Type I Error and Power of Latent Mean Methods and MANOVA in Factorially Invariant and Noninvariant Latent Variable Systems

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Abstract
This article addresses the issue of Type I error rates and relative power of structured means, multiple-indicator multiple-cause, and multivariate analysis of variance approaches for testing construct mean differences within a one-factor, two-group design. This study crosses 3 dimensions factorially: group sample size (n = 100, 200, 400, 800), factor loading pattern (8 variations), and factor mean difference (Delta kappa = .2,. 5, .8). Cases addressed include those where all factor loadings in both groups are equal, where loadings differ within a factor but are the same across groups, and where factor loadings differ across groups. Type I error rates are investigated using Monte Carlo simulation methods, while a population analysis approach is used to assess power of modeling and multivariate analysis of variance methods.