Standard errors of two-level scalability coefficients

For the construction of tests and questionnaires that require multiple raters (e.g., a child behaviour checklist completed by both parents) a novel ordinal scaling technique is currently being further developed, called two-level Mokken scale analysis. The technique uses within-rater and between-rater coefficients to assess the scalability of the test. These coefficients are generalizations of Mokken's scalability coefficients. In this paper we derived standard errors for the two-level coefficients and for their ratios. The coefficients, the estimates, the estimated standard errors and the software implementation are discussed and illustrated using a real-data example, and a small-scale simulation study demonstrates the accuracy of the estimates.