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.

Examination of Polytomous Items’ Psychometric Properties According to Nonparametric Item Response Theory Models in Different Test Conditions

“…Moreover, SE i values from skewed distributions were higher than SE i values from normal distributions. This finding supported Kuijpers, van der Ark, and Croon (2013). In this study's test conditions, tests generally fit MHM.…”

Investigating the structure of the autism-spectrum quotient using Mokken scaling.

“…The scales initially obtained were checked for violations of the model of monotone homogeneity and violat ing items were removed on the basis of Crit values > 40 as recommended by Molenaar and Sijtsma (2000). Using the recently described method (Kuijpers, van der Ark, & Croon, 2013) the 95% confidence intervals were calculated for H for item pairs, items, and the scale. Where 95% confidence intervals for scale and item H include the lower bound level for a weak scale (.30) this is reported and for item pairs, the 95% confidence intervals should not include 0.…”

Preliminary testing using Mokken scaling of an Italian translation of the Edinburgh Feeding Evaluation in Dementia (EdFED-I) scale

“…Calculating SE allows the calculation of confidence intervals (CI) and for scale and item H these should not include the lowerbound value of 0.30 and for item pairs they should not include 0 (Kuijpers, van der Ark, & Croon, 2013). Little is known about the sample size requirements for Mokken scaling.…”