A standard assumption of latent class (LC) analysis is conditional independence, that is the items of the LC are independent of the covariates given the LCs. Several approaches have been proposed for identifying violations of this assumption. The recently proposed likelihood ratio approach is compared to residual statistics (bivariate residuals…

Measurement invariance holds when a latent construct is measured in the same way across different levels of background variables (continuous or categorical) while controlling for the true value of that construct. Using Monte Carlo simulation, this paper compares the multiple indicators, multiple causes (MIMIC) model and MIMIC-interaction to a…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

Careless and insufficient effort responding (C/IER) is a situation where participants respond to survey instruments without considering the item content. This phenomena adds noise to data leading to erroneous inference. There are multiple approaches to identifying and accounting for C/IER in survey settings, of these approaches the best performing…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging…

Measurement bias is defined as a violation of measurement invariance, which can be investigated through multigroup factor analysis (MGFA), by testing across-group differences in intercepts (uniform bias) and factor loadings (nonuniform bias). Restricted factor analysis (RFA) can also be used to detect measurement bias. To also enable nonuniform…

This article proposes a model-based procedure, intended for personality measures, for exploiting the auxiliary information provided by the certainty with which individuals answer every item (response certainty). This information is used to (a) obtain more accurate estimates of individual trait levels, and (b) provide a more detailed assessment of…

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…

In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2-parameter item response theory (IRT) model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and…

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

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…

Most personality tests are made up of Likert-type items and analyzed by means of factor analysis (FA). In this type of application, the fit of the model at the level of individual respondents is almost never assessed. This article proposes procedures for assessing individual fit (scalability). The procedures are intended for the analysis of…

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 large literature emphasizes the importance of testing for measurement equivalence in scales that may be used as observed variables in structural equation modeling applications. When the same construct is measured across more than one developmental period, as in a longitudinal study, it can be especially critical to establish measurement…