Latent class mediation modeling is designed to estimate the mediation effect when both the mediator and the outcome are latent class variables. We suggest using an adjusted one-step approach in which the latent class models for the mediator and the outcome are estimated first to decide on the number of classes, then the latent class models and the mediation model are jointly estimated. We present both an empirical demonstration and a simulation study to compare the performance of this one-step approach to a standard three-step approach with modal assignment (modal) and four different modern three-step approaches. Results from the study indicate that unadjusted modal, which ignores the classification errors of the latent class models, produced biased mediation effects. On the other hand, the adjusted one-step approach and the modern three-step approaches performed well with respect to bias for estimating mediation effects, regardless of measurement quality (i.e., model entropy) and latent class size. Among the three-step approaches we investigated, the maximum likelihood method with modal assignment and the BCH correction with robust standard error estimators are good alternatives to the adjusted one-step approach, given their unbiased standard error estimations.

When estimating path coefficients among psychological constructs measured with error, structural equation modeling (SEM), which simultaneously estimates the measurement and structural parameters, is generally regarded as the gold standard. In practice, however, researchers usually first compute composite scores or factor scores, and use those as observed variables in a path analysis, for purposes of simplifying the model or avoiding model convergence issues. Whereas recent approaches, such as reliability adjustment methods and factor score regression, has been proposed to mitigate the bias induced by ignoring measurement error in composite/factor scores with continuous indicators, those approaches are not yet applicable to models with categorical indicators. In this article, we introduce the two-stage path analysis (2S-PA) with definition variables as a general framework for path modeling to handle categorical indicators, in which estimation of factor scores and path coefficients are separated. It thus allows for different estimation methods in the measurement and the structural path models and easier diagnoses of violations of model assumptions. We conducted three simulation studies, ranging from latent regression to mediation analysis with categorical indicators, and showed that 2S-PA generally produced similar estimates to those using SEM in large samples, but gave better convergence rates, less standard error bias, and better control of Type I error rates in small samples. We illustrate 2S-PA using data from a national data set, and show how researchers can implement it in Mplus and OpenMx. Possible extensions and future directions of 2S-PA are discussed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Much of the previous literature on partial measurement invariance has focused on (a) statistically detecting noninvariance, and (b) modeling partial invariance to obtain correct inferences for latent mean comparisons across groups in a single research study. However, very little guidance is provided on the practical implications of partial invariance on the instrument itself in the context of selection. In a frequently cited paper, Millsap and Kwok (2004) provided a framework for evaluating the impact of partial invariance by quantifying the magnitude of noninvariance on the efficacy of the test for selection purposes, yet our literature review found that only a few of the citations have fully captured the essence of Millsap and Kwok’s method. In this article, we briefly review the selection accuracy analysis for partial invariance and provide a user-friendly R script (also available as a Web application) that takes parameter estimates as input, automatically produces summary statistics for evaluating selection accuracy, and generates a graph for visualizing the results. Hypothetical and real data examples are provided to illustrate the use of the R script. The goal of this article is to help readers understand Millsap and Kwok’s framework of evaluating the impact of partial invariance through an accessible computer program and step-by-step demonstrations of the selection accuracy analysis.

Purpose: This study examined the psychometric properties of the Preschool Language Scales–Fifth Edition (PLS-5 English) among preschool children from low–socioeconomic status (SES) families.Method: The PLS-5 was administered individually to 169 3- to 4-year-old children enrolled in Head Start programs. We carried out a Mokken scale analysis (MSA), which is a nonparametric item response theory analysis, to examine the hierarchy among items and the reliability of test scores of the PLS-5 Auditory Comprehension (AC) and Expressive Communication (EC) scales.Results: The PLS-5 EC items retained a moderate Mokken scale with the inclusion of all the items. On the other hand, the PLS-5 AC items formed a moderate Mokken scale only with the exclusion of five unscalable items. The latent class reliability coefficients for the AC and the EC scale scores were both above .90. Several items that violated the invariant item ordering assumption were found for both scales.Conclusions: MSA can be used to examine the relationship between the latent language ability and the probability of passing an item with ordinal responses. Results indicate that for preschool children from low-SES families, it is appropriate to use the PLS-5 EC scale scores for comparing individuals' expressive language abilities; however, researchers and speech-language pathologists should be cautious when using the PLS-5 AC scale scores to evaluate individuals' receptive language abilities. Other implications of the MSA results are further discussed.

We investigated the performance of two single indicator methods: latent moderated structural equation (LMS) and reliability-adjusted product indicator (RAPI) methods, on testing interaction effects with congeneric measures, which vary in factor loadings and error variances under a common factor. Additionally, in the simulation study, we compared the performance of four reliability estimates (Cronbach’s alpha, omega composite, Coefficient H, and greatest lower bound [GLB]) to adjust for the exogenous composites’ measurement errors. Results from the study showed that: while estimating interaction effects with exogenous composites from congeneric measures, the four reliability estimates performed comparably well. Recommendations on the choice of reliability estimates between the LMS and the RAPI methods under different sample sizes and population reliability conditions are further discussed.