Bayes Factors for Evaluating Latent Monotonicity in Polytomous Item Response Theory Models

Psychometrika
Jesper Tijmstra, Maria Bolsinova

Abstract

The assumption of latent monotonicity is made by all common parametric and nonparametric polytomous item response theory models and is crucial for establishing an ordinal level of measurement of the item score. Three forms of latent monotonicity can be distinguished: monotonicity of the cumulative probabilities, of the continuation ratios, and of the adjacent-category ratios. Observable consequences of these different forms of latent monotonicity are derived, and Bayes factor methods for testing these consequences are proposed. These methods allow for the quantification of the evidence both in favor and against the tested property. Both item-level and category-level Bayes factors are considered, and their performance is evaluated using a simulation study. The methods are applied to an empirical example consisting of a 10-item Likert scale to investigate whether a polytomous item scoring rule results in item scores that are of ordinal level measurement.

References

Dec 20, 2007·Psychonomic Bulletin & Review·Eric-Jan Wagenmakers
Jun 10, 2011·The British Journal of Mathematical and Statistical Psychology·Rudy Ligtvoet, Jeroen K Vermunt
Jun 1, 1984·IEEE Transactions on Pattern Analysis and Machine Intelligence·S Geman, D Geman
Mar 25, 2014·Psychonomic Bulletin & Review·Jeffrey N Rouder
Sep 18, 2015·Psychometrika·Jesper TijmstraKlaas Sijtsma

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Software Mentioned

SOL
R package ‘ mokken ’

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