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

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  • Michael Brusco
  • Hans-Friedrich Köhn
  • Douglas Steinley

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

Suggested Citation

  • Michael Brusco & Hans-Friedrich Köhn & Douglas Steinley, 2015. "An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 949-967, December.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:949-967
    DOI: 10.1007/s11336-015-9459-8
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    References listed on IDEAS

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    Cited by:

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    2. Jules L. Ellis & Klaas Sijtsma, 2023. "A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 387-412, June.

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