Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Maxwell, Cole, and Mitchell (2011) demonstrated that simple structural equation models, when used with cross-sectional data, generally produce biased estimates of meditated effects. I extend those results by showing how simple structural equation models can produce biased estimates of meditated effects when used even with longitudinal data. Even…

Experiments that involve nested structures may assign treatment conditions either to entire groups (such as classrooms or schools) or individuals within groups (such as students). Although typically the interest in field experiments is in determining the significance of the overall treatment effect, it is equally important to examine the…

Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes ("N"), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for "N" below 50. Simulations were carried out to estimate the minimum required "N" for different…

Alternative strategies for two-sample cross-validation of covariance structure models are described and investigated. Results of an empirical sampling study show that for tighter strategies simpler models are preferred in smaller samples, but when cross-validation is employed, a more complex model is supported even for small samples. (SLD)

The sampling distributions of five popular measures of association with and without two bias adjusting methods were examined for the single factor fixed-effects multivariate analysis of variance model. The number of groups, sample sizes, number of outcomes, and the strength of association were manipulated. The results indicate that all five…

This article compares two methods for analyzing small sets of repeated measures data under normal and non-normal heteroscedastic conditions: a mixed model approach with the Kenward-Roger correction and a multivariate extension of the modified Brown-Forsythe (BF) test. These procedures differ in their assumptions about the covariance structure of…

Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or…

A strategy for evaluating/modifying covariance structure models (CSMs) is presented. The approach uses recent developments in estimation under nonstandard conditions and unified asymptotic theory related to hypothesis testing, and it determines the extent of sample size sensitivity and specification error effects by relying on existing statistical…