title: An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model.
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.
authors: Florida State University, 821 Academic Way, Tallahassee, FL, 32306-1110 , USA. mbrusco@fsu.edu.
authors: Michael J
authors: MJ
authors: Brusco
authors: University of Illinois at Urbana-Champaign, Champaign, IL, USA. hkoehn@cyrus.psych.uiuc.edu.
authors: Hans-Friedrich
authors: HF
authors: Köhn
authors: University of Missouri, Columbia, MO, USA. steinleyd@missouri.edu.
authors: Douglas
authors: D
authors: Steinley
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D011594:Psychometrics / Q000706:statistics & numerical data; D018709:Statistics, Nonparametric
keywords: exact algorithm; item selection; mokken scale analysis; nonparametric IRT; partial correlation