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Multilevel Logistic Regression for Polytomous Data and Rankings

Published online by Cambridge University Press:  01 January 2025

Anders Skrondal  and
Sophia Rabe-Hesketh
Anders Skrondal*
Affiliation:
Division of Epidemiology, Norwegian Institute of Public Health, Oslo
Sophia Rabe-Hesketh
Affiliation:
Department of Biostatistics and Computing, Institute of Psychiatry, London
*
Requests for reprints should be sent to Anders Skrondal, Division of Epidemiology, Norwegian Institute of Public Health, P.O. Box 4404 Nydalen, N-0403 Oslo, NORWAY. E-Mail: anders.skrondal@fhi.no
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Abstract

We propose a unifying framework for multilevel modeling of polytomous data and rankings, accommodating dependence induced by factor and/or random coefficient structures at different levels. The framework subsumes a wide range of models proposed in disparate methodological literatures. Partial and tied rankings, alternative specific explanatory variables and alternative sets varying across units are handled. The problem of identification is addressed. We develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software. The methodology is applied to party choice and rankings from the 1987–1992 panel of the British Election Study. Three levels are considered: elections, voters and constituencies.

Keywords

multilevel modelsgeneralized linear latent and mixed modelsfactor modelsrandom coefficient modelspolytomous datarankingsfirst choicediscrete choicepermutationsnominal datagllamm
Type
Articles
Information
Psychometrika , Volume 68 , Issue 2 , June 2003 , pp. 267 - 287
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

Parts of this work were completed while Anders Skrondal visited the Biostatistics Group at The University of Manchester, UK. gllamm and the script for the analyses in this article can be downloaded from: http://www.iop.kcl.ac.uk/IoP/Departments/BioComp/programs/gllamm.html.

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