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

Abstract

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.

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“…Moreover, some of the patients completed the CR programme earlier (due to the change in the experimental criteria) and we experienced sensor failures within some of the sessions, hence, we have incomplete (missing) data. Thus, we apply Johansen's (Johansen, 1980 ) general formulation of Welch (Welch, 1938 )-James (James, 1951 )'s statistic with Approximate Degrees of Freedom (ADF) (Welch, 1951 ; Keselman et al, 2003 ; Villacorta, 2017 ), which is suitable for non-parametric repeated measures and two-way mixed design (within-subject factor is stages and between-subject factor is condition). The results of the two-way mixed design are reported for stage and condition effects, and their interaction (whether the effect of condition, depends on the stage).…”

“…We also report the significant differences between conditions for each stage, and the pairwise significant differences between stages for each condition for analyzing longitudinal effects. Hochberg correction for multiple comparisons (pairwise tests) and Least-Squares Estimators (i.e., trimming is not applied on the data) are used, which are the default parameters of the welchADF test in R (Villacorta, 2017 ) 11 . The results are reported in the format T WJ ( df 1 , df 2 ) for the Welch-James ADF test statistic, where df 1 and df 2 are the approximate degrees of freedom for the numerator and denominator, in addition to the p -values.…”

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“…This robust estimator uses trimmed means and winsorized variances to avoid biases derived from heteroscedasticity. Bootstrapping was used to calculate empirical p-values both for between group and pairwise comparisons[31], with the help of WelchADF R package[32].…”