Loglinear Models for Observed-Score Distributions

Loglinear models have useful applications with the discrete distributions typically encountered in psychometrics. These applications are primarily focused on the estimation of observed-score distributions (Hanson, 1990; Holland and Thayer, 1987, 2000; Rosenbaum and Thayer, 1987). The test score distributions obtained from fitting loglinear models to sample distributions can be used in place of the sample distribution to improve the stability, interpretability, and smoothness of estimated univariate distributions, conditional distributions, and equipercentile equating functions (von Davier et al., 2004; Kolen and Brennan, 2004; Liou and Cheng, 1995; Livingston, 1993). This chapter reviews fundamental statistical concepts and applications of loglinear models for estimating observed-score distributions.