Response time models (RTMs) are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular RTMs. Several existing statistics for testing normality and the fit of factor analysis models are repurposed for testing the fit of the lognormal model. A…

Response-time models are of increasing interest in educational and psychological testing. This paper focuses on the lognormal model for response times (van der Linden, 2006), which is one of the most popular response-time models. Several existing statistics for testing normality and the fit of factor-analysis models are repurposed for testing the…

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

The Social Support Questionnaire for Children (SSQC) is a 50-item scale that assesses children's social support from parents, relatives, nonrelative adults, siblings, and peers. The SSQC demonstrates good psychometric properties (e.g., internal consistency, factorial validity). Furthermore, the SSQC appears to be an ethnically sensitive measure of…

This paper documents the creation, implementation and analysis of a survey instrument designed to reveal patterns of use and attitudes towards the value of social media by UK teachers. The study was motivated to discover which teachers use social media professionally, how they use it (both personally and professionally) and attitudes to social…

This rejoinder discusses the general comments on how to use Bayesian structural equation modeling (BSEM) wisely and how to get more people better trained in using Bayesian methods. Responses to specific comments cover how to handle sign switching, nonconvergence and nonidentification, and prior choices in latent variable models. Two new…

Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…

Parameter recovery was assessed within mixture confirmatory factor analysis across multiple estimator conditions under different simulated levels of mixture class separation. Mixture class separation was defined in the measurement model (through factor loadings) and the structural model (through factor variances). Maximum likelihood (ML) via the…

Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte…

Developed Markov Chain Monte Carlo procedures to perform Bayesian inference, model checking, and model comparison in heterogeneous factor analysis. Tested the approach with synthetic data and data from a consumption emotion study involving 54 consumers. Results show that traditional psychometric methods cannot fully capture the heterogeneity in…

The Standardized Letter of Recommendation (SLR), a 28-item form, was created by ETS to supplement the qualitative rating of graduate school applicants' nonacademic qualities with a quantitative approach. The purpose of this study was to evaluate the following psychometric properties of the SLR using the Rasch rating-scale model: dimensionality,…

This study assessed the factor structure of the LanguEdge™ test and the invariance of its factors across language groups. Confirmatory factor analyses of individual tasks and subsets of items in the four sections of the test, Listening, Reading, Speaking, and Writing, was carried out for Arabic-, Chinese-, and Spanish-speaking test takers. Two…