Comparing Estimation Methods for Categorical Marginal Models

  • Renske E. KuijpersEmail author
  • Wicher P. Bergsma
  • L. Andries van der Ark
  • Marcel A. Croon
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 89)


Categorical marginal models are flexible models for modelling dependent or clustered categorical data which do not involve any specific assumptions about the nature of the dependencies. Categorical marginal models are used for different purposes, including hypothesis testing, assessing model fit, and regression problems. Two different estimation methods are used to estimate marginal models: maximum likelihood (ML) and generalized estimating equations (GEE). We explored three different cases to find out to what extent the two types of estimation methods are appropriate for investigating different types of research questions. The results suggest that ML may be preferred for assessing model fit because GEE has limited fit indices, whereas both methods can be used to assess the effect of independent factors in regression. Moreover, ML is asymptotically efficient, while GEE loses efficiency when the working correlation matrix is not correctly specified. However, for parameter estimation in regression GEE is easier to apply from a computational perspective.



The authors would like to thank Klaas Sijtsma for commenting on earlier versions of the manuscript.


  1. Agresti A (2013) Categorical data analysis. Wiley, HobokenzbMATHGoogle Scholar
  2. Aitchison J, Silvey SD (1958) Maximum likelihood estimation of parameters subject to restraints. Ann Math Stat 29:813–828CrossRefzbMATHMathSciNetGoogle Scholar
  3. Bergsma WP (1997) Marginal models for categorical data. Tilburg University Press, TilburgzbMATHGoogle Scholar
  4. Bergsma WP, Van der Ark LA (2013) cmm: An R-package for categorical marginal models (Version 0.7) [computer software]. Accessed 24 Feb 2013
  5. Bergsma WP, Croon MA, Hagenaars JA (2009) Marginal models: for dependent, clustered, and longitudinal categorical data. Springer, New YorkGoogle Scholar
  6. Bergsma WP, Croon MA, Van der Ark LA (2012) The empty set and zero likelihood problems in maximum empirical likelihood estimation. Electron J Stat 6:2356–2361CrossRefzbMATHMathSciNetGoogle Scholar
  7. Bergsma WP, Croon MA, Hagenaars JA (2013) Advancements in marginal modelling for categorical data. Sociol Methodol 43:1–41CrossRefGoogle Scholar
  8. Cronbach LJ (1951) Coefficient alpha and the internal structure of tests. Psychometrika 16: 297–334CrossRefGoogle Scholar
  9. Kesteloot H, Geboers J, Joossens JV (1989) On the within-population relationship between nutrition and serum lipids, the birnh study. Eur Heart J 10:196–202Google Scholar
  10. Kritzer HM (1977) Analyzing measures of association derived from contingency tables. Sociol Methods Res 5:35–50CrossRefGoogle Scholar
  11. Kuijpers RE, Van der Ark LA, Croon MA (2013a) Testing hypotheses involving Cronbach’s alpha using marginal models. Br J Math Stat Psychol 66:503–520. doi: 10.1111/bmsp.12010MathSciNetGoogle Scholar
  12. Kuijpers RE, Van der Ark LA, Croon MA (2013b) Standard errors and confidence intervals for scalability coefficients in Mokken scale analysis using marginal models. Sociol Methodol 43:42–69CrossRefGoogle Scholar
  13. Lang JB (2004) Multinomial-Poisson homogeneous models for contingency tables. Annals of Statistics, 32:340–383.CrossRefzbMATHMathSciNetGoogle Scholar
  14. Liang K-Y, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13–22CrossRefzbMATHMathSciNetGoogle Scholar
  15. Lipsitz S, Fitzmaurice G (2009) Generalized estimating equations for longitudinal data analysis. In: Fitzmaurice G, Davidian M, Verbeke G, Molenberghs G (eds) Longitudinal data analysis. Chapman & Hall/CRC, Boca Raton, pp 43–78Google Scholar
  16. Molenberghs G, Verbeke G (2005) Models for discrete longitudinal data. Springer, New YorkzbMATHGoogle Scholar
  17. Nunnally JC (1978) Psychometric theory. McGraw-Hill, New YorkGoogle Scholar
  18. Owen AB (2001) Empirical likelihood. Chapman & Hall/CRC, LondonzbMATHGoogle Scholar
  19. Pawitan Y (2001) In all likelihood: statistical modelling and inference using likelihood. Clarendon Press, OxfordGoogle Scholar
  20. Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling: multilevel, longitudinal, and structural equation models. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  21. Van der Ark LA, Croon MA, Sijtsma K (2008) Mokken scale analysis for dichotomous items using marginal models. Psychometrika 73:183–208CrossRefzbMATHMathSciNetGoogle Scholar
  22. Van der Ark LA, Bergsma WP, Croon MA (2013) Augmented empirical likelihood estimation of categorical marginal models for large sparse contingency tables (under review)Google Scholar
  23. Van der Veen G (1992) Principes in praktijk: CNV-leden over collectieve acties [Principles into practice. Labour union members on means of political pressure]. J.H. Kok, KampenGoogle Scholar
  24. Yan J, Højsgaard S, Halekoh U (2012) geepack: Generalized Estimating Equation package. (Version 1.1-6) [computer software]. Accessed 13 Dec 2013

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Renske E. Kuijpers
    • 1
    Email author
  • Wicher P. Bergsma
    • 2
  • L. Andries van der Ark
    • 3
  • Marcel A. Croon
    • 4
  1. 1.Department of Methodology and StatisticsTilburg UniversityTilburgThe Netherlands
  2. 2.London School of EconomicsLondonUK
  3. 3.University of AmsterdamAmsterdamThe Netherlands
  4. 4.Tilburg UniversityTilburgThe Netherlands

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