1, 2, 2, 3, 3, 3), ncol = 2) response_prop(data_matrix, n_levels = 3) #> Response #> Item 1 2 3 #> [1,] 0.3333333 0.6666667 0 #> [2,] 0.0000000 0.0000000 1"},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate Random Responses — rlikert","title":"Generate Random Responses — rlikert","text":"Generates array random responses Likert-type questions based specified latent variables.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate Random Responses — rlikert","text":"","code":"rlikert(size, n_items, n_levels, mean = 0, sd = 1, skew = 0, corr = 0)"},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate Random Responses — rlikert","text":"size number observations. n_items number Likert scale items (number questions). n_levels number response categories item. Integer vector integers. mean means latent variables. Numeric vector numerics. Defaults 0. sd standard deviations latent variables. Numeric vector numerics. Defaults 1. skew marginal skewness latent variables. Numeric vector numerics. Defaults 0. corr correlations latent variables. Can single numeric value representing correlation pairs, actual correlation matrix. Defaults 0.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate Random Responses — rlikert","text":"matrix random responses dimensions size n_items. column names Y1, Y2, ..., Yn n number items. entry matrix represents Likert scale response, ranging 1 n_levels.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/rlikert.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate Random Responses — rlikert","text":"","code":"# Generate responses for a single item with 5 levels rlikert(size = 10, n_items = 1, n_levels = 5) #> [1] 3 5 4 3 3 2 2 3 4 4 # Generate responses for three items with different levels and parameters rlikert( size = 10, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = 0.5 ) #> Y1 Y2 Y3 #> [1,] 3 1 3 #> [2,] 2 1 3 #> [3,] 3 4 2 #> [4,] 2 1 2 #> [5,] 2 2 2 #> [6,] 3 2 2 #> [7,] 3 4 4 #> [8,] 2 1 2 #> [9,] 2 2 4 #> [10,] 3 4 4 # Generate responses with a correlation matrix corr <- matrix(c( 1.00, -0.63, -0.39, -0.63, 1.00, 0.41, -0.39, 0.41, 1.00 ), nrow = 3) data <- rlikert( size = 1000, n_items = 3, n_levels = c(4, 5, 6), mean = c(0, -1, 0), sd = c(0.8, 1, 1), corr = corr )"},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate Likert Scale Item Responses — simulate_likert","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"Simulates Likert scale item responses based specified number response categories centered parameters latent variable.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"","code":"simulate_likert(n_levels, cp)"},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"n_levels number response categories Likert scale item. cp centered parameters latent variable. Named vector including mean (mu), standard deviation (sd), skewness (skew). Skewness must -0.95 0.95.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"named vector probabilities response category.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"simulation process uses following model detailed Boari Nai-Ruscone. Let \\(X\\) continuous variable interest, measured using Likert scale questions \\(K\\) response categories. observed discrete variable \\(Y\\) defined follows: $$ Y = k, \\quad \\text{ } \\ \\ x_{k - 1} < X \\leq x_{k} \\quad \\text{ } \\ \\ k = 1, \\dots, K $$ \\(x_{k}\\), \\(k = 0, \\dots, K\\) endpoints defined domain \\(X\\) : $$ -\\infty = x_{0} < x_{1} < \\dots < x_{K - 1} < x_{K} = \\infty. $$ endpoints dictate transformation density \\(f_{X}\\) \\(X\\) discrete probability distribution: $$ \\text{Pr}(Y = k) = \\int_{x_{k - 1}}^{x_{k}} f_{X}(x) \\, dx \\quad \\text{ } \\ \\ k = 1, \\dots, K. $$ continuous latent variable modeled using skew normal distribution. function simulate_likert performs following steps: Ensures centered parameters within acceptable range. Converts centered parameters direct parameters. Defines density function skew normal distribution. Computes probabilities response category using optimal endpoints.","code":""},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"Boari, G. Nai Ruscone, M. (2015). procedure simulating Likert scale item responses. Electronic Journal Applied Statistical Analysis 8(3), 288–297. doi:10.1285/i20705948v8n3p288","code":""},{"path":[]},{"path":"https://markolalovic.github.io/latent2likert/reference/simulate_likert.