Questionnaire Reliability Under the Rasch Model

Abstract

Quality of life studies must be concerned with the accuracy, or reliability (as it is usually called in psychometrics) of measurement. A reliability coefficient gives an evaluation of a questionnaire’s ability to yield interpretable statements about the construct being measured. There are two classes of models for analyzing unidimensional scales: classical models and Item Response Theory (IRT) models. Classical models are based on a linear decomposition of the score, and reliability is estimated using Cronbach’s alpha coefficient. IRT models focus on the relationship between the probability of a correct answer and a latent variable. The Rasch model is a special IRT model which having good measurement properties. In the context of the Rasch model, or IRT models in general, no reliability coefficient similar to Cronbach Alpha is clearly defined. Some authors have studied the Fisher information of the latent parameter, which provides a measure of accuracy of the estimator. In this chapter, we present how reliability is estimated for classical models, and we propose a reliability coefficient for the Rasch model. Simulated data and data derived from the communication subscale of the Sickness Impact Profile are used to illustrate the methods.