Sufficient sample sizes for the multivariate multilevel regression model
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The three-level multivariate multilevel model (MVMM) is a multivariate extension of the conventional univariate two-level hierarchical linear model (HLM) and is used for estimating and testing the effects of explanatory variables on a set of correlated continuous outcome measures. Two simulation studies were conducted to investigate the sample size requirements for restricted maximum likelihood (REML) estimation of three-level MVMMs, the effects of sample sizes and other design characteristics on estimation, and the performance of the MVMMs compared to corresponding two-level HLMs. The model for the first study was a random-intercept MVMM, and the model for the second study was a fully-conditional MVMM. Study conditions included number of clusters, cluster size, intraclass correlation coefficient, number of outcomes, and correlations between pairs of outcomes. The accuracy and precision of estimates were assessed with parameter bias, relative parameter bias, relative standard error bias, and 95% confidence interval coverage. Empirical power and type I error rates were also calculated. Implications of the results for applied researchers and suggestions for future methodological studies are discussed.