Multivariate analysis of covariance for heterogeneous and incomplete data.

This article discusses the robustness of the multivariate analysis of covariance (MANCOVA) test for an emergent variable system and proposes a modification of this test to obtain adequate information from heterogeneous normal observations. The proposed approach for testing potential effects in heterogeneous MANCOVA models can be adopted effectively, regardless of the degree of heterogeneity and sample size imbalance. As our method was not designed to handle missing values, we also show how to derive the formulas for pooling the results of multiple-imputation-based analyses into a single final estimate.

Multilevel bootstrap analysis with assumptions violated.

Background: Likelihood-based methods can work poorly when the residuals are not normally distributed and the variances across clusters are heterogeneous.

Method: The performance of two estimation methods, the non-parametric residual bootstrap (RB) and the restricted maximum likelihood (REML) for fitting multilevel models are compared through simulation studies in terms of bias, coverage, and precision.

Results: We find that (a) both methods produce unbiased estimates of the fixed parameters, but biased estimates of the random parameters, although the REML was more prone to give biased estimates for the variance components; (b) the RB method yields substantial reductions in the difference between nominal and actual confidence interval coverage, compared with the REML method; and (c) for the square root of the mean squared error (RMSE) of the fixed effects, the RB method performed slightly better than the REML method.

[Generalization of the Brown-Forsythe approach to factorial designs].

The current paper proposes a solution that generalizes ideas of Brown and Forsythe to the problem of comparing hypotheses in two-way classification designs with heteroscedastic error structure. Unlike the standard analysis of variance, the proposed approach does not require the homogeneity assumption. A comprehensive simulation study, in which sample size of the cells, relationship between the cell sizes and unequal variance, degree of variance heterogeneity, and population distribution shape were systematically manipulated, shows that the proposed approximation was generally robust when normality and heterogeneity were jointly violated.