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

Michael J. Brusco, Hans Friedrich Köhn, Douglas Steinley

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)949-967
Number of pages19
JournalPsychometrika
Volume80
Issue number4
DOIs
StatePublished - Dec 1 2015

Keywords

  • exact algorithm
  • item selection
  • mokken scale analysis
  • nonparametric IRT
  • partial correlation

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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