lmSelect_fit: Best-subset regression

In lmSubsets: Exact Variable-Subset Selection in Linear Regression

Description

Low-level interface to best-variable-subset selection in ordinary linear regression.

Usage

lmSelect_fit(x, y, weights = NULL, offset = NULL, include = NULL,
             exclude = NULL, penalty = "BIC", tolerance = 0,
             nbest = 1, ..., pradius = NULL)

Arguments

x	double[,]—the model matrix
y	double[]—the model response
weights	double[]—the model weights
offset	double[]—the model offset
include	logical[], integer[], character[]—the regressors to force in
exclude	logical[], integer[], character[]—the regressors to force out
penalty	double, character, "function"—the penalty per model parameter
tolerance	double—the approximation tolerance
nbest	integer—the number of best subsets
...	ignored
pradius	integer—the preordering radius

Details

The best variable-subset model is determined, where the "best" model is the one with the lowest information criterion value. The information criterion belongs to the AIC family.

The regression data is specified with the x, y, weights, and offset parameters. See lm.fit() for further details.

To force regressors into or out of the regression, a list of regressors can be passed as an argument to the include or exclude parameters, respectively.

The information criterion is specified with the penalty parameter. Accepted values are "AIC", "BIC", or a "numeric" value representing the penalty-per-model-parameter. A custom selection criterion may be specified by passing an R function as an argument. The expected signature is function (size, rss), where size is the number of predictors (including the intercept, if any), and rss is the residual sum of squares. The function must be non-decreasing in both parameters.

An approximation tolerance can be specified to speed up the search.

The number of returned submodels is determined by the nbest parameter.

The preordering radius is given with the pradius parameter.

Value

A list with the following components:

NOBS	integer—number of observations in model (before weights processing)
nobs	integer—number of observations in model (after weights processing)
nvar	integer—number of regressors in model
weights	double[]—model weights
intercept	logical—is TRUE if model contains an intercept term, FALSE otherwise
include	logical[]—regressors forced into the regression
exclude	logical[]—regressors forced out of the regression
size	integer[]—subset sizes
ic	information criterion
tolerance	double—approximation tolerance
nbest	integer—number of best subsets
submodel	"data.frame"—submodel information
subset	"data.frame"—selected subsets

References

Hofmann M, Gatu C, Kontoghiorghes EJ, Colubi A, Zeileis A (2020). lmSubsets: Exact variable-subset selection in linear regression for R. Journal of Statistical Software, 93, 1–21. doi: 10.18637/jss.v093.i03.

See Also

• lmSelect() for the high-level interface

• lmSubsets_fit() for all-subsets regression

Examples

data("AirPollution", package = "lmSubsets")

x <- as.matrix(AirPollution[, names(AirPollution) != "mortality"])
y <-           AirPollution[, names(AirPollution) == "mortality"]

f <- lmSelect_fit(x, y)
f

lmSubsets documentation built on Feb. 8, 2021, 1:06 a.m.