This is the summary() method for vsel objects (returned by varsel() or
cv_varsel()). Apart from some general information about the varsel() or
cv_varsel() run, it shows the full-data predictor ranking, basic
information about the (CV) variability in the ranking of the predictors (if
available; inferred from cv_proportions()), and estimates for
user-specified predictive performance statistics. For a graphical
representation, see plot.vsel(). For extracting the predictive performance
results printed at the bottom of the output created by this summary()
method, see performances().
An object of class vsel (returned by varsel() or
cv_varsel()).
Maximum submodel size (number of predictor terms) for which
the performance statistics are calculated. Using NULL is effectively the
same as length(ranking(object)$fulldata). Note that nterms_max does not
count the intercept, so use nterms_max = 0 for the intercept-only model.
For plot.vsel(), nterms_max must be at least 1.
One or more character strings determining which performance
statistics (i.e., utilities or losses) to estimate based on the
observations in the evaluation (or "test") set (in case of
cross-validation, these are all observations because they are partitioned
into multiple test sets; in case of varsel() with d_test = NULL, these
are again all observations because the test set is the same as the training
set). Available statistics are:
"elpd": expected log (pointwise) predictive density (for a new
dataset). Estimated by the sum of the observation-specific log predictive
density values (with each of these predictive density values being
a---possibly weighted---average across the parameter draws).
"mlpd": mean log predictive density, that is, "elpd" divided by the
number of observations.
"gmpd": geometric mean predictive density (GMPD), that is, exp() of
"mlpd". The GMPD is especially helpful for discrete response families
(because there, the GMPD is bounded by zero and one). For the corresponding
standard error, the delta method is used. The corresponding confidence
interval type is "exponentiated normal approximation" because the
confidence interval bounds are the exponentiated confidence interval bounds
of the "mlpd".
"mse": mean squared error (only available in the situations mentioned
in section "Details" below).
"rmse": root mean squared error (only available in the situations
mentioned in section "Details" below). For the corresponding standard error
and lower and upper confidence interval bounds, bootstrapping is used.
"acc" (or its alias, "pctcorr"): classification accuracy (only
available in the situations mentioned in section "Details" below). By
"classification accuracy", we mean the proportion of correctly classified
observations. For this, the response category ("class") with highest
probability (the probabilities are model-based) is taken as the prediction
("classification") for an observation.
"auc": area under the ROC curve (only available in the situations
mentioned in section "Details" below). For the corresponding standard error
and lower and upper confidence interval bounds, bootstrapping is used.
One or more items from "mean", "se", "lower", "upper",
"diff", and "diff.se" indicating which of these to compute for each
item from stats (mean, standard error, lower and upper confidence
interval bounds, mean difference to the corresponding statistic of the
reference model, and standard error of this difference, respectively; note
that for the GMPD, "diff", and "diff.se" actually refer to the ratio
vs. the reference model, not the difference). The confidence interval
bounds belong to normal-approximation (or bootstrap or exponentiated
normal-approximation; see argument stats) confidence intervals with
(nominal) coverage 1 - alpha. Items "diff" and "diff.se" are only
supported if deltas is FALSE.
If TRUE, the submodel statistics are estimated relatively to
the baseline model (see argument baseline). For the GMPD, the term
"relatively" refers to the ratio vs. the baseline model (i.e., the submodel
statistic divided by the baseline model statistic). For all other stats,
"relatively" refers to the difference from the baseline model (i.e., the
submodel statistic minus the baseline model statistic).
A number determining the (nominal) coverage 1 - alpha of the
normal-approximation (or bootstrap or exponentiated normal-approximation;
see argument stats) confidence intervals. For example, in case of the
normal approximation, alpha = 2 * pnorm(-1) corresponds to a confidence
interval stretching by one standard error on either side of the point
estimate.
For summary.vsel(): Only relevant if deltas is TRUE.
For plot.vsel(): Always relevant. Either "ref" or "best", indicating
whether the baseline is the reference model or the best submodel found (in
terms of stats[1]), respectively.
Only relevant for the latent projection. A single logical
value indicating whether to calculate the performance statistics on the
original response scale (TRUE) or on latent scale (FALSE).
Passed to argument cumulate of cv_proportions(). Affects
column cv_proportions_diag of the summary table.
Arguments passed to the internal function which is used for
bootstrapping (if applicable; see argument stats). Currently, relevant
arguments are B (the number of bootstrap samples, defaulting to 2000)
and seed (see set.seed(), but defaulting to NA so that set.seed()
is not called within that function at all).
An object of class vselsummary. The elements of this object are not
meant to be accessed directly but instead via helper functions
(print.vselsummary() and performances.vselsummary()).
The stats options "mse" and "rmse" are only available for:
the traditional projection,
the latent projection with resp_oscale = FALSE,
the latent projection with resp_oscale = TRUE in combination with
<refmodel>$family$cats being NULL.
The stats option "acc" (= "pctcorr") is only available for:
the binomial() family in case of the traditional projection,
all families in case of the augmented-data projection,
the binomial() family (on the original response scale) in case of the
latent projection with resp_oscale = TRUE in combination with
<refmodel>$family$cats being NULL,
all families (on the original response scale) in case of the latent
projection with resp_oscale = TRUE in combination with
<refmodel>$family$cats being not NULL.
The stats option "auc" is only available for:
the binomial() family in case of the traditional projection,
the binomial() family (on the original response scale) in case of the
latent projection with resp_oscale = TRUE in combination with
<refmodel>$family$cats being NULL.
# Data:
dat_gauss <- data.frame(y = df_gaussian$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)
print(summary(vs), digits = 1)
#>
#> Family: gaussian
#> Link function: identity
#>
#> Formula: y ~ X1 + X2 + X3 + X4 + X5
#> Observations: 100
#> Projection method: traditional
#> Search method: L1
#> Maximum submodel size for the search: 3
#> Number of projected draws in the search: 1 (from clustered projection)
#> Number of projected draws in the performance evaluation: 10 (from clustered projection)
#> Argument `refit_prj`: TRUE
#>
#> Submodel performance evaluation summary with `deltas = FALSE` and `cumulate = FALSE`:
#> size ranking_fulldata cv_proportions_diag elpd elpd.se elpd.diff elpd.diff.se
#> 0 (Intercept) NA -249 5 -39.1 5.8
#> 1 X1 NA -231 6 -20.5 4.5
#> 2 X5 NA -220 6 -9.7 3.4
#> 3 X3 NA -211 7 -0.4 0.9
#>
#> Reference model performance evaluation summary with `deltas = FALSE`:
#> elpd elpd.se
#> -210 7