Fitting Full-Information Item Factor Models and an Empirical Investigation of Bridge Sampling
Abstract Based on item response theory, Bock and Aitken introduced a method of item factor analysis, termed full-information item factor (FIIF) analysis by Bartholomew because it uses all distinct item response vectors as data. But a limitation of their fitting algorithm is its reliance on fixed-point Gauss—Hermite quadrature, which can produce appreciable numerical errors, especially in high-dimension problems. The first purpose of this article is to offer more reliable methods by using recent advances in statistical computation. Specifically, we illustrate two ways of implementing Monte Carlo Expectation Maximization (EM) algorithm to fit a FIIF model, using the Gibbs sampler to carry out the computation for the E steps. We also show how to use bridge sampling to simulate the likelihood ratios for monitoring the convergence of a Monte Carlo EM, a strategy that is useful in general. Simulations demonstrate substantial improvement over Bock and Aitken's algorithm in recovering known factor loadings in hig...