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.
project(
object,
nterms = NULL,
solution_terms = predictor_terms,
predictor_terms = NULL,
refit_prj = TRUE,
ndraws = 400,
nclusters = NULL,
seed = NA,
verbose = getOption("projpred.verbose_project", TRUE),
...
)An object which can be used as input to get_refmodel() (in
particular, objects of class refmodel).
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.
Deprecated. Please use argument predictor_terms
instead.
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.
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.
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.
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.
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.)
A single logical value indicating whether to print out
additional information during the computations. More precisely, this gets
passed as verbose_divmin to the divergence minimizer function of the
refmodel object. For the built-in divergence minimizers, this only has an
effect in case of sequential computations (not in case of parallel
projection, which is described in projpred-package).
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).
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:
disProjected draws for the dispersion parameter.
ceThe 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_prjWeights for the projected draws.
predictor_termsA character vector of the submodel's predictor terms.
outdminA 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_refA numeric vector of length equal to the number of posterior draws in the reference model, containing the cluster indices of these draws.
wdraws_refA 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_prjA single logical value indicating whether the
projected draws have constant weights (TRUE) or not (FALSE).
refmodelThe 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).
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.
# 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, verbose = FALSE)
# 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,
verbose = FALSE)
# 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, verbose = FALSE)