Abstract
We present the beta item factor analytic (beta IFA) model as a modeling approach for asymmetric, bounded, and continuous item response data. The beta IFA model is based on the mean-precision beta distribution and is capable of directly accommodating asymmetry (skewness) in the response distribution without the need for data transformations while simultaneously respecting the bounds of the response range. An expectation-maximization (EM) algorithm based on marginal maximum likelihood is derived and the performance of the algorithm is investigated across a simulation study. A second simulation study compares the beta IFA model to normal-theory factor analysis under different data generating mechanisms. Results from the first simulation study indicate that the EM algorithm can accurately recovery model parameters in sample sizes as small as 250 with as few as 5 items. The second simulation study revealed that the beta IFA model outperforms normal-theory factor analysis under asymmetric response distributions but performs similar to normal-theory factor analysis under symmetric response distributions. An empirical application of the beta IFA model is presented to demonstrate the use of the model and algorithm with real data.
Alfonso J. Martinez
Assistant Professor of Psychometrics and Quantitative Psychology
My research interests include generalized latent variable modeling, Bayesian analysis, and computational statistics.