The welchADF Package for Robust Hypothesis Testing in Unbalanced Multivariate Mixed Models with Heteroscedastic and Non-normal Data

A new R package is presented for dealing with non-normality and variance heterogeneity of sample data when conducting hypothesis tests of main effects and interactions in mixed models. The proposal departs from an existing SAS program which implements Johansen’s general formulation of Welch-James’s statistic with approximate degrees of freedom, which makes it suitable for testing any linear hypothesis concerning cell means in univariate and multivariate mixed model designs when the data pose non-normality and non-homogeneous variance. Improved type I error rate control is obtained using bootstrapping for calculating an empirical critical value, whereas robustness against non-normality is achieved through trimmed means and Winsorized variances. A wrapper function eases the application of the test in common situations, such as performing omnibus tests on all effects and interactions, pairwise contrasts, and tetrad contrasts of two-way interactions. The package is demonstrated in several problems including unbalanced univariate and multivariate designs.