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 language | English (US) |
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Pages (from-to) | 949-967 |
Number of pages | 19 |
Journal | Psychometrika |
Volume | 80 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1 2015 |
Keywords
- exact algorithm
- item selection
- mokken scale analysis
- nonparametric IRT
- partial correlation
ASJC Scopus subject areas
- General Psychology
- Applied Mathematics