ArticlePsychometrika2015
An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model.
Article in Psychometrika, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models.Psychometrika · 2023Article
- Incomplete Tests of Conditional Association for the Assessment of Model Assumptions.Psychometrika · 2022Article
- A two-step, test-guided Mokken scale analysis, for nonclustered and clustered data.Quality of life research : an international journal of quality of life aspects of treatment, care and rehabilitation · 2022Article
- Advances in nonparametric item response theory for scale construction in quality-of-life research.Quality of life research : an international journal of quality of life aspects of treatment, care and rehabilitation · 2022Review
- Article
- A comparison of latent class, K-means, and K-median methods for clustering dichotomous data.Psychological methods · 2017Article
Corrections and comments
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
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.
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Registered trials
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