Bias in point estimates and standard errors of Mokken’s scalability coefficients

Mokken scale analysis uses three types of scalability coefficients to assess the quality of (a) pairs of items, (b) individual items, and (c) an entire scale. Both the point estimates and the standard errors of the scalability coefficients assume that the sample ordering of the item steps is identical to the population ordering, but due to sampling error, the sample ordering may be incorrect and, consequently, the estimates and the standard errors may be biased. Two simulation studies were used to investigate the bias of the estimates and the standard errors of the scalability coefficients, as well as the coverage of the 95% confidence intervals. Distance between item steps was the most important design factor. In addition, sample size, number of items, number of answer categories, and item discrimination were included in the design. Bias of the standard errors was negligible. Bias of the estimates was largest when all item steps were identical in the population, especially for small sample sizes. Furthermore, bias of the estimates decreased as number of answer categories increased and as item discrimination decreased. Coverage of the 95% confidence intervals was close to .950, but for small sample size coverage deteriorated. Coverage also became poorer as number of items increased, in particular for dichotomous items.