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

Wijbrandt H. van Schuur

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

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.

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References

1969Statistical Theories of Mental Test Scores 1961Probabilistic Models for Some Intelligence and Attainment Tests 1997Modernization and Postmodernization 1997Modernization and Postmodernization: Cultural, Economic, and Political Change in 43 Societies 2000Item response theory for psychologists 1968ESTIMATION OF LATENT ABILITY USING A RESPONSE PATTERN OF GRADED SCORES1 1997Handbook of Modern Item Response Theory 1968Some latent trait models and their use in inferring an examinee's ability

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