A Multidimensional Unfolding Latent Trait Model for Binary Data

28 Pages Posted: 24 Sep 2007

See all articles by Alberto Maydeu Olivares

Alberto Maydeu Olivares

Fundación Instituto de Empresa, S.L.

Adolfo Hernandez

University of Exeter

Roderick McDonald

University of Illinois at Urbana-Champaign

Date Written: November 2, 2005

Abstract

We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields closed form expressions for the moments of the multivariate Bernoulli (MVB) distribution. As a result, cell probabilities can be computed also in closed form, regardless of the dimensionality of the latent traits. The model is an ideal point model in the sense that a respondent - precisely at the ideal point (the mode of the item response function) - endorses the item with probability one.

Keywords: item response theory, categorical data analysis

JEL Classification: C00

Suggested Citation

Maydeu Olivares, Alberto and Hernandez, Adolfo and McDonald, Roderick, A Multidimensional Unfolding Latent Trait Model for Binary Data (November 2, 2005). Instituto de Empresa Business School Working Paper No. WP05-11. Available at SSRN: https://ssrn.com/abstract=1016119 or http://dx.doi.org/10.2139/ssrn.1016119

Alberto Maydeu Olivares (Contact Author)

Fundación Instituto de Empresa, S.L. ( email )

Mª Molina, 11,13,15
Madrid, Madrid 28006
Spain
915 689 732 (Phone)

Adolfo Hernandez

University of Exeter ( email )

Northcote House
The Queen's Drive
Exeter, Devon EX4 4QJ
United Kingdom

Roderick McDonald

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

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