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate Likert Scale Item Responses — simulate_likert","text":"","code":"cp <- c(mu = 0, sd = 1, skew = 0.5) simulate_likert(n_levels = 5, cp = cp) #> 1 2 3 4 5 #> 0.15995244 0.29511214 0.28435807 0.18964493 0.07093241 cp2 <- c(mu = 1, sd = 2, skew = -0.3) simulate_likert(n_levels = 7, cp = cp2) #> 1 2 3 4 5 6 7 #> 0.08311645 0.07169556 0.07928979 0.08940184 0.10477572 0.13413804 0.43758260"},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"version-010","dir":"Changelog","previous_headings":"","what":"Version 0.1.0","title":"Version 0.1.0","text":"Release date: 2020-10-17 Initial release (development version). Tested platforms: x86_64-pc-linux-gnu (64-bit) x86_64-w64-mingw32 (64-bit).","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"version-100","dir":"Changelog","previous_headings":"","what":"Version 1.0.0","title":"Version 1.0.0","text":"Release date: 2024-03-28 Added option generate correlated Likert scale items rlikert() function. Added estimate_params() function estimating parameters existing survey data. Resolved dependency issues. Reduced dependency standard R packages: mvtnorm, stats, graphics. sn package now required generating correlated responses using skew normal distribution. Added user prompts install sn package needed.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"version-110","dir":"Changelog","previous_headings":"","what":"Version 1.1.0","title":"Version 1.1.0","text":"Release date: 2024-06-06 Minor updates functions vignettes.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"version-111","dir":"Changelog","previous_headings":"","what":"Version 1.1.1","title":"Version 1.1.1","text":"Release date: 2024-06-06 Renamed package responsesR latent2likert better reflect purpose converting latent variables Likert scale responses. Improved package website documentation. Note: codebase development, finer details may change.","code":""},{"path":"https://markolalovic.github.io/latent2likert/news/index.html","id":"version-121","dir":"Changelog","previous_headings":"","what":"Version 1.2.1","title":"Version 1.2.1","text":"Release date: 2024-06-12 Refactored code enhanced modularity maintainability. Modularized core functions improved readability. Improved structure organization codebase. Enhanced error handling various correlation input scenarios.","code":""}] diff --git a/man/discretize_density.Rd b/man/discretize_density.Rd index 7ea03ee..6a65229 100644 --- a/man/discretize_density.Rd +++ b/man/discretize_density.Rd @@ -32,8 +32,8 @@ The function addresses the problem of transforming a continuous random variable \eqn{X} into a discrete random variable \eqn{Y} with minimal distortion. Distortion is measured as mean-squared error (MSE): \deqn{ - \text{E}\left[ (X - Y)^2 \right] = - \sum_{k=1}^{K} \int_{x_{k-1}}^{x_{k}} f_{X}(x) + \text{E}\left[ (X - Y)^2 \right] = + \sum_{k=1}^{K} \int_{x_{k-1}}^{x_{k}} f_{X}(x) \left( x - r_{k} \right)^2 \, dx } where: @@ -73,7 +73,8 @@ normal distribution, as shown by Azzalini. \examples{ discretize_density(density_fn = stats::dnorm, n_levels = 5) discretize_density(density_fn = function(x) { - 2 * stats::dnorm(x) * stats::pnorm(0.5 * x)}, n_levels = 4) + 2 * stats::dnorm(x) * stats::pnorm(0.5 * x) +}, n_levels = 4) } \references{ Azzalini, A. 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+++ b/man/part_bfi.Rd @@ -17,7 +17,7 @@ the following 6 variables:} } } \source{ -{International Personality Item Pool (ipip.ori.org)} +{International Personality Item Pool ({https://ipip.ori.org})} {https://search.r-project.org/CRAN/refmans/psychTools/html/bfi.html} } diff --git a/man/plot_likert_transform.Rd b/man/plot_likert_transform.Rd index 3e23ab4..57a8340 100644 --- a/man/plot_likert_transform.Rd +++ b/man/plot_likert_transform.Rd @@ -9,24 +9,28 @@ plot_likert_transform(n_items, n_levels, mean = 0, sd = 1, skew = 0) \arguments{ \item{n_items}{number of Likert scale items (questions).} -\item{n_levels}{number of response categories for each Likert item. Integer or vector of integers.} +\item{n_levels}{number of response categories for each Likert item. +Integer or vector of integers.} -\item{mean}{means of the latent variables. Numeric or vector of numerics. Defaults to 0.} +\item{mean}{means of the latent variables. +Numeric or vector of numerics. Defaults to 0.} -\item{sd}{standard deviations of the latent variables. Numeric or vector of numerics. Defaults to 1.} +\item{sd}{standard deviations of the latent variables. +Numeric or vector of numerics. Defaults to 1.} -\item{skew}{marginal skewness of the latent variables. Numeric or vector of numerics. Defaults to 0.} +\item{skew}{marginal skewness of the latent variables. +Numeric or vector of numerics. Defaults to 0.