Table of Contents
ISRN Computational Mathematics
Volume 2013, Article ID 617475, 8 pages
Research Article

Conditional Maximum Likelihood Estimation in Polytomous Rasch Models Using SAS

Department of Biostatistics, University of Copenhagen, Denmark

Received 29 November 2012; Accepted 29 January 2013

Academic Editors: L. S. Heath, H. J. Ruskin, and P. B. Vasconcelos

Copyright © 2013 Karl Bang Christensen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.