From 4683b4050185920278bfc462c51a369521253aa8 Mon Sep 17 00:00:00 2001 From: Nicholas Clark Date: Mon, 15 Jan 2024 09:11:10 +1000 Subject: [PATCH] fix cmdchecks; add links to seminar --- NAMESPACE | 3 + R/families.R | 4 +- R/globals.R | 2 +- README.Rmd | 2 + README.md | 83 ++--- docs/articles/mvgam_overview.html | 311 +++++++++--------- .../Histogram of NDVI effects-1.png | Bin 18995 -> 18717 bytes .../figure-html/Plot NDVI effect-1.png | Bin 124704 -> 125813 bytes ...ted temporal functions using newdata-1.png | Bin 102475 -> 102912 bytes ...dcasts on the linear predictor scale-1.png | Bin 67943 -> 68201 bytes .../Plot posterior hindcasts-1.png | Bin 174897 -> 174197 bytes .../Plot posterior residuals-1.png | Bin 486969 -> 483974 bytes .../Plot random effect estimates-1.png | Bin 47477 -> 47604 bytes .../Plot smooth term derivatives-1.png | Bin 221749 -> 221197 bytes ...otting predictions against test data-1.png | Bin 158102 -> 162475 bytes .../figure-html/unnamed-chunk-13-1.png | Bin 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insertions(+), 204 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 9cc52ceb..8c08ea78 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -186,6 +186,7 @@ importFrom(stats,cor) importFrom(stats,cov) importFrom(stats,cov2cor) importFrom(stats,dbeta) +importFrom(stats,dbinom) importFrom(stats,density) importFrom(stats,dgamma) importFrom(stats,dlnorm) @@ -208,6 +209,7 @@ importFrom(stats,na.fail) importFrom(stats,na.pass) importFrom(stats,pacf) importFrom(stats,pbeta) +importFrom(stats,pbinom) importFrom(stats,pgamma) importFrom(stats,plnorm) importFrom(stats,plogis) @@ -216,6 +218,7 @@ importFrom(stats,poisson) importFrom(stats,ppois) importFrom(stats,predict) importFrom(stats,printCoefmat) +importFrom(stats,qbinom) importFrom(stats,qcauchy) importFrom(stats,qnorm) importFrom(stats,qqline) diff --git a/R/families.R b/R/families.R index 73904953..7711267d 100644 --- a/R/families.R +++ b/R/families.R @@ -1,5 +1,7 @@ #' Supported mvgam families -#' @importFrom stats make.link dgamma pgamma rgamma qnorm plnorm runif pbeta dlnorm dpois pnorm ppois plogis gaussian poisson Gamma dnbinom rnbinom dnorm dbeta +#' @importFrom stats make.link dgamma pgamma rgamma qnorm plnorm runif pbeta dlnorm dpois +#' @importFrom stats pnorm ppois plogis gaussian poisson Gamma dnbinom rnbinom dnorm dbeta +#' @importFrom stats rbinom pbinom dbinom qbinom qlogis #' @importFrom brms lognormal student rstudent_t qstudent_t dstudent_t pstudent_t #' @param link a specification for the family link function. At present these cannot #' be changed diff --git a/R/globals.R b/R/globals.R index 89eb33e6..0bb42e71 100644 --- a/R/globals.R +++ b/R/globals.R @@ -10,4 +10,4 @@ utils::globalVariables(c("y", "year", "smooth_vals", "smooth_num", "term", "data_test", "object", "row_num", "trends_test", "trend", "trend_series", "trend_y", ".", "gam", "group", "mod", "row_id", "byvar", "direction", - "index..time..index")) + "index..time..index", "trend_test")) diff --git a/README.Rmd b/README.Rmd index e37f6827..df593d54 100644 --- a/README.Rmd +++ b/README.Rmd @@ -26,6 +26,7 @@ The goal of `mvgam` is to fit Bayesian Dynamic Generalized Additive Models to ti ## Resources A series of [vignettes cover data formatting, forecasting and several extended case studies of DGAMs](https://nicholasjclark.github.io/mvgam/){target="_blank"}. A number of other examples have also been compiled: +* [Ecological Forecasting with Dynamic Generalized Additive Models](https://www.youtube.com/watch?v=0zZopLlomsQ){target="_blank"} * [mvgam case study 1: model comparison and data assimilation](https://rpubs.com/NickClark47/mvgam){target="_blank"} * [mvgam case study 2: multivariate models](https://rpubs.com/NickClark47/mvgam2){target="_blank"} * [mvgam case study 3: distributed lag models](https://rpubs.com/NickClark47/mvgam3){target="_blank"} @@ -212,6 +213,7 @@ plot(lynx_mvgam, type = 'residuals') * `poisson()` for count data * `nb()` for overdispersed count data * `tweedie()` for overdispersed count data +* `nmix()` for count data with imperfect detection Note that only `poisson()`, `nb()`, and `tweedie()` are available if using `JAGS`. All families, apart from `tweedie()`, are supported if using `Stan`. See `??mvgam_families` for more information. Below is a simple example for simulating and modelling proportional data with `Beta` observations over a set of seasonal series with independent Gaussian Process dynamic trends: ```{r beta_sim, message=FALSE, warning=FALSE, fig.width=6.5, fig.height=6.5, dpi=160} diff --git a/README.md b/README.md index 6230bd4d..19c7be45 100644 --- a/README.md +++ b/README.md @@ -24,6 +24,9 @@ target="_blank">vignettes cover data formatting, forecasting and several extended case studies of DGAMs. A number of other examples have also been compiled: +- Ecological Forecasting with Dynamic Generalized Additive + Models - mvgam case study 1: model comparison and data assimilation - mvgam @@ -314,29 +317,29 @@ summary(lynx_mvgam) #> #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) 5.900 6.600 7.00 1.01 302 -#> s(season).1 -0.610 0.035 0.69 1.00 910 -#> s(season).2 -0.180 0.840 1.90 1.00 341 -#> s(season).3 -0.031 1.300 2.50 1.00 313 -#> s(season).4 -0.470 0.420 1.40 1.00 901 -#> s(season).5 -1.300 -0.180 0.91 1.00 385 -#> s(season).6 -1.100 -0.057 1.10 1.00 534 -#> s(season).7 -0.700 0.390 1.40 1.00 631 -#> s(season).8 -0.970 0.340 1.90 1.00 282 -#> s(season).9 -1.100 -0.230 0.75 1.00 392 -#> s(season).10 -1.300 -0.680 -0.01 1.01 548 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) 6.10 6.600 7.000 1.00 355 +#> s(season).1 -0.59 0.046 0.710 1.00 1022 +#> s(season).2 -0.26 0.770 1.800 1.00 443 +#> s(season).3 -0.12 1.100 2.400 1.00 399 +#> s(season).4 -0.51 0.410 1.300 1.00 890 +#> s(season).5 -1.20 -0.130 0.950 1.01 503 +#> s(season).6 -1.00 -0.011 1.100 1.01 699 +#> s(season).7 -0.71 0.340 1.400 1.00 711 +#> s(season).8 -0.92 0.180 1.800 1.00 371 +#> s(season).9 -1.10 -0.290 0.710 1.00 476 +#> s(season).10 -1.30 -0.660 0.027 1.00 595 #> #> Approximate significance of GAM observation smooths: #> edf Chi.sq p-value -#> s(season) 4.43 19440 0.24 +#> s(season) 5.08 17751 0.25 #> #> Latent trend AR parameter estimates: #> 2.5% 50% 97.5% Rhat n_eff -#> ar1[1] 0.71 1.10 1.400 1 594 -#> ar2[1] -0.81 -0.38 0.074 1 1367 -#> ar3[1] -0.47 -0.11 0.340 1 401 -#> sigma[1] 0.40 0.50 0.640 1 1125 +#> ar1[1] 0.74 1.10 1.400 1 635 +#> ar2[1] -0.84 -0.40 0.062 1 1514 +#> ar3[1] -0.47 -0.13 0.290 1 540 +#> sigma[1] 0.40 0.50 0.640 1 1154 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters @@ -345,7 +348,7 @@ summary(lynx_mvgam) #> 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Wed Dec 06 5:18:32 PM 2023. +#> Samples were drawn using NUTS(diag_e) at Mon Jan 15 8:57:57 AM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) @@ -450,6 +453,7 @@ plotted on the outcome scale, for example: ``` r require(ggplot2) #> Loading required package: ggplot2 +#> Warning: package 'ggplot2' was built under R version 4.3.2 plot_predictions(lynx_mvgam, condition = 'season', points = 0.5) + theme_classic() ``` @@ -466,7 +470,7 @@ plot(lynx_mvgam, type = 'forecast', newdata = lynx_test) #> Out of sample CRPS: - #> [1] 2832.494 + #> [1] 2892.767 And the estimated latent trend component, again using the more flexible `plot_mvgam_...()` option to show first derivatives of the estimated @@ -524,6 +528,7 @@ families. Currently, the package can handle data for the following: - `poisson()` for count data - `nb()` for overdispersed count data - `tweedie()` for overdispersed count data +- `nmix()` for count data with imperfect detection Note that only `poisson()`, `nb()`, and `tweedie()` are available if using `JAGS`. All families, apart from `tweedie()`, are supported if @@ -587,41 +592,41 @@ summary(mod, include_betas = FALSE) #> #> Observation precision parameter estimates: #> 2.5% 50% 97.5% Rhat n_eff -#> phi[1] 5.5 8.3 12 1 1641 -#> phi[2] 5.6 8.6 13 1 1725 -#> phi[3] 5.8 8.5 12 1 2063 +#> phi[1] 5.4 8.3 12 1 1692 +#> phi[2] 5.6 8.7 13 1 1512 +#> phi[3] 5.6 8.4 12 1 1786 #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) -0.24 0.18 0.45 1 799 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) -0.15 0.2 0.46 1.01 891 #> #> Approximate significance of GAM observation smooths: #> edf Chi.sq p-value -#> s(season) 5.00 16.30 1.1e-05 *** -#> s(season):seriesseries_1 3.83 0.12 0.97 -#> s(season):seriesseries_2 3.72 0.08 0.99 -#> s(season):seriesseries_3 3.78 0.83 0.57 +#> s(season) 5.00 15.00 1.2e-05 *** +#> s(season):seriesseries_1 3.82 0.12 0.98 +#> s(season):seriesseries_2 3.94 0.09 0.98 +#> s(season):seriesseries_3 3.99 0.74 0.51 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Latent trend marginal deviation (alpha) and length scale (rho) estimates: #> 2.5% 50% 97.5% Rhat n_eff -#> alpha_gp[1] 0.046 0.42 0.95 1 573 -#> alpha_gp[2] 0.350 0.71 1.30 1 1098 -#> alpha_gp[3] 0.180 0.48 0.97 1 1077 -#> rho_gp[1] 1.200 3.90 13.00 1 1487 -#> rho_gp[2] 1.700 7.30 34.00 1 399 -#> rho_gp[3] 1.400 4.90 20.00 1 834 +#> alpha_gp[1] 0.095 0.42 0.94 1.00 793 +#> alpha_gp[2] 0.370 0.73 1.30 1.00 901 +#> alpha_gp[3] 0.150 0.46 0.94 1.00 899 +#> rho_gp[1] 1.200 3.80 13.00 1.01 451 +#> rho_gp[2] 1.800 7.50 33.00 1.03 254 +#> rho_gp[3] 1.200 4.60 19.00 1.00 1281 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters #> Rhat looks reasonable for all parameters -#> 4 of 2000 iterations ended with a divergence (0.2%) +#> 3 of 2000 iterations ended with a divergence (0.15%) #> *Try running with larger adapt_delta to remove the divergences #> 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Wed Dec 06 5:19:47 PM 2023. +#> Samples were drawn using NUTS(diag_e) at Mon Jan 15 8:59:01 AM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) @@ -637,11 +642,11 @@ for(i in 1:3){ ``` #> Out of sample CRPS: - #> [1] 2.09906 + #> [1] 2.079879 #> Out of sample CRPS: - #> [1] 1.843141 + #> [1] 1.843941 #> Out of sample CRPS: - #> [1] 1.754107 + #> [1] 1.728574 diff --git a/docs/articles/mvgam_overview.html b/docs/articles/mvgam_overview.html index c131ab7f..71b41a49 100644 --- a/docs/articles/mvgam_overview.html +++ b/docs/articles/mvgam_overview.html @@ -77,7 +77,7 @@