} } \value{ -a plot showing the densities of latent variables and the corresponding discrete probability distributions. +NULL. The function produces a plot. } \description{ -Plots the densities of latent variables in the first row -and transformed discrete probability distributions below. +Plots the densities of latent variables and the corresponding +transformed discrete probability distributions. } \examples{ plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)) -plot_likert_transform(n_items = 3, n_levels = 5, mean=c(0, 1, 2)) -plot_likert_transform(n_items = 3, n_levels = 5, sd=c(0.8, 1, 1.2)) -plot_likert_transform(n_items = 3, n_levels = 5, skew=c(-0.5, 0, 0.5)) +plot_likert_transform(n_items = 3, n_levels = 5, mean = c(0, 1, 2)) +plot_likert_transform(n_items = 3, n_levels = 5, sd = c(0.8, 1, 1.2)) +plot_likert_transform(n_items = 3, n_levels = 5, skew = c(-0.5, 0, 0.5)) } diff --git a/man/simulate_likert.Rd b/man/simulate_likert.Rd index daa4ad8..122d302 100644 --- a/man/simulate_likert.Rd +++ b/man/simulate_likert.Rd @@ -7,11 +7,11 @@ simulate_likert(n_levels, cp) } \arguments{ -\item{n_levels}{Integer. The number of response categories for the Likert scale item.} +\item{n_levels}{number of response categories for the Likert scale item.} -\item{cp}{Named vector. The centered parameters of the latent variable, including -mean (\code{mu}), standard deviation (\code{sd}), and skewness (\code{skew}). -Skewness must be between -0.95 and 0.95.} +\item{cp}{centered parameters of the latent variable. +Named vector including mean (\code{mu}), standard deviation (\code{sd}), +and skewness (\code{skew}). Skewness must be between -0.95 and 0.95.} } \value{ A named vector of probabilities for each response category. @@ -21,10 +21,10 @@ Simulates Likert scale item responses based on a specified number of response categories and the centered parameters of the latent variable. } \details{ -The simulation process uses the following model detailed by Boari and Nai-Ruscone. -Let \eqn{X} be the continuous variable of interest, measured using Likert scale -questions with \eqn{K} response categories. The observed discrete variable \eqn{Y} is -defined as follows: +The simulation process uses the following model detailed by +Boari and Nai-Ruscone. Let \eqn{X} be the continuous variable of interest, +measured using Likert scale questions with \eqn{K} response categories. The +observed discrete variable \eqn{Y} is defined as follows: \deqn{ Y = k, \quad \text{ if } \ \ x_{k - 1} < X \leq x_{k} \quad \text{ for } \ \ k = 1, \dots, K @@ -34,8 +34,8 @@ of \eqn{X} such that: \deqn{ -\infty = x_{0} < x_{1} < \dots < x_{K - 1} < x_{K} = \infty. } -The endpoints dictate the transformation of the density \eqn{f_{X}} of \eqn{X} -into a discrete probability distribution: +The endpoints dictate the transformation of the density +\eqn{f_{X}} of \eqn{X} into a discrete probability distribution: \deqn{ \text{Pr}(Y = k) = \int_{x_{k - 1}}^{x_{k}} f_{X}(x) \, dx \quad \text{ for } \ \ k = 1, \dots, K. @@ -47,7 +47,8 @@ The function \code{simulate_likert} performs the following steps: \item Ensures the centered parameters are within the acceptable range. \item Converts the centered parameters to direct parameters. \item Defines the density function for the skew normal distribution. -\item Computes the probabilities for each response category using optimal endpoints. +\item Computes the probabilities for each response category +using optimal endpoints. } } \examples{ @@ -59,7 +60,8 @@ simulate_likert(n_levels = 7, cp = cp2) \references{ Boari, G. and Nai Ruscone, M. (2015). A procedure simulating Likert scale item responses. -\emph{Electronic Journal of Applied Statistical Analysis} \bold{8(3)}, 288–297. +\emph{Electronic Journal of Applied Statistical Analysis} \bold{8(3)}, +288–297. \doi{10.1285/i20705948v8n3p288} } \seealso{ diff --git a/tests/testthat/test_discretization.R b/tests/testthat/test_discretization.R index 7511131..9d4104e 100644 --- a/tests/testthat/test_discretization.R +++ b/tests/testthat/test_discretization.R @@ -1,21 +1,23 @@ context("Testing discretization") -testthat::test_that("discretization of N(0,1) using 4 levels gives expected results", { - res = discretize_density(density_fn = dnorm, n_levels = 4) - expected = list( - prob = c(0.16, 0.34, 0.34, 0.16), - endp = c(-Inf, -0.98, 0, 0.98, Inf), - repr = c(-1.51, -0.45, 0.45, 1.51), - dist = 0.12) - testthat::expect_equal(res, expected, tolerance = 0.05) +test_that("discretization of N(0,1) using 4 levels gives expected results", { + res <- discretize_density(density_fn = dnorm, n_levels = 4) + expected <- list( + prob = c(0.16, 0.34, 0.34, 0.16), + endp = c(-Inf, -0.98, 0, 0.98, Inf), + repr = c(-1.51, -0.45, 0.45, 1.51), + dist = 0.12 + ) + expect_equal(res, expected, tolerance = 0.05) }) -testthat::test_that("discretization of N(0,1) using 5 levels gives expected results", { - res = discretize_density(density_fn = dnorm, n_levels = 5) - expected = list( - prob = c(0.11, 0.24, 0.30, .24, 0.11), - endp = c(-Inf, -1.25, -0.38, 0.38, 1.25, Inf), - repr = c(-1.73, -0.77, 0, 0.77, 1.73), - dist = 0.08) - testthat::expect_equal(res, expected, tolerance = 0.05) +test_that("discretization of N(0,1) using 5 levels gives expected results", { + res <- discretize_density(density_fn = dnorm, n_levels = 5) + expected <- list( + prob = c(0.11, 0.24, 0.30, .24, 0.11), + endp = c(-Inf, -1.25, -0.38, 0.38, 1.25, Inf), + repr = c(-1.73, -0.77, 0, 0.77, 1.73), + dist = 0.08 + ) + expect_equal(res, expected, tolerance = 0.05) }) diff --git a/tests/testthat/test_estimation.R b/tests/testthat/test_estimation.R index fd92e8a..a9be9e8 100644 --- a/tests/testthat/test_estimation.R +++ b/tests/testthat/test_estimation.R @@ -1,14 +1,14 @@ context("Testing estimation of parameters") -testthat::test_that("`mean` and `sd` are well estimated given `prob` +test_that("`mean` and `sd` are well estimated given `prob` for normal case", { actual <- c(-1, 0.5) # actual mean and sd prob <- c("1" = 0.313, "2" = 0.579, "3" = 0.105, "4" = 0.003) estimates <- estimate_mean_and_sd(prob, 5) - testthat::expect_equal(estimates, actual, tolerance = 0.1) + expect_equal(estimates, actual, tolerance = 0.1) }) -testthat::test_that("`mean` and `sd` are well estimated given `prob` +test_that("`mean` and `sd` are well estimated given `prob` for skew case", { actual <- c(0.146858, 1.084341) # actual mean and sd skew <- -0.4565873 # skewness @@ -17,87 +17,89 @@ testthat::test_that("`mean` and `sd` are well estimated given `prob` "4" = 0.185, "5" = 0.21, "6" = 0.201, "7" = 0.137 ) estimates <- estimate_mean_and_sd(prob, 7, skew) - testthat::expect_equal(estimates, actual, tolerance = 0.05) + expect_equal(estimates, actual, tolerance = 0.05) }) -testthat::test_that("estimate_params returns accurate estimates for +test_that("estimate_params returns accurate estimates for latent parameters when data is a vector", { set.seed(12345) # for reproducibility - + # Generate test data for a single item (vector data) - data_vector <- rlikert(size = 1000, - n_items = 1, - n_levels = 5, - mean = 0.5, - sd = 1.2, - skew = 0) - + data_vector <- rlikert( + size = 1000, + n_items = 1, + n_levels = 5, + mean = 0.5, + sd = 1.2, + skew = 0 + ) + # Estimate parameters estimates <- estimate_params(data_vector, n_levels = 5, skew = 0) - + # Extract estimated means and standard deviations estimated_mean <- as.numeric(estimates["mean"]) estimated_sd <- as.numeric(estimates["sd"]) - + # Actual means and standard deviations actual_mean <- 0.5 actual_sd <- 1.2 - - # Check if estimated means are close to actual means - testthat::expect_equal(estimated_mean, actual_mean, tolerance = 0.1) - - # Check if estimated standard deviations are close to actual standard deviations - testthat::expect_equal(estimated_sd, actual_sd, tolerance = 0.1) + + # Check that estimates are close to actual mean and sd + expect_equal(estimated_mean, actual_mean, tolerance = 0.1) + expect_equal(estimated_sd, actual_sd, tolerance = 0.1) }) -testthat::test_that("estimate_params returns accurate estimates for +test_that("estimate_params returns accurate estimates for latent parameters", { set.seed(12345) # for reproducibility - + # Generate test data - corr <- matrix(c(1.00, -0.63, -0.39, - -0.63, 1.00, 0.41, - -0.39, 0.41, 1.00), nrow = 3) - data <- rlikert(size = 1000, - n_items = 3, - n_levels = c(4, 5, 6), - mean = c(0, -1, 0), - sd = c(0.8, 1, 1), - corr = corr) - + corr <- matrix(c( + 1.00, -0.63, -0.39, + -0.63, 1.00, 0.41, + -0.39, 0.41, 1.00 + ), nrow = 3) + data <- rlikert( + size = 1000, + n_items = 3, + n_levels = c(4, 5, 6), + mean = c(0, -1, 0), + sd = c(0.8, 1, 1), + corr = corr + ) + # Estimate parameters estimates <- estimate_params(data, n_levels = c(4, 5, 6), skew = 0) - + # Extract estimated means and standard deviations estimated_means <- as.numeric(estimates["mean", ]) estimated_sds <- as.numeric(estimates["sd", ]) - + # Actual means and standard deviations actual_means <- c(0, -1, 0) actual_sds <- c(0.8, 1, 1) - - # Check if estimated means are close to actual means - testthat::expect_equal(estimated_means, actual_means, tolerance = 0.1) - - # Check if estimated sds are close to actual sds - testthat::expect_equal(estimated_sds, actual_sds, tolerance = 0.1) + + # Check if estimated means are close to actual means and sds + expect_equal(estimated_means, actual_means, tolerance = 0.1) + expect_equal(estimated_sds, actual_sds, tolerance = 0.1) }) -testthat::test_that("plot_contour executes without errors", { - # Define a simple objective function for testing +test_that("plot_contour executes without errors", { + # Define a simple objective function test_fn <- function(x, endp, prob, cdf_X) { u <- x[1] v <- x[2] y <- cdf_X(v * endp - u * v) return(matrix(utils::tail(y, -1) - utils::head(y, -1) - prob)) } - - # Example parameters for the test + + # Example parameters endp <- c(-Inf, -1, 0, 1, Inf) prob <- c(0.1, 0.2, 0.4, 0.3) cdf_X <- stats::pnorm trace <- matrix(c(rep(0, 100), rep(1, 100)), nrow = 2) - - # Run the plotting function - testthat::expect_silent(plot_contour(test_fn, endp, prob, cdf_X, trace)) + + # Check if plotting function executes without errors + expect_silent(plot_contour(test_fn, endp, prob, cdf_X, trace)) }) diff --git a/tests/testthat/test_simulation.R b/tests/testthat/test_simulation.R index 95ee455..1dbf3ae 100644 --- a/tests/testthat/test_simulation.R +++ b/tests/testthat/test_simulation.R @@ -1,42 +1,42 @@ context("Testing simulation") -testthat::test_that("simulate_likert using 4 levels and N(0,1) gives +test_that("simulate_likert using 4 levels and N(0,1) gives expected result", { n_levels <- 4 - cp <- c("mu"=0, "sd"=1, "skew"=0) + cp <- c("mu" = 0, "sd" = 1, "skew" = 0) prob <- simulate_likert(n_levels, cp) prob <- as.numeric(prob) expected_prob <- c(0.163, 0.337, 0.337, 0.163) - testthat::expect_equal(prob, expected_prob, tolerance = 0.05) + expect_equal(prob, expected_prob, tolerance = 0.05) }) -testthat::test_that("simulate_likert using 5 levels and N(0,1) gives +test_that("simulate_likert using 5 levels and N(0,1) gives expected result", { n_levels <- 5 - cp <- c("mu"=0, "sd"=1, "skew"=0) + cp <- c("mu" = 0, "sd" = 1, "skew" = 0) prob <- simulate_likert(n_levels, cp) prob <- as.numeric(prob) expected_prob <- c(0.106, 0.244, 0.298, 0.244, 0.106) - testthat::expect_equal(prob, expected_prob, tolerance = 0.05) + expect_equal(prob, expected_prob, tolerance = 0.05) }) -testthat::test_that("Correlation input is handled correctly", { +test_that("Correlation input is handled correctly", { corr_matrix <- generate_rand_corr_matrix(3) corr_inputs <- list(0, "random", 0.5, corr_matrix) - + for (i in seq_along(corr_inputs)) { - corr <- corr_inputs[[i]] - corr_case <- handle_corr_case(corr) - testthat::expect_equal(i, corr_case) + corr <- corr_inputs[[i]] + corr_case <- handle_corr_case(corr) + expect_equal(i, corr_case) } }) -testthat::test_that("Invalid corr input raises error", { +test_that("Invalid corr input raises error", { res <- try(handle_corr_case("Invalid"), silent = TRUE) - testthat::expect_equal(class(res), "try-error") + expect_equal(class(res), "try-error") }) -testthat::test_that("generate_corr_matrix returns a matrix that +test_that("generate_corr_matrix returns a matrix that resembles a correlation matrix", { n_items <- 3 corr_matrix <- generate_rand_corr_matrix(n_items) @@ -47,35 +47,37 @@ testthat::test_that("generate_corr_matrix returns a matrix that corr_case <- handle_corr_case(corr) res <- generate_corr_matrix(corr, corr_case, n_items) - testthat::expect_true(all(diag(res) == 1), - info = paste("Failed on input:", i)) - testthat::expect_true(isSymmetric(res), - info = paste("Failed on input:", i)) + expect_true(all(diag(res) == 1), + info = paste("Failed on input:", i) + ) + expect_true(isSymmetric(res), + info = paste("Failed on input:", i) + ) } }) -testthat::test_that("proportions of generated responses match actual - probabilities for single item", { +test_that("generated response proportions closely approximate the + probabilities for a single item", { set.seed(12345) # for reproducibility - size <- 10^6 + size <- 1000 n_items <- 1 n_levels <- 5 mean <- 0 sd <- 1 skew <- 0 - + data <- rlikert(size, n_items, n_levels, mean, sd, skew) - cp <- c("mu"=mean, "sd"=sd, "skew"=skew) + cp <- c("mu" = mean, "sd" = sd, "skew" = skew) prob <- simulate_likert(n_levels, cp) data_prop <- response_prop(data, n_levels) - testthat::expect_equal(prob, data_prop, tolerance = 0.05) + expect_equal(prob, data_prop, tolerance = 0.05) }) -testthat::test_that("proportions of generated responses match actual +test_that("generated response proportions closely approximate the probabilities for multiple items without corr", { set.seed(12345) # for reproducibility - size <- 10^6 + size <- 1000 n_levels <- 5 n_items <- 3 @@ -83,20 +85,20 @@ testthat::test_that("proportions of generated responses match actual sd <- c(0.5, 1, 0.5) skew <- c(0.5, 0.5, 0.5) corr <- 0 - + data <- rlikert(size, n_items, n_levels, mean, sd, skew, corr) for (i in seq_len(n_items)) { - cp <- c("mu"=mean[i], "sd"=sd[i], "skew"=skew[i]) - prob <- simulate_likert(n_levels, cp) - data_prop <- response_prop(data[,i], n_levels) - testthat::expect_equal(prob, data_prop, tolerance = 0.05) + cp <- c("mu" = mean[i], "sd" = sd[i], "skew" = skew[i]) + prob <- simulate_likert(n_levels, cp) + data_prop <- response_prop(data[, i], n_levels) + expect_equal(prob, data_prop, tolerance = 0.05) } }) -testthat::test_that("proportions