hellwig: Hellwig's method for choosing an optimal subset of predictors

In mbojan/mbstats: Michal's Beautiful Selection of Totally Awesome and Trustworthy Statistical functions

Description

Hellwig's method selects a subset of predictors in a linear model such that they are correlated with the response but relatively uncorrelated among each other.

Usage

hellwig(y, x, method = "pearson")

Arguments

y	numeric, response variable
x	numeric matrix of predictors
method	character, type of correlation measures used, passed to cor()

Details

Given m predictors Hellwig's method consists of evaluating all 2^m - 1 combinations using the following steps:

1. Individual capacity of a predictor variable in a subset is given by:

   h_kj = r_0j^2 / sum_{i \in I} r_ij

   where r_0j is correlation of j-th predictor with the response variable, r_ij is a correlation i-th and j-th predictors, and I is the set of predictors under consideration.

2. Integral capacity of information for every combination k is equal to:

   H_k = sum_j h_kj

The subset with the highest value of H_k should be selected.

Value

Data frame with two columns:

• k – combination of predictor variables in the form of x-y-z where x, y, z... are the indices of columns in x, and

• h – the capacity of the subset H_k.

Examples

set.seed(1234)
x <- matrix(rnorm(1000), 250, 4)
y <- rnorm(250)
hellwig(y, x)

mbojan/mbstats documentation built on Dec. 21, 2021, 3:56 p.m.