Measuring Variability and Change With an Item Response Model for Polytomous Variables

Abstract

An extension of the graded response model of Samejima (1969) for the measurement of variability and change is presented. In this model it is assumed that an occasion-specific latent variable is decomposed into (a) a person-specific variable (a trait variable) and (b) an occasion-specific deviation variable measuring the variability caused by situational and/or interactional effects. Furthermore, it is assumed that interindividual differences in intraindividual trait change occur between a priori specified periods of time. The correlations of the latent trait variables between periods of time indicate the degree of (trait) change. It is shown how the parameters of the model can be estimated and some implications of the model can be tested with structural equation models for ordered variables. Finally, the model is illustrated by an application to the measurement of students’ interest in the topic of radioactivity. Based on the results of a longitudinal study of students over 4’years, it is shown that a model considering two periods of time—one before and one after the incident in Chernobyl—fits well. According to the accepted model, it can be concluded that 30% to 60% of the variance of interest in radioactivity on an occasion of measurement are due to situational and/or interactional effects. The autocorrelations of the latent trait variables between both periods of time (r = .72 and r = .76, respectively) indicate that there are interindividual differences in intraindividual changes on the level of the latent trait variables.