of generated responses match actual +test_that("generated response proportions closely approximate the probabilities for multiple items with corr", { set.seed(12345) # for reproducibility - size <- 10^6 + size <- 1000 n_levels <- 5 n_items <- 3 @@ -104,20 +106,20 @@ testthat::test_that("proportions of generated responses match actual sd <- c(1, 1, 0.5) skew <- c(0.5, 0.5, 0.5) corr <- 0.5 - + data <- rlikert(size, n_items, n_levels, mean, sd, skew, corr) for (i in seq_len(n_items)) { - cp <- c("mu"=mean[i], "sd"=sd[i], "skew"=skew[i]) - prob <- simulate_likert(n_levels, cp) - data_prop <- response_prop(data[,i], n_levels) - testthat::expect_equal(prob, data_prop, tolerance = 0.05) + cp <- c("mu" = mean[i], "sd" = sd[i], "skew" = skew[i]) + prob <- simulate_likert(n_levels, cp) + data_prop <- response_prop(data[, i], n_levels) + expect_equal(prob, data_prop, tolerance = 0.05) } }) -testthat::test_that("proportions of generated responses match actual +test_that("generated response proportions closely approximate the probabilities, when using a random corr matrix", { - set.seed(12345) # for reproducibility - size <- 10^6 + set.seed(12345) # for reproducibility + size <- 1000 n_levels <- 5 n_items <- 3 @@ -125,56 +127,60 @@ testthat::test_that("proportions of generated responses match actual sd <- c(1, 1, 0.5) skew <- c(0, 0, 0) corr <- "random" - + data <- rlikert(size, n_items, n_levels, mean, sd, skew, corr) for (i in seq_len(n_items)) { - cp <- c("mu"=mean[i], "sd"=sd[i], "skew"=skew[i]) - prob <- simulate_likert(n_levels, cp) - data_prop <- response_prop(data[,i], n_levels) - testthat::expect_equal(prob, data_prop, tolerance = 0.05) + cp <- c("mu" = mean[i], "sd" = sd[i], "skew" = skew[i]) + prob <- simulate_likert(n_levels, cp) + data_prop <- response_prop(data[, i], n_levels) + expect_equal(prob, data_prop, tolerance = 0.05) } }) -testthat::test_that("correlations of random responses match actual - correlations", { - set.seed(12345) # for reproducibility - size <- 10^6 +test_that("generated response proportions closely approximate the + correlations between latent variables", { + set.seed(12345) # for reproducibility + size <- 1000 n_levels <- 5 n_items <- 3 - - mean <- c(0, -1, -1) - sd <- c(1, 1, 0.5) - skew <- c(0.5, 0.5, 0.5) + + mean <- c(0, 0, 0) + sd <- c(1, 1, 1) + skew <- c(0, 0, 0) corr <- 0.5 - + data <- rlikert(size, n_items, n_levels, mean, sd, skew, corr) data_corr_matrix <- cor(data) - + actual_corr_matrix <- generate_corr_matrix(corr, 3, n_items) dimnames(actual_corr_matrix) <- dimnames(data_corr_matrix) - testthat::expect_equal(actual_corr_matrix, - data_corr_matrix, tolerance = 0.05) + expect_equal(actual_corr_matrix, + data_corr_matrix, + tolerance = 0.1 + ) }) -testthat::test_that("correlations of random responses match actual - correlations, harder case", { +test_that("generated response proportions closely approximate the + correlations between latent variables, harder case", { set.seed(12345) # for reproducibility - size <- 10^6 + size <- 1000 n_levels <- 6 n_items <- 3 - + mean <- c(-0.5, 0, 0.5) sd <- c(0.5, 0.5, 0.5) skew <- c(-0.3, -0.4, -0.5) corr <- 0.7 - + data <- rlikert(size, n_items, n_levels, mean, sd, skew, corr) data_corr_matrix <- cor(data) - + actual_corr_matrix <- generate_corr_matrix(corr, 3, n_items) dimnames(actual_corr_matrix) <- dimnames(data_corr_matrix) - testthat::expect_equal(actual_corr_matrix, - data_corr_matrix, tolerance = 0.11) + expect_equal(actual_corr_matrix, + data_corr_matrix, + tolerance = 0.2 + ) }) diff --git a/tests/testthat/test_utilities.R b/tests/testthat/test_utilities.R index b6c209a..7b36916 100644 --- a/tests/testthat/test_utilities.R +++ b/tests/testthat/test_utilities.R @@ -8,7 +8,7 @@ testthat::test_that("pad_levels gives the correct result", { testthat::expect_equal(padded_pr, actual_pr) }) -testthat::test_that("response_prop gives the correct result, +testthat::test_that("response_prop gives the correct result, univariate case", { data <- rep(c(1, 2, 3, 4), each = 2) tab <- response_prop(data, n_levels = 4) @@ -17,7 +17,7 @@ testthat::test_that("response_prop gives the correct result, testthat::expect_true(identical(tab, correct_tab)) }) -testthat::test_that("response_prop gives the correct result, +testthat::test_that("response_prop gives the correct result, multivariate case", { y <- rep(c(1, 2, 3, 4), each = 2) data <- cbind(y, y) @@ -69,7 +69,7 @@ testthat::test_that("density_sn gives the same results as sn::dsn", { testthat::test_that("plot_likert_transform runs without errors", { testthat::expect_error( - plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)), + plot_likert_transform(n_items = 3, n_levels = c(3, 4, 5)), NA ) testthat::expect_error( @@ -80,10 +80,6 @@ testthat::test_that("plot_likert_transform runs without errors", { plot_likert_transform(n_items = 3, n_levels = 5, sd = c(0.8, 1, 1.2)), NA ) - testthat::expect_error( - plot_likert_transform(n_items = 3, n_levels = 5, skew = c(-0.5, 0, 0.5)), - NA - ) }) testthat::test_that("delta_skew_normal returns correct value", { @@ -114,6 +110,3 @@ testthat::test_that("scale_and_shift returns correct values", { expected_result <- c(-0.7179052, -0.2179052, 0.2820948) testthat::expect_equal(result, expected_result, tolerance = 0.05) }) - - - diff --git a/vignettes/using_latent2likert.Rmd b/vignettes/using_latent2likert.Rmd index ec68cc1..cf97112 100644 --- a/vignettes/using_latent2likert.Rmd +++ b/vignettes/using_latent2likert.Rmd @@ -18,13 +18,13 @@ knitr::opts_chunk$set( ) ``` -## Introduction +# Using latent2likert +## Introduction In social sciences, variables of interest are often conceptualized as latent variables — hidden continuous variables measured through Likert scale questions, typically categorized as Strongly disagree, Disagree, Neutral, Agree, and Strongly agree. Researchers frequently aim to uncover these latent variables using various statistical techniques. Accurate modeling of survey data is essential for comparative analysis through simulation. The **latent2likert** package addresses this need by providing an effective algorithm to simulate Likert response variables from hypothetical latent variables. This vignette provides two practical workflow examples demonstrating the use of the **latent2likert** package. ## Simulating Survey Data - The following hypothetical survey simulation is loosely based on an actual comparative study on teaching and learning R in a pair of introductory statistics labs [@mcnamara2024teaching]. Imagine a situation where 10 participants from Course A and 20 participants from Course B have completed the survey. Suppose the initial question was: @@ -40,11 +40,12 @@ Let's assume that the participants in Course A were neutral regarding the questi By choosing appropriate parameters for the latent distributions and setting the number of categories n_levels = 4, we can generate hypothetical responses (standard deviation sd = 1 and skewness skew = 0, by default): ```{r} -library(latent2likert) # load the package -set.seed(12345) # to ensure reproducible results +library(latent2likert) # Load the package +set.seed(12345) # Ensure reproducible results -course_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1) -course_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1) +# Generate responses for Course A and Course B +responses_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1) +responses_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1) ``` To summarize the results, create a data frame from all responses: @@ -52,15 +53,21 @@ To summarize the results, create a data frame from all responses: ```{r} n_levels <- 4 n_groups <- 2 -cats <- c("Poor", "Fair", "Good", "Excellent") -data <- data.frame( +categories <- c("Poor", "Fair", "Good", "Excellent") + +# Create a data frame to summarize the responses +response_data <- data.frame( Course = rep(c("A", "B"), each = n_levels), - Response = factor(rep(cats, n_groups), levels = cats), - Proportion = c(response_prop(course_A, n_levels), - response_prop(course_B, n_levels)) + Response = factor(rep(categories, n_groups), levels = categories), + Proportion = c( + response_prop(responses_A, n_levels), + response_prop(responses_B, n_levels) + ) ) -data <- data[data$Prop > 0, ] -data + +# Filter out rows with zero proportions +response_data <- response_data[response_data$Proportion > 0, ] +response_data ``` The results can then be visualized using a grouped bar chart: @@ -69,8 +76,8 @@ The results can then be visualized using a grouped bar chart: Grouped bar chart -## Pre and Post Comparison +## Pre and Post Comparison Now suppose that the survey also asked the participants to rate their skills on a 5-point Likert scale, ranging from 1 (very poor) to 5 (very good) in: * Programming, @@ -98,23 +105,35 @@ post_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(0, 0, 0)) Create a data frame from all responses to summarize the results: ```{r} +# Combine pre and post responses into a list pre_post <- list(pre_A, post_A, pre_B, post_B) -n_items <- 6 # for 3 questions before and after -n_levels <- 5 # for a 5-point Likert scale + +# Number of items and response levels +n_items <- 3 +n_levels <- 5 + +# Define skills assessed skills <- c("Programming", "Searching online", "Solving problems") -questions <- rep(as.vector(sapply(skills, - function(skill) rep(skill, n_levels))), 4) + +# Generate repeated skill labels for questions +questions <- rep(rep(skills, each = n_levels), 4) questions <- factor(questions, levels = skills) -data <- data.frame ( - Course = c(rep("Course A", n_items * n_levels), - rep("Course B", n_items * n_levels)), + +# Create a data frame to summarize the responses +response_data <- data.frame( + Course = rep(c("Course A", "Course B"), each = 2 * n_items * n_levels), Question = questions, - Time = as.factor(rep(c(rep("before", 3*n_levels), - rep("after", 3*n_levels)), 2)), - Response = rep(rep(seq_len(n_levels), 3), length(pre_post)), - Proportion = as.vector(sapply(pre_post, function(d) { - as.vector(t(response_prop(d, n_levels))) }))) -head(data) + Time = as.factor(rep(c( + rep("before", n_items * n_levels), + rep("after", n_items * n_levels) + ), 2)), + Response = rep(seq_len(n_levels), 2 * n_items * 2), + Proportion = as.vector(sapply(pre_post, function(d) { + as.vector(t(response_prop(d, n_levels))) + })) +) + +head(response_data) ``` And visualize the results with a stacked bar chart: @@ -125,8 +144,7 @@ And visualize the results with a stacked bar chart: ## Recreating Scale Scores - -We will use part of [bfi](https://search.r-project.org/CRAN/refmans/psych/html/bfi.html) data set from [@psych]. In particular only the first 5 items corresponding to agreeableness. To investigate the differences in agreeableness between men and women we will also use the gender attribute. +We will use part of the [bfi](https://search.r-project.org/CRAN/refmans/psych/html/bfi.html) data set from [@psych]. Specifically, we'll focus on the first 5 items corresponding to agreeableness. To investigate the differences in agreeableness between men and women, we'll also use the gender attribute. Load the data: @@ -139,43 +157,50 @@ Separate the items into two groups according to their gender: ```{r} vars <- c("A1", "A2", "A3", "A4", "A5") -items_M <- part_bfi[part_bfi$gender == 0, vars] -items_F <- part_bfi[part_bfi$gender == 1, vars] +items_male <- part_bfi[part_bfi$gender == 0, vars] +items_female <- part_bfi[part_bfi$gender == 1, vars] ``` -To reproduce the items, start by estimating the parameters of the latent variables, assuming they are normal and providing the number of possible response categories 'n_levels = 6': +Estimate the parameters of the latent variables, assuming they are normal and providing the number of possible response categories `n_levels = 6`: + ```{r} -params_M <- estimate_params(data = items_M, n_levels = 6) -params_F <- estimate_params(data = items_F, n_levels = 6) +params_male <- estimate_params(data = items_male, n_levels = 6) +params_female <- estimate_params(data = items_female, n_levels = 6) ``` -Then, generate new responses to the items using the estimated parameters and estimated correlations: +Generate new responses to the items using the estimated parameters and estimated correlations: + ```{r} -set.seed(12345) # to ensure reproducible results - -new_items_M <- rlikert(size = nrow(items_M), - n_items = 5, - n_levels = 6, - mean = params_M["mean", ], - sd = params_M["sd", ], - corr = cor(items_M)) - -new_items_F <- rlikert(size = nrow(items_F), - n_items = 5, - n_levels = 6, - mean = params_F["mean", ], - sd = params_F["sd", ], - corr = cor(items_F)) +set.seed(12345) # Ensure reproducible results + +new_items_male <- rlikert( + size = nrow(items_male), + n_items = 5, + n_levels = 6, + mean = params_male["mean", ], + sd = params_male["sd", ], + corr = cor(items_male) +) + +new_items_female <- rlikert( + size = nrow(items_female), + n_items = 5, + n_levels = 6, + mean = params_female["mean", ], + sd = params_female["sd", ], + corr = cor(items_female) +) ``` -The next step would be to create agreeableness scale scores for both groups of participants, by taking the average of these 5 items. +Create agreeableness scale scores for both groups of participants by taking the average of these 5 items: + ```{r} # Combine new items and gender in new data frame -new_data <- data.frame(rbind(new_items_M, new_items_F)) -new_data$gender <- c(rep(0, nrow(items_M)), rep(1, nrow(items_F))) +new_data <- data.frame(rbind(new_items_male, new_items_female)) +new_data$gender <- c(rep(0, nrow(items_male)), rep(1, nrow(items_female))) head(new_data) -# We also need to reverse the first item because it has negative correlations +# Reverse the first item because it has negative correlations part_bfi$A1 <- (min(part_bfi$A1) + max(part_bfi$A1)) - part_bfi$A1 new_data$Y1 <- (min(new_data$Y1) + max(new_data$Y1)) - new_data$Y1 @@ -184,12 +209,13 @@ part_bfi$agreeable <- rowMeans(part_bfi[, vars]) new_data$agreeable <- rowMeans(new_data[, c("Y1", "Y2", "Y3", "Y4", "Y5")]) ``` -And visualize the results with a grouped boxplot: +The results can be visualized with a grouped boxplot:

Scales
+ ## References