caa a22 4500 60624218X CHVBK 20210128101317.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s11336-015-9459-8 doi (NATIONALLICENCE)springer-10.1007/s11336-015-9459-8 An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model [Elektronische Daten] [Michael Brusco, Hans-Friedrich Köhn, Douglas Steinley] 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. The Psychometric Society, 2015 nonparametric IRT nationallicence partial correlation nationallicence mokken scale analysis nationallicence item selection nationallicence exact algorithm nationallicence Brusco Michael Florida State University, 821 Academic Way, 32306-1110, Tallahassee, FL, USA aut Köhn Hans-Friedrich University of Illinois at Urbana-Champaign, Champaign, IL, USA aut Steinley Douglas University of Missouri, Columbia, MO, USA aut Psychometrika Springer US; http://www.springer-ny.com 80/4(2015-12-01), 949-967 0033-3123 80:4<949 2015 80 11336 https://doi.org/10.1007/s11336-015-9459-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11336-015-9459-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brusco Michael Florida State University, 821 Academic Way, 32306-1110, Tallahassee, FL, USA aut NATIONALLICENCE 700 1- Köhn Hans-Friedrich University of Illinois at Urbana-Champaign, Champaign, IL, USA aut NATIONALLICENCE 700 1- Steinley Douglas University of Missouri, Columbia, MO, USA aut NATIONALLICENCE 773 0- Psychometrika Springer US; http://www.springer-ny.com 80/4(2015-12-01), 949-967 0033-3123 80:4<949 2015 80 11336