varsel {projpred}

Run search and performance evaluation without cross-validation

Description

Run the search part and the evaluation part for a projection predictive variable selection. The search part determines the predictor ranking (also known as solution path), i.e., the best submodel for each submodel size (number of predictor terms). The evaluation part determines the predictive performance of the submodels along the predictor ranking. A special method is varsel.vsel() because it re-uses the search results from an earlier varsel() (or cv_varsel()) run, as illustrated in the main vignette.

Usage

varsel(object, ...)

## Default S3 method:
varsel(object, ...)

## S3 method for class 'vsel'
varsel(object, ...)

## S3 method for class 'refmodel'
varsel(
  object,
  d_test = NULL,
  method = "forward",
  ndraws = NULL,
  nclusters = 20,
  ndraws_pred = 400,
  nclusters_pred = NULL,
  refit_prj = !inherits(object, "datafit"),
  nterms_max = NULL,
  verbose = TRUE,
  search_control = NULL,
  lambda_min_ratio = 1e-05,
  nlambda = 150,
  thresh = 1e-06,
  penalty = NULL,
  search_terms = NULL,
  search_out = NULL,
  seed = NA,
  ...
)

Arguments

object

An object of class refmodel (returned by get_refmodel() or init_refmodel()) or an object that can be passed to argument object of get_refmodel().

...

For varsel.default(): Arguments passed to get_refmodel() as well as to varsel.refmodel(). For varsel.vsel(): Arguments passed to varsel.refmodel(). For varsel.refmodel(): Arguments passed to the divergence minimizer (see argument div_minimizer of init_refmodel() as well as section "Draw-wise divergence minimizers" of projpred-package) when refitting the submodels for the performance evaluation (if refit_prj is TRUE).

d_test

A list of the structure outlined in section "Argument d_test" below, providing test data for evaluating the predictive performance of the submodels as well as of the reference model. If NULL, the training data is used.

method

The method for the search part. Possible options are "forward" for forward search and "L1" for L1 search. See also section "Details" below.

ndraws

Number of posterior draws used in the search part. Ignored if nclusters is not NULL or in case of L1 search (because L1 search always uses a single cluster). 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

Number of clusters of posterior draws used in the search part. Ignored in case of L1 search (because L1 search always uses a single cluster). For the meaning of NULL, see argument ndraws. See also section "Details" below.

ndraws_pred

Only relevant if refit_prj is TRUE. Number of posterior draws used in the evaluation part. Ignored if nclusters_pred is not NULL. If both (nclusters_pred and ndraws_pred) are NULL, the number of posterior draws from the reference model is used for ndraws_pred. See also section "Details" below.

nclusters_pred

Only relevant if refit_prj is TRUE. Number of clusters of posterior draws used in the evaluation part. For the meaning of NULL, see argument ndraws_pred. See also section "Details" below.

refit_prj

For the evaluation part, should the submodels along the predictor ranking be fitted again (TRUE) or should their fits from the search part be re-used (FALSE)?

nterms_max

Maximum submodel size (number of predictor terms) up to which the search is continued. If NULL, then min(19, D) is used where D is the number of terms in the reference model (or in search_terms, if supplied). Note that nterms_max does not count the intercept, so use nterms_max = 0 for the intercept-only model. (Correspondingly, D above does not count the intercept.)

verbose

A single logical value indicating whether to print out additional information during the computations.

search_control

A list of "control" arguments (i.e., tuning parameters) for the search. In case of forward search, these arguments are passed to the divergence minimizer (see argument div_minimizer of init_refmodel() as well as section "Draw-wise divergence minimizers" of projpred-package). In case of forward search, NULL causes ... to be used not only for the performance evaluation, but also for the search. In case of L1 search, possible arguments are:

• lambda_min_ratio: Ratio between the smallest and largest lambda in the L1-penalized search (default: 1e-5). This parameter essentially determines how long the search is carried out, i.e., how large submodels are explored. No need to change this unless the program gives a warning about this.

• nlambda: Number of values in the lambda grid for L1-penalized search (default: 150). No need to change this unless the program gives a warning about this.