Nicholas J Clark

-

2024-01-12

+

2024-01-15

Source:
vignettes/mvgam_overview.Rmd
mvgam_overview.Rmd
@@ -93,7 +93,9 @@

Dynamic GAMs\(\tilde{\boldsymbol{y}}_{i,t}\) is the +independently of the observation process. An introduction to the package +and some worked examples are also shown in this seminar: Ecological Forecasting with Dynamic Generalized Additive +Models. Briefly, assume \(\tilde{\boldsymbol{y}}_{i,t}\) is the conditional expectation of response variable \(\boldsymbol{i}\) at time \(\boldsymbol{t}\). Assuming \(\boldsymbol{y_i}\) is drawn from an exponential distribution with an invertible link function, the linear predictor for a multivariate Dynamic GAM can be written as:

@@ -443,17 +445,17 @@

Manipulating data for modellingdata <- sim_mvgam(n_series = 4, T = 24) head(data$data_train, 12)
##    y season year   series time
-## 1  2      1    1 series_1    1
-## 2  0      1    1 series_2    1
-## 3  1      1    1 series_3    1
-## 4  0      1    1 series_4    1
-## 5  5      2    1 series_1    2
-## 6  4      2    1 series_2    2
-## 7  7      2    1 series_3    2
-## 8  0      2    1 series_4    2
-## 9  0      3    1 series_1    3
-## 10 1      3    1 series_2    3
-## 11 4      3    1 series_3    3
+## 1  1      1    1 series_1    1
+## 2  7      1    1 series_2    1
+## 3  8      1    1 series_3    1
+## 4  1      1    1 series_4    1
+## 5  2      2    1 series_1    2
+## 6  5      2    1 series_2    2
+## 7  1      2    1 series_3    2
+## 8  2      2    1 series_4    2
+## 9  1      3    1 series_1    3
+## 10 0      3    1 series_2    3
+## 11 1      3    1 series_3    3
 ## 12 0      3    1 series_4    3

Notice how we have four different time series in these simulated data, but we do not spread the outcome values into different columns. @@ -647,8 +649,8 @@

GLMs with temporal random effects## 1 vector[1] mu_raw; 1 s(year_fac) pop mean ## 2 vector<lower=0>[1] sigma_raw; 1 s(year_fac) pop sd ## prior example_change -## 1 mu_raw ~ std_normal(); mu_raw ~ normal(0.9, 0.59); -## 2 sigma_raw ~ student_t(3, 0, 2.5); sigma_raw ~ exponential(0.61); +## 1 mu_raw ~ std_normal(); mu_raw ~ normal(-0.6, 0.26); +## 2 sigma_raw ~ student_t(3, 0, 2.5); sigma_raw ~ exponential(0.52); ## new_lowerbound new_upperbound ## 1 NA NA ## 2 NA NA @@ -684,33 +686,33 @@

GLMs with temporal random effects## ## ## GAM coefficient (beta) estimates: -## 2.5% 50% 97.5% Rhat n_eff -## s(year_fac).1 1.80 2.1 2.3 1 2467 -## s(year_fac).2 2.50 2.7 2.8 1 2762 -## s(year_fac).3 3.00 3.1 3.2 1 3040 -## s(year_fac).4 3.10 3.3 3.4 1 3381 -## s(year_fac).5 1.90 2.1 2.3 1 3455 -## s(year_fac).6 1.50 1.7 2.0 1 3422 -## s(year_fac).7 1.80 2.0 2.3 1 3417 -## s(year_fac).8 2.80 3.0 3.1 1 3207 -## s(year_fac).9 3.10 3.3 3.4 1 3011 -## s(year_fac).10 2.60 2.8 2.9 1 2673 -## s(year_fac).11 2.90 3.1 3.2 1 3767 -## s(year_fac).12 3.10 3.2 3.3 1 2400 -## s(year_fac).13 2.00 2.3 2.5 1 2857 -## s(year_fac).14 2.50 2.6 2.8 1 2272 -## s(year_fac).15 1.90 2.2 2.4 1 2637 -## s(year_fac).16 1.90 2.1 2.3 1 2868 -## s(year_fac).17 -0.31 1.1 1.9 1 583 +## 2.5% 50% 97.5% Rhat n_eff +## s(year_fac).1 1.8 2.1 2.3 1.00 2439 +## s(year_fac).2 2.5 2.7 2.8 1.00 3112 +## s(year_fac).3 3.0 3.1 3.2 1.00 3182 +## s(year_fac).4 3.1 3.3 3.4 1.00 2476 +## s(year_fac).5 1.9 2.1 2.3 1.00 2944 +## s(year_fac).6 1.5 1.8 2.0 1.00 3386 +## s(year_fac).7 1.8 2.0 2.3 1.00 2740 +## s(year_fac).8 2.8 3.0 3.1 1.00 2897 +## s(year_fac).9 3.1 3.2 3.4 1.00 2916 +## s(year_fac).10 2.6 2.8 2.9 1.00 2911 +## s(year_fac).11 2.9 3.1 3.2 1.00 2772 +## s(year_fac).12 3.1 3.2 3.3 1.00 3060 +## s(year_fac).13 2.0 2.2 2.5 1.00 2228 +## s(year_fac).14 2.5 2.6 2.8 1.00 3100 +## s(year_fac).15 1.9 2.2 2.4 1.00 2161 +## s(year_fac).16 1.9 2.1 2.3 1.00 3331 +## s(year_fac).17 -0.3 1.1 1.9 1.01 532 ## ## GAM group-level estimates: ## 2.5% 50% 97.5% Rhat n_eff -## mean(s(year_fac)) 2.00 2.40 2.7 1.02 229 -## sd(s(year_fac)) 0.46 0.68 1.0 1.01 302 +## mean(s(year_fac)) 2.10 2.40 2.8 1.03 198 +## sd(s(year_fac)) 0.45 0.66 1.1 1.01 238 ## ## Approximate significance of GAM observation smooths: ## edf Chi.sq p-value -## s(year_fac) 13.4 23802 <2e-16 *** +## s(year_fac) 13.2 24457 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## @@ -721,7 +723,7 @@

