Mokken scale analysis: Between the Guttman scale and parametric item response theory

This article introduces a model of ordinal unidimensional measurement known as Mokken scale analysis. Mokken scaling is based on principles of Item Response Theory (IRT) that originated in the Guttman scale. I compare the Mokken model with both Classical Test Theory (reliability or factor analysis) and parametric IRT models (especially with the one-parameter logistic model known as the Rasch model). Two nonparametric probabilistic versions of the Mokken model are described: the model of Monotone Homogeneity and the model of Double Monotonicity. I give procedures for dealing with both dichotomous and polytomous data, along with two scale analyses of data from the World Values Study that demonstrate the usefulness of the Mokken model.