On variable selection in joint modeling of mean and dispersion

TL;DR

This paper introduces a new variable selection procedure for joint modeling of mean and dispersion, improving model accuracy and robustness in experimental design by combining hypothesis testing with fit quality criteria.

Contribution

The paper proposes a novel variable selection method for JMMD based on hypothesis testing and fit quality, addressing a gap in existing literature.

Findings

The procedure is effective across various simulation scenarios.

It outperforms existing methods in selecting relevant variables.

Application to real industrial data demonstrates practical utility.

Abstract

The joint modeling of mean and dispersion (JMMD) provides an efficient method to obtain useful models for the mean and dispersion, especially in problems of robust design experiments. However, in the literature on JMMD there are few works dedicated to variable selection and this theme is still a challenge. In this article, we propose a procedure for selecting variables in JMMD, based on hypothesis testing and the quality of the model's fit. A criterion for checking the goodness of fit is used, in each iteration of the selection process, as a filter for choosing the terms that will be evaluated by a hypothesis test. Three types of criteria were considered for checking the quality of the model fit in our variable selection procedure. The criteria used were: the extended Akaike information criterion, the corrected Akaike information criterion and a specific criterion for the JMMD, proposed by us, a type of extended adjusted coefficient of determination. Simulation studies were carried out to verify the efficiency of our variable selection procedure. In all situations considered, the proposed procedure proved to be effective and quite satisfactory. The variable selection process was applied to a real example from an industrial experiment.