GLMs with temporal random effects## 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) ## E-FMI indicated no pathological behavior ## -## Samples were drawn using NUTS(diag_e) at Fri Jan 12 3:51:59 PM 2024. +## Samples were drawn using NUTS(diag_e) at Mon Jan 15 9:06:57 AM 2024. ## For each parameter, n_eff is a crude measure of effective sample size, ## and Rhat is the potential scale reduction factor on split MCMC chains ## (at convergence, Rhat = 1) @@ -738,23 +740,23 @@

GLMs with temporal random effectsdplyr::glimpse(beta_post)
## Rows: 2,000
 ## Columns: 17
-## $ `s(year_fac).1`  <dbl> 2.06435, 2.18026, 2.10259, 2.15858, 2.08945, 2.03449,…
-## $ `s(year_fac).2`  <dbl> 2.66297, 2.76049, 2.58599, 2.84501, 2.65126, 2.77843,…
-## $ `s(year_fac).3`  <dbl> 2.99574, 3.07175, 3.07301, 3.05926, 3.09694, 2.96840,…
-## $ `s(year_fac).4`  <dbl> 3.24798, 3.28896, 3.30628, 3.25715, 3.22578, 3.27270,…
-## $ `s(year_fac).5`  <dbl> 2.13139, 2.07544, 1.97331, 2.08521, 2.29660, 2.08273,…
-## $ `s(year_fac).6`  <dbl> 1.42739, 2.02722, 1.71548, 1.92531, 1.73130, 1.49182,…
-## $ `s(year_fac).7`  <dbl> 1.93186, 2.21940, 2.11423, 2.18194, 2.03794, 2.12441,…
-## $ `s(year_fac).8`  <dbl> 2.94445, 3.01923, 3.01388, 2.95011, 3.01846, 2.93042,…
-## $ `s(year_fac).9`  <dbl> 3.19531, 3.27323, 3.38481, 3.30585, 3.13491, 3.18199,…
-## $ `s(year_fac).10` <dbl> 2.74548, 2.88965, 2.78905, 2.90565, 2.72434, 2.75425,…
-## $ `s(year_fac).11` <dbl> 3.01341, 3.09803, 3.14241, 3.10061, 3.05058, 3.02510,…
-## $ `s(year_fac).12` <dbl> 3.13730, 3.30920, 3.24322, 3.20736, 3.18905, 3.23454,…
-## $ `s(year_fac).13` <dbl> 2.18607, 2.26127, 2.15356, 2.14097, 2.43450, 2.22882,…
-## $ `s(year_fac).14` <dbl> 2.38431, 2.50610, 2.49737, 2.66538, 2.47568, 2.75505,…
-## $ `s(year_fac).15` <dbl> 2.22367, 2.34576, 2.24644, 2.22469, 2.27891, 2.17492,…
-## $ `s(year_fac).16` <dbl> 2.27256, 2.11722, 1.97474, 2.07540, 2.08201, 1.86904,…
-## $ `s(year_fac).17` <dbl> 1.189810, 1.151540, 0.804486, 1.526610, 0.851250, 1.1…
+## $ `s(year_fac).1` <dbl> 2.30080, 2.19798, 2.04816, 2.01919, 2.19020, 1.91288,… +## $ `s(year_fac).2` <dbl> 2.72378, 2.69498, 2.64144, 2.73021, 2.80479, 2.63429,… +## $ `s(year_fac).3` <dbl> 3.04055, 2.94148, 3.27943, 3.05446, 3.13977, 3.14182,… +## $ `s(year_fac).4` <dbl> 3.31494, 3.28852, 3.19607, 3.15786, 3.12430, 3.15365,… +## $ `s(year_fac).5` <dbl> 2.24893, 2.16990, 1.99415, 2.11878, 2.20520, 2.09616,… +## $ `s(year_fac).6` <dbl> 1.69947, 1.60053, 1.92989, 1.49806, 1.58634, 1.98859,… +## $ `s(year_fac).7` <dbl> 2.05134, 2.03602, 2.13280, 2.11045, 2.26266, 1.83901,… +## $ `s(year_fac).8` <dbl> 2.99787, 2.97008, 2.99874, 2.91971, 2.91366, 3.02957,… +## $ `s(year_fac).9` <dbl> 3.33622, 3.20377, 3.32396, 3.24947, 3.20354, 3.23998,… +## $ `s(year_fac).10` <dbl> 2.82800, 2.76225, 2.76828, 2.72482, 2.75613, 2.79170,… +## $ `s(year_fac).11` <dbl> 3.10896, 3.01869, 3.16489, 2.99758, 3.12221, 3.17723,… +## $ `s(year_fac).12` <dbl> 3.21659, 3.04013, 3.37160, 3.30859, 3.26822, 3.30016,… +## $ `s(year_fac).13` <dbl> 2.36270, 2.33583, 2.26894, 2.07640, 2.18187, 2.36848,… +## $ `s(year_fac).14` <dbl> 2.69838, 2.64463, 2.66172, 2.59959, 2.59452, 2.64214,… +## $ `s(year_fac).15` <dbl> 2.25933, 2.25514, 2.07515, 2.15506, 2.17237, 2.20526,… +## $ `s(year_fac).16` <dbl> 2.09584, 2.10991, 1.83435, 2.20681, 2.26212, 1.92478,… +## $ `s(year_fac).17` <dbl> 0.4150130, 0.4578770, 0.2064460, 0.9136730, 1.0479400…

