The random intercept cross-lagged panel model (RICLPM) decomposes longitudinal associations between two processes X and Y into stable between-person associations and temporal within-person changes. In a recent study, Bailey et al. demonstrated through a simulation study that the between-person variance components in the RICLPM can occur only due…

In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be…

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, noniterative estimator for latent variable models. Associated with this estimator are equation-specific tests of model misspecification. One issue with equation-specific tests is that they lack specificity, in that they indicate…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Exploratory structural equation modeling (ESEM) allows for the estimation of all cross-loadings, which leads to the number of parameters estimated substantially greater than that in conventional SEM. This study examined the sensitivity of fit measures (CFI, RMSEA, AIC, BIC, SaBIC, LRT) to measurement noninvariance in ESEM. Results suggested that…

This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a…

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

Confidence intervals (CIs) for parameters are usually constructed based on the estimated standard errors. These are known as Wald CIs. This article argues that likelihood-based CIs (CIs based on likelihood ratio statistics) are often preferred to Wald CIs. It shows how the likelihood-based CIs and the Wald CIs for many statistics and psychometric…

The effects of misspecifying intercept-covariate interactions in a 4 time-point latent growth model were the focus of this investigation. The investigation was motivated by school growth studies in which students' entry-level skills may affect their rate of growth. We studied the latent interaction of intercept and a covariate in predicting growth…

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term…

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…