Student Ability Assessment Based on Two IRT Models

The aim of this work is to analyze a part of the data collected in the Computer Science Department during the Informatics exams in the year 2003. Two different Item Response Theory models for ordered polytomous variables are considered in order to get an evaluation of student ability. Ordered polytomous variables are used for a problem solving process that contains a finite number of steps so that the ability of a student can be evaluated on the basis of the step achieved, namely, higher steps achieved are related to higher ability. The models considered are the Partial Credit Model and the Graded Response Model. The choice of these models has been dic-tated by the fact that although they are defined into different theoretical frameworks, the former belongs to the Rasch family (Masters, 1982) and the latter can be viewed as a Generalized Linear Latent Variable Model (Bartholomew and Knott, 1999), and hence they present different properties, both of them allow to treat ordinal observed variables. The analysis of the real data set through the two approaches allows to highlight their advantages and disadvantages.