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…

The root mean square error of approximation (RMSEA) is one of the most widely reported measures of misfit/fit in applications of structural equation modeling. When the RMSEA is of interest, so too should be the accompanying confidence interval. A narrow confidence interval reveals that the plausible parameter values are confined to a relatively…

Maxwell, Cole, and Mitchell (2011) extended the work of Maxwell and Cole (2007), which raised important questions about whether mediation analyses based on cross-sectional data can shed light on longitudinal mediation process. The latest article considers longitudinal processes that can only be partially explained by an intervening variable, and…

A method for selecting between K-dimensional linear factor models and (K + 1)-class latent profile models is proposed. In particular, it is shown that the conditional covariances of observed variables are constant under factor models but nonlinear functions of the conditioning variable under latent profile models. The performance of a convenient…

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…

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing…

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for 1 group of people versus another, irrespective of mean differences on the construct. This study focuses on the use of multiple-indicator multiple-cause (MIMIC) structural equation models for DIF testing, parameterized as item…

The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification…

Examined several hypotheses about the suitability of the noncentral chi square in applied research using Monte Carlo simulation experiments with seven sample sizes and three distinct model types, each with five specifications. Results show that, in general, for models with small to moderate misspecification, the noncentral chi-square is well…

The search for cut-off criteria of fit indices for model fit evaluation (e.g., Hu & Bentler, 1999) assumes that these fit indices are sensitive to model misspecification, but not to different types of models. If fit indices were sensitive to different types of models that are misspecified to the same degree, it would be very difficult to establish…

Sample size recommendations in confirmatory factor analysis (CFA) have recently shifted away from observations per variable or per parameter toward consideration of model quality. Extending research by Marsh, Hau, Balla, and Grayson (1998), simulations were conducted to determine the extent to which CFA model convergence and parameter estimation…

Bifactor and second-order factor models are two alternative approaches for representing general constructs comprised of several highly related domains. Bifactor and second-order models were compared using a quality of life data set (N = 403). The bifactor model identified three, rather than the hypothesized four, domain specific factors beyond the…