An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model

Michael Brusco (), Hans-Friedrich Köhn () and Douglas Steinley ()

Psychometrika, 2015, vol. 80, issue 4, 949-967

Abstract: The monotone homogeneity model (MHM—also known as the unidimensional monotone latent variable model) is a nonparametric IRT formulation that provides the underpinning for partitioning a collection of dichotomous items to form scales. Ellis (Psychometrika 79:303–316, 2014 , doi: 10.1007/s11336-013-9341-5 ) has recently derived inequalities that are implied by the MHM, yet require only the bivariate (inter-item) correlations. In this paper, we incorporate these inequalities within a mathematical programming formulation for partitioning a set of dichotomous scale items. The objective criterion of the partitioning model is to produce clusters of maximum cardinality. The formulation is a binary integer linear program that can be solved exactly using commercial mathematical programming software. However, we have also developed a standalone branch-and-bound algorithm that produces globally optimal solutions. Simulation results and a numerical example are provided to demonstrate the proposed method. Copyright The Psychometric Society 2015

Keywords: nonparametric IRT; partial correlation; mokken scale analysis; item selection; exact algorithm (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11336-015-9459-8

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