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 models 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.
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