With any model fitted in mvgam, the underlying Stan code can be viewed using the code function:

@@ -875,7 +877,7 @@

## $ test_observations : NULL ## $ test_times : NULL ## $ hindcasts :List of 1 -## ..$ PP: num [1:2000, 1:199] 5 3 14 7 9 6 7 9 7 11 ... +## ..$ PP: num [1:2000, 1:199] 6 9 9 5 4 8 8 5 6 9 ... ## .. ..- attr(*, "dimnames")=List of 2 ## .. .. ..$ : NULL ## .. .. ..$ : chr [1:199] "ypred[1,1]" "ypred[2,1]" "ypred[3,1]" "ypred[4,1]" ... @@ -888,7 +890,7 @@

 hc <- hindcast(model1, type = 'link')
 range(hc$hindcasts$PP)
-
## [1] -2.24966  3.46014
+
## [1] -1.65123  3.47762

Objects of class mvgam_forecast have an associated plot function as well:

@@ -940,14 +942,14 @@ 

Automatic forecasting for new dataplot(model1b, type = 'forecast')

## Out of sample DRPS:
-## [1] 180.2378
+## [1] 182.1551

We can also view the test data in the forecast plot to see that the predictions do not capture the temporal variation in the test set

 plot(model1b, type = 'forecast', newdata = data_test)

## Out of sample DRPS:
-## [1] 180.2378
+## [1] 182.1551

As with the hindcast function, we can use the forecast function to automatically extract the posterior distributions for these predictions. This also returns an object of @@ -975,12 +977,12 @@

Automatic forecasting for new data## ..$ PP: int [1:39] NA 0 0 10 3 14 18 NA 28 46 ... ## $ test_times : num [1:39] 161 162 163 164 165 166 167 168 169 170 ... ## $ hindcasts :List of 1 -## ..$ PP: num [1:2000, 1:160] 10 7 11 7 8 11 5 9 7 11 ... +## ..$ PP: num [1:2000, 1:160] 11 10 4 6 7 3 12 5 4 8 ... ## .. ..- attr(*, "dimnames")=List of 2 ## .. .. ..$ : NULL ## .. .. ..$ : chr [1:160] "ypred[1,1]" "ypred[2,1]" "ypred[3,1]" "ypred[4,1]" ... ## $ forecasts :List of 1 -## ..$ PP: num [1:2000, 1:39] 9 8 6 14 12 11 11 9 6 10 ... +## ..$ PP: num [1:2000, 1:39] 9 9 16 3 9 8 11 20 9 10 ... ## .. ..- attr(*, "dimnames")=List of 2 ## .. .. ..$ : NULL ## .. .. ..$ : chr [1:39] "ypred[161,1]" "ypred[162,1]" "ypred[163,1]" "ypred[164,1]" ... @@ -1037,33 +1039,33 @@

Adding predictors as “fixed” eff ## ## GAM coefficient (beta) estimates: ## 2.5% 50% 97.5% Rhat n_eff -## ndvi 0.32 0.39 0.46 1 1941 -## s(year_fac).1 1.10 1.40 1.70 1 2704 -## s(year_fac).2 1.80 2.00 2.20 1 2165 -## s(year_fac).3 2.20 2.40 2.60 1 2034 -## s(year_fac).4 2.30 2.50 2.70 1 2187 -## s(year_fac).5 1.20 1.40 1.60 1 2687 -## s(year_fac).6 1.00 1.30 1.50 1 2437 -## s(year_fac).7 1.10 1.40 1.70 1 3079 -## s(year_fac).8 2.10 2.30 2.50 1 2295 -## s(year_fac).9 2.70 2.90 3.00 1 2301 -## s(year_fac).10 2.00 2.20 2.40 1 2581 -## s(year_fac).11 2.30 2.40 2.60 1 2190 -## s(year_fac).12 2.50 2.70 2.80 1 2097 -## s(year_fac).13 1.40 1.60 1.80 1 3245 -## s(year_fac).14 0.56 2.00 3.40 1 1688 -## s(year_fac).15 0.73 2.00 3.40 1 1698 -## s(year_fac).16 0.52 2.00 3.20 1 1581 -## s(year_fac).17 0.66 2.00 3.30 1 1633 +## ndvi 0.32 0.39 0.46 1 1786 +## s(year_fac).1 1.10 1.40 1.70 1 2685 +## s(year_fac).2 1.80 2.00 2.20 1 2607 +## s(year_fac).3 2.20 2.40 2.60 1 2057 +## s(year_fac).4 2.30 2.50 2.70 1 2129 +## s(year_fac).5 1.20 1.40 1.60 1 2567 +## s(year_fac).6 1.00 1.30 1.50 1 2267 +## s(year_fac).7 1.10 1.40 1.70 1 2636 +## s(year_fac).8 2.10 2.30 2.50 1 2082 +## s(year_fac).9 2.70 2.90 3.00 1 2173 +## s(year_fac).10 2.00 2.20 2.40 1 2669 +## s(year_fac).11 2.30 2.40 2.60 1 2050 +## s(year_fac).12 2.60 2.70 2.80 1 2114 +## s(year_fac).13 1.40 1.60 1.80 1 2484 +## s(year_fac).14 0.68 2.00 3.30 1 1519 +## s(year_fac).15 0.76 2.00 3.40 1 1648 +## s(year_fac).16 0.64 2.00 3.20 1 1658 +## s(year_fac).17 0.61 2.00 3.30 1 1370 ## ## GAM group-level estimates: -## 2.5% 50% 97.5% Rhat n_eff -## mean(s(year_fac)) 1.6 2.0 2.3 1.01 394 -## sd(s(year_fac)) 0.4 0.6 1.0 1.00 493 +## 2.5% 50% 97.5% Rhat n_eff +## mean(s(year_fac)) 1.6 2.00 2.30 1.00 456 +## sd(s(year_fac)) 0.4 0.59 0.99 1.02 352 ## ## Approximate significance of GAM observation smooths: ## edf Chi.sq p-value -## s(year_fac) 10.8 2810 <2e-16 *** +## s(year_fac) 10.3 2802 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## @@ -1074,7 +1076,7 @@

