projpred (version 2.1.2)

project: Projection onto submodel(s)

Description

Project the posterior of the reference model onto the parameter space of a single submodel consisting of a specific combination of predictor terms or (after variable selection) onto the parameter space of a single or multiple submodels of specific sizes.

Usage

project(
  object,
  nterms = NULL,
  solution_terms = NULL,
  refit_prj = TRUE,
  ndraws = 400,
  nclusters = NULL,
  seed = sample.int(.Machine$integer.max, 1),
  regul = 1e-04,
  ...
)

Value

If the projection is performed onto a single submodel (i.e., length(nterms) == 1 || !is.null(solution_terms)), an object of class projection which is a list containing the following elements:

dis

Projected draws for the dispersion parameter.

kl

The KL divergence from the submodel to the reference model.

weights

Weights for the projected draws.

solution_terms

A character vector of the submodel's predictor terms, ordered in the way in which the terms were added to the submodel.

submodl

A list containing the submodel fits (one fit per projected draw).

p_type

A single logical value indicating whether the reference model's posterior draws have been clustered for the projection (TRUE) or not (FALSE).

refmodel

The reference model object.

If the projection is performed onto more than one submodel, the output from above is returned for each submodel, giving a list with one element for each submodel.

Arguments

object

An object which can be used as input to get_refmodel() (in particular, objects of class refmodel).

nterms

Only relevant if object is of class vsel (returned by varsel() or cv_varsel()). Ignored if !is.null(solution_terms). Number of terms for the submodel (the corresponding combination of predictor terms is taken from object). If a numeric vector, then the projection is performed for each element of this vector. If NULL (and is.null(solution_terms)), then the value suggested by the variable selection is taken (see function suggest_size()). Note that nterms does not count the intercept, so use nterms = 0 for the intercept-only model.

solution_terms

If not NULL, then this needs to be a character vector of predictor terms for the submodel onto which the projection will be performed. Argument nterms is ignored in that case. For an object which is not of class vsel, solution_terms must not be NULL.

refit_prj

A single logical value indicating whether to fit the submodels (again) (TRUE) or to retrieve the fitted submodels from object (FALSE). For an object which is not of class vsel, refit_prj must be TRUE.

ndraws

Only relevant if refit_prj is TRUE. Number of posterior draws to be projected. Ignored if nclusters is not NULL or if the reference model is of class datafit (in which case one cluster is used). If both (nclusters and ndraws) are NULL, the number of posterior draws from the reference model is used for ndraws. See also section "Details" below.

nclusters

Only relevant if refit_prj is TRUE. Number of clusters of posterior draws to be projected. Ignored if the reference model is of class datafit (in which case one cluster is used). For the meaning of NULL, see argument ndraws. See also section "Details" below.

seed

Pseudorandom number generation (PRNG) seed by which the same results can be obtained again if needed. If NULL, no seed is set and therefore, the results are not reproducible. See set.seed() for details. Here, this seed is used for clustering the reference model's posterior draws (if !is.null(nclusters)) and for drawing new group-level effects when predicting from a multilevel submodel (however, not yet in case of a GAMM).

regul

A number giving the amount of ridge regularization when projecting onto (i.e., fitting) submodels which are GLMs. Usually there is no need for regularization, but sometimes we need to add some regularization to avoid numerical problems.

...

Arguments passed to get_refmodel() (if get_refmodel() is actually used; see argument object) as well as to the divergence minimizer (if refit_prj is TRUE).

Details

Arguments ndraws and nclusters are automatically truncated at the number of posterior draws in the reference model (which is 1 for datafits). Using less draws or clusters in ndraws or nclusters than posterior draws in the reference model may result in slightly inaccurate projection performance. Increasing these arguments affects the computation time linearly.

Examples

if (requireNamespace("rstanarm", quietly = TRUE)) {
  # Data:
  dat_gauss <- data.frame(y = df_gaussian$y, df_gaussian$x)

  # The "stanreg" fit which will be used as the reference model (with small
  # values for `chains` and `iter`, but only for technical reasons in this
  # example; this is not recommended in general):
  fit <- rstanarm::stan_glm(
    y ~ X1 + X2 + X3 + X4 + X5, family = gaussian(), data = dat_gauss,
    QR = TRUE, chains = 2, iter = 500, refresh = 0, seed = 9876
  )

  # Variable selection (here without cross-validation and with small values
  # for `nterms_max`, `nclusters`, and `nclusters_pred`, but only for the
  # sake of speed in this example; this is not recommended in general):
  vs <- varsel(fit, nterms_max = 3, nclusters = 5, nclusters_pred = 10,
               seed = 5555)

  # Projection onto the best submodel with 2 predictor terms (with a small
  # value for `nclusters`, but only for the sake of speed in this example;
  # this is not recommended in general):
  prj_from_vs <- project(vs, nterms = 2, nclusters = 10, seed = 9182)

  # Projection onto an arbitrary combination of predictor terms (with a small
  # value for `nclusters`, but only for the sake of speed in this example;
  # this is not recommended in general):
  prj <- project(fit, solution_terms = c("X1", "X3", "X5"), nclusters = 10,
                 seed = 9182)
}