Rethinking the Exploration of Dichotomous Data: Mokken Scale Analysis Versus Factorial Analysis

Abstract

The need to determine the correct dimensionality of theoretical constructs and generate valid measurement instruments when underlying items are categorical has generated a significant volume of research in the social sciences. This article presents two studies contrasting different categorical exploratory techniques. The first study compares Mokken scale analysis (MSA) and two-factor-based exploratory techniques for noncontinuous variables: item factor analysis and Normal Ogive Harmonic Analysis Robust Method (NOHARM). Comparisons are conducted across techniques and in reference to the common principal component analysis model using simulated data under conditions of two-dimensionality with different degrees of correlation (r = .0 to .6). The second study shows the theoretical and practical results of using MSA and NOHARM (the factorial technique which functioned best in the first study) on two nonsimulated data sets. The nonsimulated data are particularly interesting because MSA was used to solve a theoretical debate. Based on the results from both studies, we show that the ability of NOHARM to detect dimensionality and scalability is similar to MSA when the data comprise two uncorrelated latent dimensions; however, NOHARM is preferable when data are drawn from instruments containing latent dimensions weakly or moderately correlated. This article discusses the theoretical and practical implications of these findings.