• thresh: Convergence threshold when computing the L1 path (default: 1e-6). Usually, there is no need to change this.

lambda_min_ratio

Deprecated (please use search_control instead). Only relevant for L1 search. Ratio between the smallest and largest lambda in the L1-penalized search. This parameter essentially determines how long the search is carried out, i.e., how large submodels are explored. No need to change this unless the program gives a warning about this.

nlambda

Deprecated (please use search_control instead). Only relevant for L1 search. Number of values in the lambda grid for L1-penalized search. No need to change this unless the program gives a warning about this.

thresh

Deprecated (please use search_control instead). Only relevant for L1 search. Convergence threshold when computing the L1 path. Usually, there is no need to change this.

penalty

Only relevant for L1 search. A numeric vector determining the relative penalties or costs for the predictors. A value of 0 means that those predictors have no cost and will therefore be selected first, whereas Inf means those predictors will never be selected. If NULL, then 1 is used for each predictor.

search_terms

Only relevant for forward search. A custom character vector of predictor term blocks to consider for the search. Section "Details" below describes more precisely what "predictor term block" means. The intercept ("1") is always included internally via union(), so there's no difference between including it explicitly or omitting it. The default search_terms considers all the terms in the reference model's formula.

search_out

Intended for internal use.

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 varsel()) upon exiting varsel(). Here, seed is used for clustering the reference model's posterior draws (if !is.null(nclusters) or !is.null(nclusters_pred)) and for drawing new group-level effects when predicting from a multilevel submodel (however, not yet in case of a GAMM).

Details

Arguments ndraws, nclusters, nclusters_pred, and ndraws_pred 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, nclusters, nclusters_pred, or ndraws_pred than posterior draws in the reference model may result in slightly inaccurate projection performance. Increasing these arguments affects the computation time linearly.

For argument method, there are some restrictions: For a reference model with multilevel or additive formula terms or a reference model set up for the augmented-data projection, only the forward search is available. Furthermore, argument search_terms requires a forward search to take effect.

L1 search is faster than forward search, but forward search may be more accurate. Furthermore, forward search may find a sparser model with comparable performance to that found by L1 search, but it may also start overfitting when more predictors are added.

An L1 search may select an interaction term before all involved lower-order interaction terms (including main-effect terms) have been selected. In projpred versions > 2.6.0, the resulting predictor ranking is automatically modified so that the lower-order interaction terms come before this interaction term, but if this is conceptually undesired, choose the forward search instead.

The elements of the search_terms character vector don't need to be individual predictor terms. Instead, they can be building blocks consisting of several predictor terms connected by the + symbol. To understand how these building blocks work, it is important to know how projpred's forward search works: It starts with an empty vector chosen which will later contain already selected predictor terms. Then, the search iterates over model sizes j \in \{0, ..., J\} (with J denoting the maximum submodel size, not counting the intercept). The candidate models at model size j are constructed from those elements from search_terms which yield model size j when combined with the chosen predictor terms. Note that sometimes, there may be no candidate models for model size j. Also note that internally, search_terms is expanded to include the intercept ("1"), so the first step of the search (model size 0) always consists of the intercept-only model as the only candidate.

As a search_terms example, consider a reference model with formula y ~ x1 + x2 + x3. Then, to ensure that x1 is always included in the candidate models, specify search_terms = c("x1", "x1 + x2", "x1 + x3", "x1 + x2 + x3") (or, in a simpler way that leads to the same results, search_terms = c("x1", "x1 + x2", "x1 + x3"), for which helper function force_search_terms() exists). This search would start with y ~ 1 as the only candidate at model size 0. At model size 1, y ~ x1 would be the only candidate. At model size 2, y ~ x1 + x2 and y ~ x1 + x3 would be the two candidates. At the last model size of 3, y ~ x1 + x2 + x3 would be the only candidate. As another example, to exclude x1 from the search, specify search_terms = c("x2", "x3", "x2 + x3") (or, in a simpler way that leads to the same results, search_terms = c("x2", "x3")).

Value

An object of class vsel. The elements of this object are not meant to be accessed directly but instead via helper functions (see the main vignette and projpred-package).

Argument d_test

If not NULL, then d_test needs to be a list with the following elements:

• data: a data.frame containing the predictor variables for the test set.

• offset: a numeric vector containing the offset values for the test set (if there is no offset, use a vector of zeros).

• weights: a numeric vector containing the observation weights for the test set (if there are no observation weights, use a vector of ones).

• y: a vector or a factor containing the response values for the test set. In case of the latent projection, this has to be a vector containing the latent response values, but it can also be a vector full of NAs if latent-scale post-processing is not needed.

• y_oscale: Only needs to be provided in case of the latent projection where this needs to be a vector or a factor containing the original (i.e., non-latent) response values for the test set.

See Also

cv_varsel()

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)
# Now see, for example, `?print.vsel`, `?plot.vsel`, `?suggest_size.vsel`,
# and `?ranking` for possible post-processing functions.