The selection step with the input of the solution paths.

A function to select the relevant predictors by partitioning the solution paths (the SPSP algorithm) based on the user provided solution paths BETA.

Usage

SPSP_step(
  x,
  y,
  family = c("gaussian", "binomial"),
  BETA,
  standardize = TRUE,
  intercept = TRUE,
  init = 1,
  R = NULL,
  ...
)

Arguments

x: independent variables as a matrix, of dimension nobs x nvars; each row is an observation vector.
y: response variable. Quantitative for family="gaussian" or family="poisson" (non-negative counts). For family="binomial" should be either a factor with two levels.
family: either a character string representing one of the built-in families, or else a glm() family object.
BETA: the solution paths obtained from a prespecified fitting step fitfun.SP = lasso.glmnet etc. It must be a p by k matrix, should be thicker and thicker, each column corresponds to a lambda, and lambda gets smaller and smaller. It is the returned coefficient matrix beta from a glmnet object, or a ncvreg object.
standardize: whether need standardization.
intercept: logical. If x is a data.frame, this argument determines if the resulting model matrix should contain a separate intercept or not.
init: initial coefficients, starting from init-th estimator of the solution paths. The default is 1.
R: sorted adjacent distances, default is NULL. Will be calculated inside.
...: Additional optional arguments.

Value

A list containing at least the following components:

beta_SPSP: the estimated coefficients of SPSP selected model;
S0: the estimated relevant sets;
nonzero: the selected covariates;
zero: the covariates that are not selected;
thres: the boundaries for abs(beta);
R: the sorted adjacent distances;
intercept: the estimated intercept when intercept == T.

This object has attribute contains:

mod.fit: the fitted penalized regression within the input function fitfun.SP;
family: the family of fitted object;
fitfun.SP: the function to obtain the solution paths for the SPSP algorithm;
args.fitfun.SP: a named list containing additional arguments for the function fitfun.SP.

Examples

data(HighDim)
library(glmnet)

x <- as.matrix(HighDim[,-1])
y <- HighDim[,1]

lasso_fit <- glmnet(x = x, y = y, alpha = 1, intercept = FALSE)

# SPSP+Lasso method
K <- dim(lasso_fit$beta)[2]
LBETA <- as.matrix(lasso_fit$beta)

spsp_lasso_1 <- SPSP_step(x = x, y = y, BETA = LBETA, 
                          init = 1, standardize = FALSE, intercept = FALSE)
head(spsp_lasso_1$nonzero)
#> [1] "X1" "X2" "X3"
head(spsp_lasso_1$beta_SPSP)
#>       X1       X2       X3       X4       X5       X6 
#> 3.034047 2.042406 1.473175 0.000000 0.000000 0.000000