Mokken Scale Analysis: Between the Guttman Scale and Parametric Item Response Theory

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