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

Michael J. Brusco, Hans Friedrich Koehn, 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

Fingerprint

Exact Method
Homogeneity
Partitioning
Monotone
Mathematical programming
Mathematical Programming
Formulation
Latent Variable Models
Software
Integer Program
Branch and Bound Algorithm
Linear Program
Cardinality
Optimal Solution
Model
Binary
Numerical Examples
Demonstrate
Framework
Simulation

Keywords

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

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

Cite this

An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model. / Brusco, Michael J.; Koehn, Hans Friedrich; Steinley, Douglas.

In: Psychometrika, Vol. 80, No. 4, 01.12.2015, p. 949-967.

Research output: Contribution to journalArticle

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