Multidimensional Beta Factor Analysis for Bounded and Asymmetric Item Response Data

Abstract

In this presentation, we propose a multidimensional beta factor-analytic model (beta IFA) for modeling bounded and skewed item response data. The beta IFA model is based on the beta distribution, a flexible distribution that can accommodate a variety of response distributions (e.g., bimodal, heavily skewed). In addition, the beta IFA respects the bounds of the response range and will not provide out-of-range predictions. We present the model as a compromise between normal-theory factor analysis (NTFA; which assume that response variables are continuous, unbounded, and symmetric) and ordinal factor analysis (which assumes underlying latent category thresholds). We derive an expectation-maximization algorithm for full-information maximum likelihood estimation and an expected a posteriori procedure for estimating factor scores. We investigate the performance of the algorithm/model via three simulation studies. In Simulation Study I, we examine the performance of the algorithm in a one-factor setting by varying sample size and test length. Simulation Study II focuses on performance in the multi-dimensional case with correlated latent factors. Simulation Study III compares the beta IFA model to NTFA under different data-generating model mechanisms. Results from Simulation Studies I and II provide evidence that the algorithm performs well in small- and large-sample settings with as few as ten items. Simulation study III demonstrates that the beta IFA model performs comparable to NTFA with respect to model fit when the latter is the data-generating model but outperforms NTFA when item response data are skewed. We demonstrate the utility of the model with real data via three empirical applications.

Alfonso J. Martinez

Assistant Professor of Psychometrics and Quantitative Psychology

My research interests include generalized latent variable modeling, Bayesian analysis, and computational statistics.