Obtaining values for latent variables in factor analysis models, also referred to as factor scores, has long been of interest to researchers. However, many treatments of factor analysis do not focus on inference about the latent variables, and even fewer do so from a Bayesian perspective. Researchers may therefore be ill-acquainted with Bayesian…

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the…

A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and…

Although there is recognition that there may be differential outcomes for groups of students within schools, examination of outcomes for subgroups presents challenges to researchers and policymakers. It complicates analytic procedures, particularly when the number of students per school in the subgroup is small. We explored five alternatives for…

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their…

A common practice in educational assessment is to construct multiple forms of an assessment that consists of tasks with similar psychometric properties. This study utilizes a Bayesian multilevel item response model and descriptive graphical representations to evaluate the psychometric similarity of variations of the same task. These approaches for…

A conceptual distinction is drawn between indicators, which serve to define latent variables, and outcomes, which do not. However, commonly used frequentist and Bayesian estimation procedures do not honor this distinction. They allow the outcomes to influence the latent variables and the measurement model parameters for the indicators, rendering…

Specialized imputation routines for multilevel data are widely available in software packages, but these methods are generally not equipped to handle a wide range of complexities that are typical of behavioral science data. In particular, existing imputation schemes differ in their ability to handle random slopes, categorical variables,…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

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 approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…

In this paper we describe the development and refinement of "evidence rules" and "measurement models" within the "evidence model" of the "evidence-centered design" (ECD) framework in the context of the "Packet Tracer" digital learning environment of the "Cisco Networking Academy." Using…

This paper aims to describe a Bayesian approach to modeling and estimating cognitive models both in terms of statistical machinery and actual instrument development. Such a method taps the knowledge of experts to provide initial estimates for the probabilistic relationships among the variables in a multivariate latent variable model and refines…