Adding predictors as “fixed” eff ## 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) ## E-FMI indicated no pathological behavior ## -## Samples were drawn using NUTS(diag_e) at Fri Jan 12 3:53:06 PM 2024. +## Samples were drawn using NUTS(diag_e) at Mon Jan 15 9:07:58 AM 2024. ## For each parameter, n_eff is a crude measure of effective sample size, ## and Rhat is the potential scale reduction factor on split MCMC chains ## (at convergence, Rhat = 1) @@ -1085,24 +1087,24 @@

Adding predictors as “fixed” eff
 coef(model2)
##                     2.5%       50%     97.5% Rhat n_eff
-## ndvi           0.3219343 0.3896115 0.4561312    1  1941
-## s(year_fac).1  1.1213810 1.4014750 1.6763905    1  2704
-## s(year_fac).2  1.8000682 2.0033650 2.2080812    1  2165
-## s(year_fac).3  2.1762575 2.3832750 2.5682495    1  2034
-## s(year_fac).4  2.3162657 2.5098600 2.6993935    1  2187
-## s(year_fac).5  1.1848087 1.4253400 1.6454560    1  2687
-## s(year_fac).6  1.0015992 1.2699300 1.5162433    1  2437
-## s(year_fac).7  1.1421785 1.4162100 1.6830155    1  3079
-## s(year_fac).8  2.0869212 2.2735250 2.4629585    1  2295
-## s(year_fac).9  2.7231583 2.8611750 2.9968915    1  2301
-## s(year_fac).10 1.9826495 2.1869100 2.3888603    1  2581
-## s(year_fac).11 2.2645230 2.4408950 2.6059805    1  2190
-## s(year_fac).12 2.5381555 2.6944350 2.8382668    1  2097
-## s(year_fac).13 1.3885932 1.6143500 1.8470717    1  3245
-## s(year_fac).14 0.5566057 1.9835550 3.3532650    1  1688
-## s(year_fac).15 0.7313315 1.9786150 3.3730625    1  1698
-## s(year_fac).16 0.5209962 1.9957750 3.1762922    1  1581
-## s(year_fac).17 0.6614678 1.9759650 3.2837728    1  1633
+## ndvi 0.3214333 0.3900135 0.4563159 1 1786 +## s(year_fac).1 1.1140800 1.4079600 1.6670795 1 2685 +## s(year_fac).2 1.7910845 2.0025550 2.1936545 1 2607 +## s(year_fac).3 2.1944393 2.3821600 2.5643877 1 2057 +## s(year_fac).4 2.3301122 2.5071400 2.6851682 1 2129 +## s(year_fac).5 1.1836370 1.4268450 1.6446277 1 2567 +## s(year_fac).6 1.0164710 1.2687300 1.5169110 1 2267 +## s(year_fac).7 1.1292298 1.4117000 1.6742532 1 2636 +## s(year_fac).8 2.0858535 2.2694550 2.4555455 1 2082 +## s(year_fac).9 2.7214870 2.8538250 2.9875630 1 2173 +## s(year_fac).10 1.9630840 2.1858000 2.3866162 1 2669 +## s(year_fac).11 2.2738888 2.4383000 2.6029485 1 2050 +## s(year_fac).12 2.5519082 2.6920100 2.8434890 1 2114 +## s(year_fac).13 1.4001263 1.6197550 1.8443220 1 2484 +## s(year_fac).14 0.6821051 1.9962300 3.3376105 1 1519 +## s(year_fac).15 0.7618126 2.0004150 3.3627562 1 1648 +## s(year_fac).16 0.6390487 1.9976450 3.2277897 1 1658 +## s(year_fac).17 0.6054341 1.9780000 3.3044415 1 1370

Look at the estimated effect of ndvi using plot.mvgam with type = 'pterms'

@@ -1118,24 +1120,24 @@ 

Adding predictors as “fixed” eff dplyr::glimpse(beta_post)

