Mokken Scale Analysis in R

Mokken scale analysis (MSA) is a scaling procedure for both dichotomous and polytomous items. It consists of an item selection algorithm to partition a set of items into Mokken scales and several methods to check the assumptions of two nonparametric item response theory models: the monotone homogeneity model and the double monotonicity model. First, we present an R package mokken for MSA and explain the procedures. Second, we show how to perform MSA in R using test data obtained with the Adjective Checklist.

Advances in nonparametric item response theory for scale construction in quality-of-life research

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering

Evaluating model fit in two-level Mokken scale analysis

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the existing model-fit procedure from traditional (one-level) Mokken scale analyses can be used for investigating model fit at both level 1 (respondent level) and level 2 (cluster level) of two-level Mokken scale analysis. However, the traditional model-fit procedure requires some modifications before it can be used at level 2. In this paper, we made these modifications and investigated the resulting model-fit procedure. For two model assumptions, monotonicity and invariant item ordering, we investigated the false-positive count and the sensitivity count of the level 2 model-fit procedure, with respect to the number of model violations detected, and the number of detected model violations deemed statistically significant. For monotonicity, the detection of model violations was satisfactory, but the significance test lacked power. For invariant item ordering, both aspects were satisfactory

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. However, we show that MEL tends to break down for large, sparse contingency tables. As a solution, we propose a new method, which we call maximum augmented empirical likelihood (MAEL) estimation and which involves augmentation of the empirical likelihood support with a number of well-chosen cells. Simulation results show good finite sample performance for very large contingency tables

Bias of two-level scalability coefficients and their standard errors

Multivariate analysis of psychological dat