Title: Mokken's Scalability Coefficients for Multilevel Data

Authors: Letty Koopman, Bonne Zijlstra, Andries van der Ark

Affiliation: University of Amsterdam

Abstract:
A commonly used scaling procedure for questionnaires measuring social and
behavioural constructs is Mokken scale analysis, of which scalability
coefficients are arguably the most popular aspect. Data to investigate these
questionnaires are often collected in clusters, for example from students
nested in classrooms, resulting in multilevel data. The traditional
(one-level) method of estimating scalability coefficients and their standard
errors assumes that the sample is a simple random sample of the population, an
assumption that is violated in multilevel data. As a result, the quality of a
scale may be overestimated or questionable items may be admitted in the final
version of a questionnaire. We discuss a new estimation method for scalability
coefficients and their standard errors in multilevel data, which outperformed
the one-level method, especially for larger groups or stronger dependency in
the data. We demonstrate the difference between the methods using the scores
on a quality of life in school measure, discuss some simulation results, and
demonstrate how to compute the estimates using the R-package mokken.