The deviance information criterion (DIC) is widely used to select the parsimonious, well-fitting model. We examined how priors impact model complexity (pD) and the DIC for Bayesian CFA. Study 1 compared the empirical distributions of pD and DIC under multivariate (i.e., inverse Wishart) and separation strategy (SS) priors. The former treats the…

This study aims to compare the results of the factor analysis performed with Frequentist and Bayesian approaches. The number of sub-dimensions of the measurement tool obtained from different methods, the variation of the items in the sub-dimensions, and the fit statistics' differentiation were examined. 778 students constitute the study sample.…

This simulation study was conducted to compare the performances of Frequentist and Bayesian approaches in the context of power to detect model misspecification in terms of omitted cross-loading in CFA models with respect to the several variables (number of omitted cross-loading, magnitude of main loading, number of factors, number of indicators…

Large-scale surveys such as the Programme for International Student Assessment (PISA), the Teaching and Learning International Survey (TALIS), and the Programme for the International Assessment of Adult Competences (PIAAC) use advanced statistical models to estimate scores of latent traits from multiple observed responses. The comparison of such…

Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, maximum likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian…

The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of…

Bayesian structural equation modeling (BSEM) was used to investigate the latent structure of the Differential Ability Scales-Second Edition core battery using the standardization sample normative data for ages 7-17. Results revealed plausibility of a three-factor model, consistent with publisher theory, expressed as either a higher-order (HO) or a…

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…

This author has had the privilege of knowing Professor Maydeu-Olivares for almost a decade and although their paths cross only occasionally, such instances were always enjoyable and enlightening. Edwards states that Maydeu-Olivares' target article for this issue, ("Goodness-of-Fit Assessment of Item Response Theory Models") provides…

The purpose of this study was to reveal whether the low, medium, and high level self-regulated learning strategies of third year students at the Education Faculty of Cumhuriyet University can be predicted by the variables of gender, academic self-efficacy, and general academic average. The study uses the Relational Screening Model. The dependent…

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…

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…

It is shown that the common and unique variance estimates produced by a type of estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. A simple alternative method of specifying the Bayesian parameters required by the procedure is…

Recent work in factor analysis of categorical variables is reviewed, emphasizing a generalized least squares solution and a maximum likelihood approach. A common factor model for dichotomous items is introduced, and the estimation of factor loadings from matrices of tetracorrelations is discussed. (LMO)