## Rows: 2,000
 ## Columns: 18
-## $ ndvi             <dbl> 0.355167, 0.354315, 0.400233, 0.388748, 0.341074, 0.4…
-## $ `s(year_fac).1`  <dbl> 1.45330, 1.39405, 1.45254, 1.11547, 1.66909, 1.17323,…
-## $ `s(year_fac).2`  <dbl> 2.05506, 2.07679, 1.97119, 1.99876, 2.01560, 2.07635,…
-## $ `s(year_fac).3`  <dbl> 2.59536, 2.35567, 2.37899, 2.32072, 2.48880, 2.40466,…
-## $ `s(year_fac).4`  <dbl> 2.63194, 2.56439, 2.55642, 2.43839, 2.67447, 2.47027,…
-## $ `s(year_fac).5`  <dbl> 1.54866, 1.44661, 1.48310, 1.35734, 1.53211, 1.42122,…
-## $ `s(year_fac).6`  <dbl> 1.28962, 1.44256, 1.13824, 1.43169, 1.27521, 1.37027,…
-## $ `s(year_fac).7`  <dbl> 1.60251, 1.39342, 1.47103, 1.40323, 1.46742, 1.40967,…
-## $ `s(year_fac).8`  <dbl> 2.33166, 2.34704, 2.19045, 2.30872, 2.34791, 2.26251,…
-## $ `s(year_fac).9`  <dbl> 2.96146, 2.87900, 2.85271, 2.76788, 2.92536, 2.87675,…
-## $ `s(year_fac).10` <dbl> 2.16140, 2.41945, 1.98341, 2.39724, 2.20351, 2.18907,…
-## $ `s(year_fac).11` <dbl> 2.51912, 2.52120, 2.45377, 2.36322, 2.59581, 2.37504,…
-## $ `s(year_fac).12` <dbl> 2.75224, 2.76068, 2.70921, 2.68268, 2.78127, 2.68005,…
-## $ `s(year_fac).13` <dbl> 1.63046, 1.77451, 1.48580, 1.66704, 1.72238, 1.52178,…
-## $ `s(year_fac).14` <dbl> 1.496390, 1.016750, 1.710010, 2.178540, 2.644870, 2.6…
-## $ `s(year_fac).15` <dbl> 1.871760, 2.004820, 1.210480, 2.188060, 2.624220, 2.5…
-## $ `s(year_fac).16` <dbl> 2.634900, 2.017970, 2.073360, 2.412940, 2.959150, 2.1…
-## $ `s(year_fac).17` <dbl> 1.91701, 1.50308, 1.17690, 1.54644, 1.92542, 2.15811,…
+## $ ndvi <dbl> 0.365016, 0.383852, 0.382832, 0.374714, 0.385262, 0.3… +## $ `s(year_fac).1` <dbl> 1.26080, 1.58275, 1.32614, 1.34134, 1.36449, 1.43590,… +## $ `s(year_fac).2` <dbl> 2.11456, 1.97718, 1.83386, 1.89789, 1.95921, 2.05343,… +## $ `s(year_fac).3` <dbl> 2.30024, 2.37424, 2.42140, 2.45382, 2.38137, 2.43344,… +## $ `s(year_fac).4` <dbl> 2.58320, 2.48406, 2.51264, 2.51145, 2.41215, 2.49424,… +## $ `s(year_fac).5` <dbl> 1.65731, 1.21655, 1.27151, 1.29860, 1.40799, 1.44363,… +## $ `s(year_fac).6` <dbl> 1.11182, 1.40885, 1.23147, 1.32212, 1.30500, 1.24335,… +## $ `s(year_fac).7` <dbl> 1.55856, 1.20594, 1.60187, 1.65128, 1.18561, 1.65570,… +## $ `s(year_fac).8` <dbl> 2.31500, 2.17933, 2.19752, 2.27384, 2.21278, 2.26591,… +## $ `s(year_fac).9` <dbl> 2.86616, 2.85139, 2.92218, 2.84696, 2.80555, 2.81140,… +## $ `s(year_fac).10` <dbl> 2.25933, 2.12217, 2.14634, 2.24707, 2.19890, 2.17169,… +## $ `s(year_fac).11` <dbl> 2.52557, 2.49356, 2.62267, 2.52679, 2.43452, 2.40733,… +## $ `s(year_fac).12` <dbl> 2.72165, 2.70566, 2.67655, 2.70252, 2.68610, 2.71396,… +## $ `s(year_fac).13` <dbl> 1.55743, 1.70503, 1.48361, 1.55631, 1.58906, 1.62060,… +## $ `s(year_fac).14` <dbl> 2.566090, 1.447150, 1.984190, 2.192650, 1.231120, 1.9… +## $ `s(year_fac).15` <dbl> 1.05225, 2.12175, 1.72275, 1.93314, 1.75620, 1.66417,… +## $ `s(year_fac).16` <dbl> 1.447540, 2.158620, 1.625380, 1.515920, 2.205820, 0.7… +## $ `s(year_fac).17` <dbl> 0.828068, 0.831492, 2.645610, 2.822590, 0.700252, 2.3…

The posterior distribution for the effect of ndvi is stored in the ndvi column. A quick histogram confirms our inference that log(counts) respond positively to increases @@ -1272,26 +1274,26 @@

