Fit a ranked-sparsity model with forward stepwise RBIC (experimental)

Usage

sparseRBIC_step(
  formula,
  data,
  family = c("gaussian", "binomial", "poisson"),
  k = 1,
  poly = 1,
  ic = c("RBIC", "RAIC", "BIC", "AIC", "EBIC"),
  hier = c("strong", "weak", "none"),
  sequential = (hier[1] != "none"),
  cumulative_k = FALSE,
  cumulative_poly = TRUE,
  pool = FALSE,
  ia_formula = NULL,
  pre_process = TRUE,
  model_matrix = NULL,
  y = NULL,
  poly_prefix = "_poly_",
  int_sep = "\\:",
  pre_proc_opts = c("knnImpute", "scale", "center", "otherbin", "none"),
  filter = c("nzv", "zv"),
  extra_opts = list(),
  trace = 0,
  message = TRUE,
  ...
)

Arguments

formula: Names of the terms
data: Data
family: The family of the model
k: The maximum order of interactions to consider
poly: The maximum order of polynomials to consider
ic: The information criterion to use
hier: Should hierarchy be enforced (weak or strong)? Must be set with sequential == TRUE (see details)
sequential: Should the main effects be considered first, orders sequentially added/considered?
cumulative_k: Should penalties be increased cumulatively as order interaction increases?
cumulative_poly: Should penalties be increased cumulatively as order polynomial increases?
pool: Should interactions of order k and polynomials of order k+1 be pooled together for calculating the penalty?
ia_formula: formula to be passed to step_interact via terms argument
pre_process: Should the data be preprocessed (if FALSE, must provide model_matrix)
model_matrix: A data frame or matrix specifying the full model matrix (used if !pre_process)
y: A vector of responses (used if !pre_process)
poly_prefix: If model_matrix is specified, what is the prefix for polynomial terms?
int_sep: If model_matrix is specified, what is the separator for interaction terms?
pre_proc_opts: List of preprocessing steps (see details)
filter: The type of filter applied to main effects + interactions
extra_opts: A list of options for all preprocess steps (see details)
trace: Should intermediate results of model selection process be output
message: should experimental message be suppressed
...: additional arguments for running stepwise selection

Value

an object of class sparseRBIC containing the following:

fit: the final fit object
srprep: a recipes object used to prep the data
pen_info: coefficient-level variable counts, types + names
data: the (unprocessed) data
family: the family argument (for non-normal, eg. poisson)
info: a list containing meta-info about the procedure
stats: the IC for each fit and respective terms included

Details

This function mirrors sparseR but uses stepwise selection guided by RBIC.

Additionally, setting cumulative_poly or cumulative_k to TRUE increases the penalty cumulatively based on the order of either polynomial or interaction.

The hier hierarchy enforcement will only work if sequential == TRUE, and notably will only consider the "first gen" hierarchy, that is, that all main effects which make up an interaction are already in the model. It is therefore possible for a third order interaction (x1:x2:x3) to enter a model without x1:x2 or x2:x3, so long as x1, x2, and x3 are all in the model.

The options that can be passed to pre_proc_opts are:

knnImpute (should missing data be imputed?)
scale (should data be standardized)?
center (should data be centered to the mean or another value?)
otherbin (should factors with low prevalence be combined?)
none (should no preprocessing be done? can also specify a null object)

The options that can be passed to extra_opts are:

centers (named numeric vector which denotes where each covariate should be centered)
center_fn (alternatively, a function can be specified to calculate center such as min or median)
freq_cut, unique_cut (see ?step_nzv - these get used by the filtering steps)
neighbors (the number of neighbors for knnImpute)
one_hot (see ?step_dummy), this defaults to cell-means coding which can be done in regularized regression (change at your own risk)
raw (should polynomials not be orthogonal? defaults to true because variables are centered and scaled already by this point by default)