Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals

Abstract

The purpose of this research is twofold. First is to extend the work of Smith (1992, 1996) and Smith and Miao (1991, 1994) in comparing item fit statistics and principal component analysis as tools for assessing the unidimensionality requirement of Rasch models. Second is to demonstrate methods to explore how violations of the unidimensionality requirement influence person measurement. For the first study, rating scale data were simulated to represent varying degrees of multidimensionality and the proportion of items contributing to each component. The second study used responses to a 24 item Attention Deficit Hyperactivity Disorder scale obtained from 317 college undergraduates. The simulation study reveals both an iterative item fit approach and principal component analysis of standardized residuals are effective in detecting items simulated to contribute to multidimensionality. The methods presented in Study 2 demonstrate the potential impact of multidimensionality on norm and criterion-reference person measure interpretations. The results provide researchers with quantitative information to help assist with the qualitative judgment as to whether the impact of multidimensionality is severe enough to warrant removing items from the analysis.