Adding predictors as smooths## ## GAM coefficient (beta) estimates: ## 2.5% 50% 97.5% Rhat n_eff -## (Intercept) 2.00 2.10 2.200 1.00 976 -## ndvi 0.26 0.33 0.400 1.00 1005 -## s(time).1 -2.20 -1.10 -0.066 1.01 481 -## s(time).2 0.45 1.30 2.200 1.00 433 -## s(time).3 -0.49 0.46 1.400 1.01 377 -## s(time).4 1.60 2.50 3.400 1.01 376 -## s(time).5 -1.20 -0.20 0.730 1.01 373 -## s(time).6 -0.60 0.36 1.400 1.01 396 -## s(time).7 -1.50 -0.50 0.480 1.00 436 -## s(time).8 0.59 1.50 2.400 1.01 377 -## s(time).9 1.10 2.10 3.000 1.01 368 -## s(time).10 -0.37 0.55 1.500 1.01 370 -## s(time).11 0.80 1.70 2.700 1.01 372 -## s(time).12 0.65 1.50 2.400 1.01 365 -## s(time).13 -1.20 -0.30 0.560 1.00 601 -## s(time).14 -7.20 -4.20 -1.000 1.00 509 +## (Intercept) 2.00 2.10 2.200 1.00 1043 +## ndvi 0.26 0.33 0.390 1.00 1059 +## s(time).1 -2.10 -1.10 -0.031 1.01 337 +## s(time).2 0.44 1.30 2.300 1.02 283 +## s(time).3 -0.55 0.44 1.500 1.02 243 +## s(time).4 1.60 2.50 3.600 1.02 262 +## s(time).5 -1.20 -0.21 0.910 1.02 237 +## s(time).6 -0.62 0.37 1.600 1.02 281 +## s(time).7 -1.50 -0.54 0.590 1.02 249 +## s(time).8 0.60 1.40 2.600 1.02 248 +## s(time).9 1.20 2.10 3.200 1.02 225 +## s(time).10 -0.39 0.54 1.700 1.02 259 +## s(time).11 0.83 1.70 2.900 1.02 240 +## s(time).12 0.67 1.50 2.500 1.02 254 +## s(time).13 -1.20 -0.32 0.670 1.01 322 +## s(time).14 -7.60 -4.10 -1.200 1.01 351 ## ## Approximate significance of GAM observation smooths: ## edf Chi.sq p-value -## s(time) 9.76 679 <2e-16 *** +## s(time) 8.57 797 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## @@ -1302,7 +1304,7 @@

Adding predictors as smooths## 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) ## E-FMI indicated no pathological behavior ## -## Samples were drawn using NUTS(diag_e) at Fri Jan 12 3:53:45 PM 2024. +## Samples were drawn using NUTS(diag_e) at Mon Jan 15 9:08:44 AM 2024. ## For each parameter, n_eff is a crude measure of effective sample size, ## and Rhat is the potential scale reduction factor on split MCMC chains ## (at convergence, Rhat = 1) @@ -1429,7 +1431,7 @@

Latent dynamics in mvgamplot(model3, type = 'forecast', newdata = data_test)

## Out of sample DRPS:
-## [1] 287.0755
+## [1] 286.5788

Why is this happening? The forecasts are driven almost entirely by variation in the temporal spline, which is extrapolating linearly forever beyond the edge of the training data. Any slight @@ -1512,33 +1514,32 @@

Latent dynamics in mvgam## ## GAM coefficient (beta) estimates: ## 2.5% 50% 97.5% Rhat n_eff -## (Intercept) 0.580 1.9000 2.700 1.17 36 -## s(ndvi).1 -0.078 0.0069 0.120 1.01 1388 -## s(ndvi).2 -0.120 0.0150 0.210 1.00 915 -## s(ndvi).3 -0.038 -0.0012 0.038 1.00 2092 -## s(ndvi).4 -0.200 0.1000 0.900 1.01 561 -## s(ndvi).5 -0.049 0.1600 0.350 1.00 489 +## (Intercept) 0.890 1.9000 2.500 1.03 61 +## s(ndvi).1 -0.082 0.0110 0.220 1.00 533 +## s(ndvi).2 -0.160 0.0140 0.400 1.00 454 +## s(ndvi).3 -0.054 -0.0018 0.061 1.01 760 +## s(ndvi).4 -0.300 0.1200 1.700 1.01 268 +## s(ndvi).5 -0.100 0.1500 0.340 1.00 462 ## ## Approximate significance of GAM observation smooths: -## edf Chi.sq p-value -## s(ndvi) 1.05 89.1 0.055 . +## edf Chi.sq p-value +## s(ndvi) 0.978 95.5 0.088 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Latent trend parameter AR estimates: ## 2.5% 50% 97.5% Rhat n_eff -## ar1[1] 0.70 0.81 0.93 1.05 76 -## sigma[1] 0.67 0.80 0.95 1.00 555 +## ar1[1] 0.69 0.81 0.94 1.01 173 +## sigma[1] 0.67 0.80 0.96 1.01 518 ## ## Stan MCMC diagnostics: ## n_eff / iter looks reasonable for all parameters -## Rhats above 1.05 found for 131 parameters -## *Diagnose further to investigate why the chains have not mixed +## Rhat looks reasonable for all parameters ## 0 of 2000 iterations ended with a divergence (0%) ## 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) ## E-FMI indicated no pathological behavior ## -## Samples were drawn using NUTS(diag_e) at Fri Jan 12 3:54:58 PM 2024. +## Samples were drawn using NUTS(diag_e) at Mon Jan 15 9:10:06 AM 2024. ## For each parameter, n_eff is a crude measure of effective sample size, ## and Rhat is the potential scale reduction factor on split MCMC chains ## (at convergence, Rhat = 1) @@ -1553,8 +1554,8 @@

Latent dynamics in mvgam
 plot(model4, type = 'forecast', newdata = data_test)

-
## Out of sample CRPS:
-## [1] 150.7294
+
## Out of sample DRPS:
+## [1] 150.9452

The trend is evolving as an AR1 process, which we can also view:

 plot(model4, type = 'trend', newdata = data_test)
@@ -1569,7 +1570,7 @@

Latent dynamics in mvgam## Warning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
##        elpd_diff se_diff
 ## model4    0.0       0.0 
-## model3 -560.0      66.5
+## model3 -560.2 66.5

The higher estimated log predictive density (ELPD) value for the dynamic model suggests it provides a better fit to the in-sample data.

@@ -1584,7 +1585,7 @@

Latent dynamics in mvgamscore_mod3 <- score(fc_mod3, score = 'drps') score_mod4 <- score(fc_mod4, score = 'drps') sum(score_mod4$PP$score, na.rm = TRUE) - sum(score_mod3$PP$score, na.rm = TRUE) -
## [1] -136.3461
+
## [1] -135.6337

A strongly negative value here suggests the score for the dynamic model (model 4) is much smaller than the score for the model with a smooth function of time (model 3)

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