Investigating the Ordering Structure of Clustered Items Using Nonparametric Item Response Theory.

Educational and psychological tests with an ordered item structure enable efficient test administration procedures and allow for intuitive score interpretation and monitoring. The effectiveness of the measurement instrument relies to a large extent on the validated strength of its ordering structure. We define three increasingly strict types of ordering for the ordering structure of a measurement instrument with clustered items: a weak and a strong invariant cluster ordering and a clustered invariant item ordering.

Maximum Augmented Empirical Likelihood Estimation of Categorical Marginal Models for Large Sparse Contingency Tables.

Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation.

A two-step, test-guided Mokken scale analysis, for nonclustered and clustered data.

Purpose: Mokken scale analysis (MSA) is an attractive scaling procedure for ordinal data. MSA is frequently used in health-related quality of life research. Two of MSA's prime features are the scalability coefficients and the automated item selection procedure (AISP).

Bias of Two-Level Scalability Coefficients and Their Standard Errors.

Two-level Mokken scale analysis is a generalization of Mokken scale analysis for multi-rater data. The bias of estimated scalability coefficients for two-level Mokken scale analysis, the bias of their estimated standard errors, and the coverage of the confidence intervals has been investigated, under various testing conditions. It was found that the estimated scalability coefficients were unbiased in all tested conditions.

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.