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Computational Statistics

, Volume 33, Issue 2, pp 983–996 | Cite as

Working correlation structure selection in generalized estimating equations

  • Liya Fu
  • Yangyang Hao
  • You-Gan Wang
Original Paper
First Online:
  • 165 Downloads

Abstract

Selecting an appropriate correlation structure in analyzing longitudinal data can greatly improve the efficiency of parameter estimation, which leads to more reliable statistical inference. A number of such criteria have been proposed in the literature from different perspectives. However, little is known about the relative performance of these criteria. We review and evaluate these criteria by carrying out extensive simulation studies. Surprisingly, we find that the AIC and the BIC based on either the Gaussian working likelihood or the empirical likelihood outperform the others.

Keywords

Correlation information criterion Empirical likelihood Longitudinal data Model selection 
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Notes

Acknowledgements

This research was funded by the Australian Research Council Discovery Projects (DP130100766 and DP160104292). L. Fu’s research was partly supported by the National Science Foundation of China (Grant Nos. 11201365 and 11301408) and the Doctoral Programs Foundation of Ministry of Education of China (Grant No. 2012020112005)and the Fundamental Research Funds for the Central Universities (Grant No. xjj2017180).

Supplementary material

180_2018_800_MOESM1_ESM.pdf (280 kb)
Supplementary material 1 (pdf 280 KB)
180_2018_800_MOESM2_ESM.r (40 kb)
Supplementary material 2 (R 39 KB)

References

  1. Carey VJ, Wang Y-G (2011) Working covariance model selection for generalized estimating equations. Stat Med 30:3117–3124MathSciNetCrossRefGoogle Scholar
  2. Chen J, Lazar NA (2012) Selection of working correlation structure in generalized estimating equations via empirical likelihood. J Comput Graph Stat 21:18–41MathSciNetCrossRefGoogle Scholar
  3. Davidson R, MacKinnon JG (2004) Econometric theory and methods. Oxford University Press, OxfordGoogle Scholar
  4. Diggle PJ, Heagerty PJ, Liang KL, Zeger SL (2002) Analysis of longitudinal data. Oxford University Press, OxfordzbMATHGoogle Scholar
  5. Erhardt V (2009) Generate correlated count random variables. R package version 1.4. https://cran.rproject.org/web/packages/corcounts/index.html
  6. Fitzmaurice GM (1995) A caveat concerning independence estimating equations with multivariate binary data. Biometircs 51:309–317CrossRefzbMATHGoogle Scholar
  7. Genz A, Bretz F, Miwa T, Mi X, Leisch F, Scheipl F, Bornkamp B, Hothorn T (2014) Multivariate normal and t distributions. R package version 0.9-9997. http://CRAN.R-project.org/package=bindata
  8. Gosho M, Hamada C, Yoshimura I (2011) Criterion for the selection of a working correlation structure in the generalized estimating equation approach for longitudinal data. Commun Stat Theory Methods 40:3839–3856MathSciNetCrossRefzbMATHGoogle Scholar
  9. Gosho M, Hamada C, Yoshimura I (2014) Selection of working correlation structure in weighted generalized estimating equation mehod for incomplete longitudinal data. Commun Stat Theory Methods 43:62–81zbMATHGoogle Scholar
  10. Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econometrica 50:1029–1054MathSciNetCrossRefzbMATHGoogle Scholar
  11. Hin L-Y, Carey VJ, Wang Y-G (2007) Criteria for working-correlation-structure selection in GEE: assessment via simulation. Am Assoc 61:360–364MathSciNetGoogle Scholar
  12. Hin L-Y, Wang Y-G (2009) Working correlation structure identification in generalized estimating equations. Stat Med 28:642–658MathSciNetCrossRefGoogle Scholar
  13. Leisch F, Weingessel A, Hornik K (2011) Generation of artificial binary data. R package version 0.9-19. http://CRAN.R-project.org/package=bindata
  14. Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13–22MathSciNetCrossRefzbMATHGoogle Scholar
  15. McCullagh P, Nelder J (1989) Generalized linear models. Chapman & Hall, LondonCrossRefzbMATHGoogle Scholar
  16. McDonald BW (1993) Estimating logistic regression parameters for bivariate binary data. J R Stat Soc Ser B 55:391–397MathSciNetzbMATHGoogle Scholar
  17. Owen AB (2001) Empirical likelihood. Chapman and Hall-CRC, New YorkCrossRefzbMATHGoogle Scholar
  18. Pan W (2001) Akaike’s information criterion in generalized estimating equations. Biometrics 57:120–125MathSciNetCrossRefzbMATHGoogle Scholar
  19. Rotnitzky A, Jewell NP (1990) Hypothesis testing of regression parameteres in semparametric generalized linear models for clustere correlated data. Biomtrika 77:485–497CrossRefzbMATHGoogle Scholar
  20. Shults J, Chaganty NR (1998) Analysis of serially correlated data using quasi-least square. Biometrics 54:1622–1630CrossRefzbMATHGoogle Scholar
  21. Shults J, Sun W, Tu X, Kim HF, Amsterdam J, Hilbe JM, Ten-Have T (2009) A comparison of several approaches for choosing between working correlation structures in generalzied estimating equation analysis of longitudinal binary data. Stat Med 28:2338–2355MathSciNetCrossRefGoogle Scholar
  22. Thall PF, Vail SC (1990) Some covariance models for longitudinal count data with overdispersion. Biometrics 46:657–671MathSciNetCrossRefzbMATHGoogle Scholar
  23. Wang Y-G, Carey VJ (2003) Working correlation structure misspecification, estimation and covariate design: implications for generalised estimating equations performance. Biometrika 90:29–41MathSciNetCrossRefzbMATHGoogle Scholar
  24. Wang Y-G, Carey VJ (2004) Unbiased estimating equations from working correlation models for irregularly timed repeated measures. J Am Stat Assoc 99:845–853MathSciNetCrossRefzbMATHGoogle Scholar
  25. Wang Y-G, Hin L-Y (2010) Modeling strategies in longitudinal data analysis: covariate, variance function and correlations structure selection. Comput Stat Data Anal 54:3359–3370MathSciNetCrossRefzbMATHGoogle Scholar
  26. Wang Y-G, Zhao Y (2007) A modified pseudolikelihood approach for analysis of longitudinal data. Biometrics 63:681–689MathSciNetCrossRefzbMATHGoogle Scholar
  27. Zhu X, Zhu Z (2013) Comparison of criteria to select working correlation matrix in generalized estimating equations. Chin J Appl Probab Stat 29:515–530MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  2. 2.Logistics Research CenterShanghai Maritime UniversityShanghaiChina
  3. 3.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia

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