Conditional Maximum Likelihood Estimation in Polytomous Rasch Models Using SAS

Abstract

IRT models are widely used but often rely on distributional assumptions about the latent variable. For a simple class of IRT models, the Rasch models, conditional inference is feasible. This enables consistent estimation of item parameters without reference to the distribution of the latent variable in the population. Traditionally, specialized software has been needed for this, but conditional maximum likelihood estimation can be done using standard software for fitting generalized linear models. This paper describes an SAS macro %rasch_cml that fits polytomous Rasch models. The macro estimates item parameters using conditional maximum likelihood (CML) estimation and person locations using maximum likelihood estimator (MLE) and Warm's weighted likelihood estimation (WLE). Graphical presentations are included: plots of item characteristic curves (ICCs), and a graphical goodness-of-fit-test is also produced.