Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…

This study investigated two major approaches in testing measurement invariance for ordinal measures: multiple-group categorical confirmatory factor analysis (MCCFA) and item response theory (IRT). Unlike the ordinary linear factor analysis, MCCFA can appropriately model the ordered-categorical measures with a threshold structure. A simulation…

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as…

The latent state-trait (LST) theory is an extension of the classical test theory that allows one to decompose a test score into a true trait, a true state residual, and an error component. For practical applications, the variances of these latent variables may be estimated with standard methods of structural equation modeling (SEM). These…

In this article, we operationalize identification of mixed racial and ethnic ancestry among adolescents as a latent variable to (a) account for measurement uncertainty, and (b) compare alternative wording formats for racial and ethnic self-categorization in surveys. Two latent variable models were fit to multiple mixed-ancestry indicator data from…

The choice of constraints used to identify a simple factor model can affect the shape of the likelihood. Specifically, under some nonzero constraints, standard errors may be inestimable even at the maximum likelihood estimate (MLE). For a broader class of nonzero constraints, symmetric normal approximations to the modal region may not be…

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…

The usefulness of assessing individual fit in latent growth curve models was examined. The study used simulated data based on an unconditional and a conditional latent growth curve model with a linear component and a small quadratic component and a linear model was fit to the data. Then the overall fit of linear and quadratic models to these data…

This article reviews the problems associated with using item response theory (IRT)-based latent variable scores for analytical modeling, discusses the connection between IRT and structural equation modeling (SEM)-based latent regression modeling for discrete data, and compares regression parameter estimates obtained using predicted IRT scores and…

This study focused on misspecifications in composing parcels to represent a latent construct. Two measurement design factors, item reliability and intercorrelations among parcels, defined 12 true unidimensional parcel models. Deviations from the true model were examined via a 2-facet measurement model in which items and parcels represented the 2…