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) |
|---|---|
| Pages (from-to) | 949-967 |
| Number of pages | 19 |
| Journal | Psychometrika |
| Volume | 80 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 2015 |
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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.; Köhn, Hans Friedrich; Steinley, Douglas.
In: Psychometrika, Vol. 80, No. 4, 01.12.2015, p. 949-967.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model
AU - Brusco, Michael J.
AU - Köhn, Hans Friedrich
AU - Steinley, Douglas
PY - 2015/12/1
Y1 - 2015/12/1
N2 - 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.
AB - 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.
KW - exact algorithm
KW - item selection
KW - mokken scale analysis
KW - nonparametric IRT
KW - partial correlation
UR - http://www.scopus.com/inward/record.url?scp=84947130208&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84947130208&partnerID=8YFLogxK
U2 - 10.1007/s11336-015-9459-8
DO - 10.1007/s11336-015-9459-8
M3 - Article
C2 - 25850618
AN - SCOPUS:84947130208
VL - 80
SP - 949
EP - 967
JO - Psychometrika
JF - Psychometrika
SN - 0033-3123
IS - 4
ER -