%lrasch_mml: A SAS Macro for Marginal Maximum Likelihood Estimation in Longitudinal Polytomous Rasch Models

Abstract

Item response theory models are often applied when a number items are used to measure a unidimensional latent variable. Originally proposed and used within educational research, they are also used when focus is on physical functioning or psychological wellbeing. Modern applications often need more general models, typically models for multidimensional latent variables or longitudinal models for repeated measurements. This paper describes a SAS macro that fits two-dimensional polytomous Rasch models using a specification of the model that is sufficiently flexible to accommodate longitudinal Rasch models. The macro estimates item parameters using marginal maximum likelihood estimation. A graphical presentation of item characteristic curves is included.

Keywords

• polytomous Rasch model
• longitudinal Rasch model
• marginal maximum likelihood (MML) estimation
• item parameter drift
• response dependence
• SAS macro