Fit a ranked-sparsity model with regularized regression

Usage

sparseR(
  formula,
  data,
  family = c("gaussian", "binomial", "poisson", "coxph"),
  penalty = c("lasso", "MCP", "SCAD"),
  alpha = 1,
  ncvgamma = 3,
  lambda.min = 0.005,
  k = 1,
  poly = 1,
  gamma = 0.5,
  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(),
  ...
)

Arguments

formula: Names of the terms
data: Data
family: The family of the model
penalty: What penalty should be used (lasso, MCP, or SCAD)
alpha: The mix of L1 penalty (lower values introduce more L2 ridge penalty)
ncvgamma: The tuning parameter for ncvreg (for MCP or SCAD)
lambda.min: The minimum value to be used for lambda (as ratio of max, see ?ncvreg)
k: The maximum order of interactions to consider
poly: The maximum order of polynomials to consider
gamma: The degree of extremity of sparsity rankings (see details)
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 (for interactions, see details)
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)
...: Additional arguments (passed to fitting function)

Value

an object of class sparseR containing the following:

fit: the fit object returned by ncvreg
srprep: a recipes object used to prep the data
pen_factors: the factor multiple on penalties for ranked sparsity
results: all coefficients and penalty factors at minimum CV lambda
results_summary: a tibble of summary results at minimum CV lambda
results1se: all coefficients and penalty factors at lambda_1se
results1se_summary: a tibble of summary results at lambda_1se
data: the (unprocessed) data
family: the family argument (for non-normal, eg. poisson)
info: a list containing meta-info about the procedure

Details

Selecting gamma: higher values of gamma will penalize "group" size more. By default, this is set to 0.5, which yields equal contribution of prior information across orders of interactions/polynomials (this is a good default for most settings).

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

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)

ia_formula will by default interact all variables with each other up to order k. If specified, ia_formula will be passed as the terms argument to recipes::step_interact, so the help documentation for that function can be investigated for further assistance in specifying specific interactions.

References

For fitting functionality, the ncvreg package is used; see Breheny, P. and Huang, J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Ann. Appl. Statist., 5: 232-253.