Molenaar (2003, 2011) showed that a common factor model could be transformed into an equivalent model without factors, involving only observed variables and residual errors. He called this invertible transformation the Houdini transformation. His derivation involved concepts from time series and state space theory. This article verifies the…

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo…

Strategies for modeling mediation effects in multilevel data have proliferated over the past decade, keeping pace with the demands of applied research. Approaches for testing mediation hypotheses with 2-level clustered data were first proposed using multilevel modeling (MLM) and subsequently using multilevel structural equation modeling (MSEM) to…

We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of "rates of change" and "acceleration" in latent growth curves--information available indirectly through traditional growth…

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

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…

In many psychological questionnaires the need to analyze empirical data raises the fundamental problem of possible fake or fraudulent observations in the data. This aspect is particularly relevant for researchers working on sensitive topics such as, for example, risky sexual behaviors and drug addictions. Our contribution presents a new…

Mediation analysis uses measures of hypothesized mediating variables to test theory for how a treatment achieves effects on outcomes and to improve subsequent treatments by identifying the most efficient treatment components. Most current mediation analysis methods rely on untested distributional and functional form assumptions for valid…

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model…

Maxwell and Cole (2007) showed that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters in the special case of complete mediation. However, their results did not apply to the more typical case of partial mediation. We extend their previous work by showing that substantial bias can…

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

We examine emotion self-regulation and coregulation in romantic couples using daily self-reports of positive and negative affect. We fit these data using a damped linear oscillator model specified as a latent differential equation to investigate affect dynamics at the individual level and coupled influences for the 2 partners in each couple.…

Literature documents that the judgments people hold about themselves, their life, and their future are important ingredients of their psychological functioning and well-being and are commonly related to each other. In this article, results from a longitudinal study (N = 298, 45% males) are presented. Using an integrative Latent Curve, Latent…

In this commentary, we demonstrate how the potential outcomes framework can help understand the key identification assumptions underlying causal mediation analysis. We show that this framework can lead to the development of alternative research design and statistical analysis strategies applicable to the longitudinal data settings considered by…