Checking assumptions in two-level Mokken scale analysis

The nonparametric IRT models that underlie Mokken scale analysis consist of four main assumptions: unidimensionality, local independence, monotonicity, and invariant item ordering. These assumptions imply certain observable properties of the data. For example, local independence and monotonicity imply conditional association; for dichotomous items scores, monotonicity implies manifest monotonicity; and invariant item ordering implies manifest invariant item ordering. Mokken scale analysis provides methods to investigate the assumptions of the nonparametric IRT models by investigating the observable properties. When dealing with multi-rater data, some adjustments of the assumptions are necessary. For example, for multi-rater data, the monotonicity assumption concerns the latent trait of the subject combined with the rater effect. In addition, multi-rater data require a different way to estimate the item probabilities. As a result the methods that are used to investigate observable properties must be adapted for multi-rater data. I will discuss the necessary adaptations to make the methods from Mokken scale analysis useful in a multi-level context, and I will discuss how these adaptations may be implemented.