The relations among several alternative parameterizations of the binary factor analysis model and the 2-parameter item response theory model are discussed. It is pointed out that different parameterizations of factor analysis model parameters can be transformed into item response model theory parameters, and general formulas are provided.…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…

This study analyzes latent change scores using latent curve models (LCMs) for evaluation research with pre-post-post designs. The article extends a recent article by Willoughby, Vandergrift, Blair, and Granger (2007) on the use of LCMs for studies with pre-post-post designs, and demonstrates that intervention effects can be better tested using…

We propose a method to investigate measurement invariance in the multigroup exploratory factor model, subject to target rotation. We consider both oblique and orthogonal target rotation. This method has clear advantages over other approaches, such as the use of congruence measures. We demonstrate that the model can be implemented readily in the…

This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand…

In 1959, Campbell and Fiske introduced the use of multitrait-multimethod (MTMM) matrices in psychology, and for the past 4 decades confirmatory factor analysis (CFA) has commonly been used to analyze MTMM data. However, researchers do not always fit CFA models when MTMM data are available; when CFA modeling is used, multiple models are available…

Incomplete nonnormal data are common occurrences in applied research. Although these 2 problems are often dealt with separately by methodologists, they often cooccur. Very little has been written about statistics appropriate for evaluating models with such data. This article extends several existing statistics for complete nonnormal data to…

In the last decades there has been an increasing interest in nonlinear latent variable models. Since the seminal paper of Kenny and Judd, several methods have been proposed for dealing with these kinds of models. This article introduces an alternative approach. The methodology involves fitting some third-order moments in addition to the means and…

Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when a simple model is needed to describe nonlinear change, or when the purpose of the analysis is to evaluate hypotheses about change occurring during a particular period of time within a model for a longer overall time frame, such as…

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…

In longitudinal studies, investigators often measure multiple variables at multiple time points and are interested in investigating individual differences in patterns of change on those variables. Furthermore, in behavioral, social, psychological, and medical research, investigators often deal with latent variables that cannot be observed directly…

Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and…

Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is…

Researchers often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model. It is currently not possible to test these so-called informative hypotheses in structural equation modeling software. We offer a solution to this problem using M"plus." The hypotheses are…