Consider the conventional multilevel model Y=C[gamma]+Zu+e where [gamma] represents fixed effects and (u,e) are multivariate normal random effects. The continuous outcomes Y and covariates C are fully observed with a subset Z of C. The parameters are [theta]=([gamma],var(u),var(e)). Dempster, Rubin and Tsutakawa (1981) framed the estimation as a…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. (2020) estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores,…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores, including…

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Extreme response style (ERS) is a systematic tendency for a person to endorse extreme options (e.g., strongly disagree, strongly agree) on Likert-type or rating-scale items. In this study, we develop a new class of item response theory (IRT) models to account for ERS so that the target latent trait is free from the response style and the tendency…

In organizational studies involving multiple levels, the association between a covariate and an outcome often differs at different levels of aggregation, giving rise to widespread interest in "contextual effects models." Such models partition the regression into within- and between-cluster components. The conventional approach uses each…

An empirical Bayes-maximum likelihood estimation procedure is presented for the application of fuzzy partition models in describing high dimensional discrete response data. The model describes individuals in terms of partial membership in multiple latent categories that represent bounded discrete spaces. (SLD)

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)

A method of item factor analysis is described, which is based on Thurstone's multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm. Also assessed are the statistical significance of successive factors added to the model, provisions for guessing and omitted items, and Bayes constraints. (TJH)