Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models

Abstract

Mokken scale analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken scale analysis. Second, we proved that the method can be applied to scales consisting of large numbers of items. Third, we applied Mokken scale analysis to a set of polytomous items measuring tolerance. The analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences.