×

Analysis of GEE with a mixture working correlation matrix for diverging number of covariates. (English) Zbl 07498009

Summary: The generalized estimating equations (GEE) method has been widely used for longitudinal data analysis. L. Wang [Ann. Stat. 39, No. 1, 389–417 (2011; Zbl 1209.62138)] developed an asymptotic theory for GEE analysis of clustered binary data with diverging number of covariates. She suggested several moment estimators of the nuisance parameter in the working correlation matrix. However, these estimators might not exist when the working correlation structure is misspecified. When the number of covariates is finite, L. Xu et al. [Stat. Sin. 22, No. 2, 755–776 (2012; Zbl 1511.62183)] proposed a mix-GEE method based on a finite mixture model to capture correlations among repeated measurements. In this paper, we develop an asymptotic theory for the mix-GEE estimator with diverging number of covariates. Simulation studies are used to demonstrate the performance of the mix-GEE with diverging number of covariates, which indicate this method is more numerically stable and has a higher efficiency than the GEE with a specified working correlation matrix in diverging number of covariates framework. Finally, a real dataset is used for illustration.

MSC:

62-XX Statistics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liang, KY; Zeger, SL., Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22 (1986) · Zbl 0595.62110
[2] Crowder, M., On the use of a working correlation matrix in using generalized linear models for repeated measures, Biometrika, 82, 407-410 (1995) · Zbl 0823.62060
[3] Wang, YG; Carey, V., Working correlation structure misspecification, estimation and covariate design: implications for generalized estimating equations performance, Biometrika, 90, 29-41 (2003) · Zbl 1035.62074
[4] Leung, DHY; Wang, YG; Zhu, M., Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method, Biostatistics, 10, 436-445 (2009) · Zbl 1437.62523
[5] Bai, Y.; Fung, WK; Zhu, ZY., Weighted empirical likelihood for generalized linear models with longitudinal data, J Stat Plan Inference, 140, 3446-3456 (2010) · Zbl 1205.62098
[6] Qu, A.; Lindsay, BG; Li, B., Improving generalised estimating equations using quadratic inference functions, Biometrika, 87, 4, 823-836 (2000) · Zbl 1028.62045
[7] Xu, LL; Lin, N.; Zhang, BX, A finite mixture model for working correlation matrices in generalized estimating equations, Stat Sin, 22, 755-776 (2012) · Zbl 1511.62183
[8] Bai, Z.; Wu, Y., Limiting behavior of M-estimators of regression coefficients in high dimensional linear models, I. Scale-dependent case, J Multivar Anal, 51, 211-239 (1994) · Zbl 0816.62025
[9] He, X.; Shao, QM., On parameters of increasing dimensions, J Multivar Anal, 73, 120-135 (2000) · Zbl 0948.62013
[10] Xie, M.; Yang, Y., Asymptotics for generalized estimating equations with large cluster sizes, Ann Stat, 31, 310-347 (2003) · Zbl 1018.62019
[11] Wang, L., GEE analysis of clustered binary data with diverging number of covariates, Ann Stat, 39, 389-417 (2011) · Zbl 1209.62138
[12] Carey V, J. Gee: Generalized estimation equation solver. 2019-11-07, Version: 4.13-20.
[13] Qu, A.; Song, PX-K., Assessing robustness of generalised estimating equations and quadratic inference functions, Biometrika, 91, 2, 447-459 (2004) · Zbl 1079.62038
[14] Chaganty, NR; Joe, H., Efficiency of generalized estimating equations for binary responses, J R Stat Soc Ser B, 66, 851-860 (2004) · Zbl 1059.62076
[15] Park, CG; Shin, DW., An algorithm for generating correlated random variables in a class of infinitely divisible distributions, J Stat Comput Simul, 61, 127-139 (1998) · Zbl 0945.65003
[16] DeCosse, JJ; Miller, HH; Lesser, ML., Effect of wheat fiber and vitamins C and E on rectal polyps in patients with familial adenomatoses polyposis, J Natl Cancer Inst, 81, 1290-1297 (1989)
[17] Stukel, TA., Comparison of methods for the analysis of longitudinal interval count data, Stat Med, 12, 1339-1351 (1993)
[18] Ortega, JM; Rheinboldt, WC., Iterative solution of nonlinear equations in several variables (1970), San Diego: San Diego, Academic Press · Zbl 0241.65046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.