trim.constraints: Trimmed Constraint Matrices

Description

Deletes statistically nonsignficant regression coefficients via their constraint matrices, for future refitting.

Usage

trim.constraints(object, sig.level = 0.05, max.num = Inf,
                 intercepts = TRUE, ...)

Arguments

Value

A list of possibly simpler constraint matrices that can be fed back into the model using the

constraints argument (usually zero = NULL is needed to avoid a warning). Consequently, they are required to be of the "term"-type. After the model is refitted, applying

summaryvglm should result in regression coefficients that are `all' statistically significant.

Details

This utility function is intended to simplify an existing vglm object having variables (terms) that affect unnecessary parameters. Suppose the explanatory variables in the formula includes a simple numeric covariate called x2. This variable will affect every linear predictor if zero = NULL in the VGAM family function. This situation may correspond to the constraint matrices having unnecessary columns because their regression coefficients are statistically nonsignificant. This function attempts to delete those columns and return a possibly simplified list of constraint matrices that can make refitting a simpler model easy to do. P-values obtained from summaryvglm (with HDEtest = FALSE for increased speed) are compared to sig.level to test for statistical significance.

For terms that generate more than one column of the "lm" model matrix, such as bs and poly, the column is deleted if all regression coefficients are statistically nonsignificant. Incidentally, users should instead use sm.bs, sm.ns, sm.poly, etc., for smart and safe prediction.

One can think of this function as facilitating backward elimination for variable selection, especially if max.num = 1 and \(M=1\), however usually more than one regression coefficient is deleted here by default.

Examples

Run this code

if (FALSE)  data("xs.nz", package = "VGAMdata")
fit1 <-
  vglm(cbind(worry, worrier) ~ bs(age) + sex + ethnicity + cat + dog,
       binom2.or(zero = NULL), data = xs.nz, trace = TRUE)
summary(fit1, HDEtest = FALSE)  # 'cat' is not significant at all
dim(constraints(fit1, matrix = TRUE))
(tclist1 <- trim.constraints(fit1))  # No 'cat'
fit2 <-  # Delete 'cat' manually from the formula:
  vglm(cbind(worry, worrier) ~ bs(age) + sex + ethnicity +       dog,
       binom2.or(zero = NULL), data = xs.nz,
       constraints = tclist1, trace = TRUE)
summary(fit2, HDEtest = FALSE)  # A simplified model
dim(constraints(fit2, matrix = TRUE))  # Fewer regression coefficients