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 heterogene ous MANCOVA models can be adopted effectively, regardless of the degree of heterogeneity and sam ple 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 esti mate. Results of simulated studies and analysis of real-data show that the proposed combining rules pro vide adequate coverage and power. Based on the current evidence, the two solutions suggested could be effectively used by researchers for testing hypotheses, provided that the data conform to normality. Translational Abstract Multivariate analysis of variance (MANOVA) is the analysis strategy usually chosen in Psychological and Educational research to test the effect of an intervention on a set of dependent variables that are related. Three aspects are common in applied research: First, intervention is determined by the combina tion of more than one variable and, therefore, the design structure is factorial. Second, either if research is framed in a quasi-experimental or an experimental methodology, it is often needed to control the effect of other present variables to reduce the error variance and increase the effect of the intervention variables and their interaction, or for both reasons; thus, increasing the strength of the test. In this case MANCOVA will be used. Third, when for different reasons, the size of the groups is not the same, the response of the subjects in the different intervention conditions is not homogeneous and data loss occurs, MANCOVA analysis does not provide valid statistical inferences. In the present research, a modification of MANCOVA is developed to test the hypotheses of a factorial model and obtain adequate information regardless of the degree of heterogeneity and the imbalance of groups size. It is assumed that the interrelated system of observed variables is the causal agent of the underlying (or emergent) construct, not the other way around. To deal with missing data, formulas are developed to group the results of the analysis into a single final estimate after multiple imputation has been done. Both developments are studied by simulation, and it is concluded that they can be used with full guaran tees. An example is shown. © 2023 American Psychological Association