Hypothesis tests for multiple responses regression models in R: The htmcglm Package

This article describes the R package htmcglm implemented for performing hypothesis tests on regression and dispersion parameters of multivariate covariance generalized linear models (McGLMs). McGLMs provide a general statistical modeling framework for normal and non-normal multivariate data analysis along with a wide range of correlation structures. The proposed package considers the Wald statistics to perform general hypothesis tests and build tailored ANOVAs, MANOVAs and multiple comparison tests. The goal of the package is to provide tools to improve the interpretation of regression and dispersion parameters. We assess the effects of the covariates on the response variables by testing the regression coefficients. Similarly, we perform tests on the dispersion coefficients in order to assess the correlation between study units. It could be of interest in situations where the data observations are correlated with each other, such as in longitudinal, times series, spatial and repeated measures studies. The htmcglm package provides a user friendly interface to perform MANOVA like tests as well as multivariate hypothesis tests for models of the mcglm class. We describe the package implementation and illustrate it through the analysis of two data sets. The first deals with an experiment on soybean yield; the problem has three response variables of different types (continuous, counting and binomial) and three explanatory variables (amount of water, fertilization and block). The second dataset addresses a problem where responses are longitudinal bivariate counts of hunting animals; the explanatory variables used are the hunting method and sex of the animal. With these examples we were able to illustrate several tests in which the proposal proves to be useful for the evaluation of regression and dispersion parameters both in problems with dependent or independent observations.