Projection onto submodel(s) — project • projpred

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 = predictor_terms,
  predictor_terms = NULL,
  refit_prj = TRUE,
  ndraws = 400,
  nclusters = NULL,
  seed = NA,
  verbose = getOption("projpred.verbose", as.integer(interactive())),
  ...
)

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(predictor_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(predictor_terms)), then the value suggested by suggest_size() is taken (with default arguments for suggest_size(), implying that this suggested size is based on the ELPD). Note that nterms does not count the intercept, so use nterms = 0 for the intercept-only model.
solution_terms: Deprecated. Please use argument predictor_terms instead.
predictor_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, predictor_terms must not be NULL.
refit_prj: A single logical value indicating whether to fit the submodels (again) (TRUE) or—if object is of class vsel—to re-use the submodel fits from the full-data search that was run when creating object (FALSE). For an object which is not of class vsel, refit_prj must be TRUE. See also section "Details" below.
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. Passed to argument seed of set.seed(), but can also be NA to not call set.seed() at all. If not NA, then the PRNG state is reset (to the state before calling project()) upon exiting project(). Here, 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) and having global option projpred.mlvl_pred_new set to TRUE. (Such a prediction takes place when calculating output elements dis and ce.)
verbose: A single integer value from the set \(\{0, 1, 2\}\) (if !is.null(predictor_terms), \(1\) and \(2\) have the same effect), indicating how much information (if any) to print out during the computations. Higher values indicate that more information should be printed, 0 deactivates the verbose mode. Internally, argument verbose is coerced to integer via as.integer(), so technically, a single logical value or a single numeric value work as well.
...: 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).

Value

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

dis: Projected draws for the dispersion parameter.
ce: The cross-entropy part of the Kullback-Leibler (KL) divergence from the reference model to the submodel. For some families, this is not the actual cross-entropy, but a reduced one where terms which would cancel out when calculating the KL divergence have been dropped. In case of the Gaussian family, that reduced cross-entropy is further modified, yielding merely a proxy.
wdraws_prj: Weights for the projected draws.
predictor_terms: A character vector of the submodel's predictor terms.
outdmin: A list containing the submodel fits (one fit per projected draw). This is the same as the return value of the div_minimizer function (see init_refmodel()), except if project() was used with an object of class vsel based on an L1 search as well as with refit_prj = FALSE, in which case this is the output from an internal L1-penalized divergence minimizer.
cl_ref: A numeric vector of length equal to the number of posterior draws in the reference model, containing the cluster indices of these draws.
wdraws_ref: A numeric vector of length equal to the number of posterior draws in the reference model, giving the weights of these draws. These weights should be treated as not being normalized (i.e., they don't necessarily sum to 1).
const_wdraws_prj: A single logical value indicating whether the projected draws have constant weights (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.

The elements of an object of class projection are not meant to be accessed directly but instead via helper functions (see the main vignette and projpred-package; see also as_draws_matrix.projection(), argument return_draws_matrix of proj_linpred(), and argument nresample_clusters of proj_predict() for the intended use of the weights stored in element wdraws_prj).

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.

If refit_prj = FALSE (which is only possible if object is of class vsel), project() retrieves the submodel fits from the full-data search that was run when creating object. Usually, the search relies on a rather coarse clustering or thinning of the reference model's posterior draws (by default, varsel() and cv_varsel() use nclusters = 20). Consequently, project() with refit_prj = FALSE then inherits this coarse clustering or thinning.

Examples

# 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
)

# Run varsel() (here without cross-validation, with L1 search, and with small
# values for `nterms_max` and `nclusters_pred`, but only for the sake of
# speed in this example; this is not recommended in general):
vs <- varsel(fit, method = "L1", nterms_max = 3, 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, predictor_terms = c("X1", "X3", "X5"), nclusters = 10,
               seed = 9182)