This function can suggest an appropriate submodel size based on a decision
rule described in section "Details" below. Note that this decision is quite
heuristic and should be interpreted with caution. It is recommended to
examine the results via plot.vsel(), cv_proportions(),
plot.cv_proportions(), and/or summary.vsel() and to make the final
decision based on what is most appropriate for the problem at hand.
Usage
suggest_size(object, ...)
# S3 method for class 'vsel'
suggest_size(
object,
stat = "elpd",
pct = 0,
type = "upper",
thres_elpd = NA,
warnings = TRUE,
...
)Arguments
- object
An object of class
vsel(returned byvarsel()orcv_varsel()).- ...
Arguments passed to
summary.vsel(), except forobject,stats(which is set tostat),type, anddeltas(which is set toTRUE). See section "Details" below for some important arguments which may be passed here.- stat
Performance statistic (i.e., utility or loss) used for the decision. See argument
statsofsummary.vsel()andplot.vsel()for possible choices.- pct
A number giving the proportion (not percents) of the relative null model utility one is willing to sacrifice. See section "Details" below for more information.
- type
Either
"upper"or"lower"determining whether the decision is based on the upper or lower uncertainty interval bound, respectively. See section "Details" below for more information.- thres_elpd
Only relevant if
stat %in% c("elpd", "mlpd", "gmpd")). The threshold for the ELPD difference (taking the submodel's ELPD minus the baseline model's ELPD) above which the submodel's ELPD is considered to be close enough to the baseline model's ELPD. An equivalent rule is applied in case of the MLPD and the GMPD. See section "Details" for a formalization. SupplyingNAdeactivates this.- warnings
Mainly for internal use. A single logical value indicating whether to throw warnings if automatic suggestion fails. Usually there is no reason to set this to
FALSE.
Value
A single numeric value, giving the suggested submodel size (or NA
if the suggestion failed).
The intercept is not counted by suggest_size(), so a suggested size of
zero stands for the intercept-only model.
Details
In general (beware of special cases below), the suggested model
size is the smallest model size \(j \in \{0, 1, ...,
\texttt{nterms\_max}\}\) for which either the
lower or upper bound (depending on argument type) of the uncertainty
interval (with nominal coverage 1 - alpha; see argument alpha of
summary.vsel()) for \(U_j - U_{\mathrm{base}}\) (with
\(U_j\) denoting the \(j\)-th submodel's true utility and
\(U_{\mathrm{base}}\) denoting the baseline model's true utility)
falls above (or is equal to) $$\texttt{pct} \cdot (u_0 -
u_{\mathrm{base}})$$ where \(u_0\) denotes the null
model's estimated utility and \(u_{\mathrm{base}}\) the baseline
model's estimated utility. The baseline model is either the reference model
or the best submodel found (see argument baseline of summary.vsel()).
In doing so, loss statistics like the root mean squared error (RMSE) and
the mean squared error (MSE) are converted to utilities by multiplying them
by -1, so a call such as suggest_size(object, stat = "rmse", type = "upper") finds the smallest model size whose upper uncertainty interval
bound for the negative RMSE or MSE exceeds (or is equal to) the cutoff
(or, equivalently, has the lower uncertainty interval bound for the RMSE or
MSE below—or equal to—the cutoff). This is done to make the
interpretation of argument type the same regardless of argument stat.
For the geometric mean predictive density (GMPD), the decision rule above
is applied on log() scale. In other words, if the true GMPD is denoted by
\(U^\ast_j\) for the \(j\)-th submodel and
\(U^\ast_{\mathrm{base}}\) for the baseline model (so that
\(U_j\) and \(U_{\mathrm{base}}\) from above are given by
\(U_j = \log(U^\ast_j)\) and
\(U_{\mathrm{base}} = \log(U^\ast_{\mathrm{base}})\)), then suggest_size() yields the smallest model size whose
lower or upper (depending on argument type) uncertainty interval bound
for \(\frac{U^\ast_j}{U^\ast_{\mathrm{base}}}\) exceeds
(or is equal to)
$$(\frac{u^\ast_0}{u^\ast_{\mathrm{base}}})^{\texttt{pct}}$$ where \(u^\ast_0\) denotes the null
model's estimated GMPD and \(u^\ast_{\mathrm{base}}\) the
baseline model's estimated GMPD.
If !is.na(thres_elpd) and stat = "elpd", the decision rule above is
extended: The suggested model size is then the smallest model size \(j\)
fulfilling the rule above or \(u_j - u_{\mathrm{base}} >
\texttt{thres\_elpd}\). Correspondingly, in case
of stat = "mlpd" (and !is.na(thres_elpd)), the suggested model size is
the smallest model size \(j\) fulfilling the rule above or \(u_j -
u_{\mathrm{base}} > \frac{\texttt{thres\_elpd}}{N}\) with \(N\) denoting the number of observations.
Correspondingly, in case of stat = "gmpd" (and !is.na(thres_elpd)), the
suggested model size is the smallest model size \(j\) fulfilling the rule
above or \(\frac{u^\ast_j}{u^\ast_{\mathrm{base}}} >
\exp(\frac{\texttt{thres\_elpd}}{N})\).
For example (disregarding the special extensions in case of
!is.na(thres_elpd) with stat %in% c("elpd", "mlpd", "gmpd")), alpha = 2 * pnorm(-1), pct = 0, and type = "upper" means that we select the
smallest model size for which the upper bound of the 1 - 2 * pnorm(-1)
(approximately 68.3 %) uncertainty interval for \(U_j -
U_{\mathrm{base}}\)
(\(\frac{U^\ast_j}{U^\ast_{\mathrm{base}}}\) in case of
the GMPD) exceeds (or is equal to) zero (one in case of the GMPD), that is
(if stat is a performance statistic for which a normal-approximation
uncertainty interval is used, see argument stats of summary.vsel() and
plot.vsel()), for which the submodel's utility estimate is at most one
standard error smaller than the baseline model's utility estimate (with
that standard error referring to the utility difference).
Apart from the two summary.vsel() arguments mentioned above (alpha and
baseline), resp_oscale is another important summary.vsel() argument
that may be passed via ....
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)
print(suggest_size(vs))
#> [1] 3