R: Variable selection (without cross-validation)

varsel {projpred} | R Documentation

## Variable selection (without cross-validation)

### Description

Perform the projection predictive variable selection for GLMs, GLMMs, GAMs, and GAMMs. This variable selection consists of a search part and an evaluation part. The search part determines the 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 solution path.

### Usage

    varsel(object, ...)

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

    ## S3 method for class 'refmodel'
    varsel(
      object,
      d_test = NULL,
      method = NULL,
      ndraws = NULL,
      nclusters = 20,
      ndraws_pred = 400,
      nclusters_pred = NULL,
      refit_prj = !inherits(object, "datafit"),
      nterms_max = NULL,
      verbose = TRUE,
      lambda_min_ratio = 1e-05,
      nlambda = 150,
      thresh = 1e-06,
      regul = 1e-04,
      penalty = NULL,
      search_terms = NULL,
      seed = sample.int(.Machine$integer.max, 1),
      ...
    )

### 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()`.
`...` | Arguments passed to `get_refmodel()` as well as to the divergence minimizer (during a forward search and also during the evaluation part, but the latter only if `refit_prj` is `TRUE`).
`d_test` | For internal use only. A `list` providing information about the test set which is used for evaluating the predictive performance of the reference model. If not provided, the training set is used.
`method` | The method for the search part. Possible options are `"L1"` for L1 search and `"forward"` for forward search. If `NULL`, then `"forward"` is used if the reference model has multilevel or additive terms and `"L1"` otherwise. 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` | A single logical value indicating whether to fit the submodels along the solution path again (`TRUE`) or to retrieve their fits from the search part (`FALSE`) before using those (re-)fits in the evaluation part.
`nterms_max` | Maximum number of predictor terms until 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.
`lambda_min_ratio` | 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` | 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` | Only relevant for L1 search. Convergence threshold when computing the L1 path. Usually, there is no need to change this.
`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.
`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` | A custom character vector of terms to consider for the search. The intercept (`"1"`) needs to be included explicitly. The default considers all the terms in the reference model's formula.
`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).

### 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 `datafit`s). 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, only the forward search is available.

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 interaction terms before the corresponding main terms are selected. If this is undesired, choose the forward search instead.

### 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 vignette or type `?projpred`).

### See Also

`cv_varsel()`

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

[Package projpred version 2.1.1 Index]