From dd5dc3e1e10851cde7c75bc9de4e83bf6af0605a Mon Sep 17 00:00:00 2001
From: Nicholas Clark Usage
newdata,
family = poisson(),
unit = time,
- subgr = series,
+ species = series,
share_obs_params = FALSE,
priors,
n_lv = 2,
@@ -115,19 +115,15 @@
Argumentss(),
te()
, ti()
, t2()
, as well as time-varying
dynamic()
terms and nonparametric gp()
terms, can be added to the right hand side
to specify that the linear predictor depends on smooth functions of predictors
-(or linear functionals of these). In nmix()
family models, the formula
is used to
-set up a linear predictor for the detection probability. Details of the formula syntax used by mvgam
+(or linear functionals of these). Details of the formula syntax used by mvgam
can be found in mvgam_formulae
A character
string specifying the linear predictor
-effects for the latent factors. These are exactly like the formula
-for a GLM except that smooth terms, s()
, te()
, ti()
, t2()
, as well as time-varying
-dynamic()
terms and nonparametric gp()
terms, can be added to the right hand side
-to specify that the linear predictor depends on smooth functions of predictors
-(or linear functionals of these). Details of the formula syntax used by mvgam
-can be found in mvgam_formulae
by = trend
within calls to functional terms
+(i.e. s()
, te()
, ti()
, t2()
, dynamic()
, or gp()
) to ensure that each factor
+captures a different axis of variation. See the example below as an illustration
gr
)
-should not include a series
element in data
. Rather, this element will be created internally based
-on the supplied variables for gr
and subgr
. For example, if you are modelling
-counts for a group of species (labelled as species
in the data) across sampling sites
-(labelled as site
in the data) in three
-different geographical regions (labelled as region
), and you would like the residuals to be correlated
-within regions, then you should specify
-unit = site
, gr = region
, and subgr = species
. Internally, mvgam()
will appropriately order
-the data by unit
(in this case, by site
) and create
-the series
element for the data using something like: series = as.factor(paste0(group, '_', subgroup))
+An unquoted string representing the factor
variable that indexes
+the different outcome variables in data
(usually 'species'
in a JSDM).
+Defaults to series
to be consistent with other mvgam
models
logical
. If TRUE
and the family
has additional family-specific observation parameters (e.g. variance components in
student_t()
or gaussian()
, or dispersion parameters in nb()
or betar()
),
-these parameters will be shared across all series. This is handy if you have multiple
-time series that you believe share some properties, such as being from the same
-species over different spatial units. Default is FALSE
.
mvgam
models) that you believe share some properties,
+such as being from the same species over different spatial units. Default is FALSE
.
An optional data.frame
with prior
-definitions (in JAGS or Stan syntax). if using Stan, this can also be an object of
-class brmsprior
(see. prior
for details). See get_mvgam_priors and
-'Details' for more information on changing default prior distributions
brmsprior
(see. prior
for details).
+See get_mvgam_priors and Details' for more information on changing default prior distributions
integer
the number of latent dynamic factors to use if use_lv == TRUE
.
-Cannot be > n_series
. Defaults arbitrarily to min(2, floor(n_series / 2))
n_species
. Defaults arbitrarily to 2
list
object of class mvgam
containing model output,
the text representation of the model file,
the mgcv model output (for easily generating simulations at
-unsampled covariate values), Dunn-Smyth residuals for each series and key information needed
+unsampled covariate values), Dunn-Smyth residuals for each species and key information needed
for other functions in the package. See mvgam-class
for details.
Use methods(class = "mvgam")
for an overview on available methods
@@ -341,7 +327,26 @@ trend = 'None'
is set up and then modified to include the latent factors and their linear predictors.
Consequently, you can inspect priors for these models using get_mvgam_priors by supplying the relevant
-formula
, factor_formula
, data
and family
arguments and using trend = 'None'
+formula
, factor_formula
, data
and family
arguments and keeping the default trend = 'None'
.
+In a JSDGAM, the expectation of response \(Y_{ij}\) is modelled with
+$$g(\mu_{ij}) = X_i'\beta + u_i'\theta_j,$$
+where \(g(.)\) is a known link function,
+\(X_i'\) is a design matrix of linear predictors (with associated \(\beta\) coefficients),
+\(u_i\) are \(n_{lv}\)-variate latent factors
+(\(n_{lv}\)<<\(n_{species}\)) and
+\(\theta_j\) are species-specific loadings on the latent factors, respectively. The design matrix
+\(X\) and \(\beta\) coefficients are constructed and modelled using formula
and can contain
+any of mvgam
's predictor effects, including random intercepts and slopes, multidimensional penalized
+smooths, GP effects etc... The factor loadings \(\theta_j\) are constrained for identifiability but can
+be used to reconstruct an estimate of the species' residual variance-covariance matrix (see the example below
+for an illustration of this). The latent factors are further modelled using:
+$$
+u_i \sim \text{Normal}(Q_i\beta_{factor}, 1) \quad
+$$
+where the second design matrix \(Q\) and associated \(\beta_{factor}\) coefficients are
+constructed and modelled using factor_formula
. Again, the effects that make up this linear
+predictor can contain any of mvgam
's allowed predictor effects, providing enormous flexibility for
+modelling species' communities.
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