Modified Variance Estimators for Generalized Estimating Equations

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Description

Generalized estimating equations with the original sandwich variance estimator proposed by Liang and Zeger (1986), and eight types of more recent modified variance estimators for improving the finite small-sample performance.

Details

Generalized estimating equations with the original sandwich variance estimator proposed by Liang and Zeger (1986), and eight types of more recent modified variance estimators for improving the finite small-sample performance.

GEE.var.pan(), GEE.var.gst() and GEE.var.wl() are only for the balanced data, while the others can be used for both balanced and unbalanced data.

Author(s)

Ming Wang <mwang@phs.psu.edu>

Maintainer: Zheng Li <zheng.li@outlook.com>

References

De Backer M, De Vroey C, Lesaffre E, Scheys I, De Keyser P. Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: a double-blind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. Journal of the American Academy of Dermatology 1998; 38: 57-63.

Fay MP and Graubard BI. Small-sample adjustments for Wald-type tests using sandwich estimators. Biometrics 2001;57: 1198-1206.

Gosho M, Sato Y and Takeuchi H. Robust covariance estimator for small-sample adjustment in the generalized estimating equations: A simulation study. Science Journal of Applied Mathematics and Statistics 2014;2(1):20-25.

Kauermann G and Carroll RJ. A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association 2001;96: 1387-1398.

Morel JG, Bokossa MC, and Neerchal NK. Small sample correction for the variance of GEE estimators. Biometrical Journal 2003;45(4): 395-409.

MacKinnon JG. Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 1985;29: 305-325.

Mancl LA and DeRouen TA. A covariance estimator for GEE with improved small-sample properties. Biometrics 2001;57: 126-134.

Pan W. On the robust variance estimator in Generalized Estimating Equations. Biometrika 2001;88: 901-906.

Pottho R. F. and Roy, S. W. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 1964;51:313-326

Thall PF, and Vail SC. Some covariance models for longitudinal count data with overdispersion. Biometrics 1990; 46: 657-671.

Wang M and Long Q. Modified robust variance estimator for generalized estimating equations with improved small-sample performance. Statistics in Medicine 2011;30(11): 1278-1291.

Zeger SL and Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986; 121-130.

See Also

GEE.var.lz()

GEE.var.mk()

GEE.var.kc()

GEE.var.pan()

GEE.var.fg()

GEE.var.gst()

GEE.var.md()

GEE.var.mbn()

GEE.var.wl()

Examples

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### Run the data analysis using the package using seizure dataset (Poisson);
data(seizure)
seizure$subject <- 1:length(seizure[,1])
data_alt <- reshape(seizure, direction="long", idvar="subject", timevar="Time", 
                   varying=names(seizure)[1:4], v.names="response", times=1:4) 
data_alt <- data_alt[order(data_alt$subject),]
data_alt <- data_alt[,c(4,1:3,5,6)]

### independence working correlation structure;
formula <- response~base+trt+Time
lz.ind <- GEE.var.lz(formula,id="subject",family=poisson,
               data_alt,corstr="independence")
               
mk.ind <- GEE.var.mk(formula,id="subject",family=poisson,
                data_alt,corstr="independence")
                
pan.ind <- GEE.var.pan(formula,id="subject",family=poisson,
         data_alt,corstr="independence")
         
gst.ind <- GEE.var.gst(formula,id="subject",family=poisson,
        data_alt,corstr="independence")
        
kc.ind <- GEE.var.kc(formula,id="subject",family=poisson,
         data_alt,corstr="independence") 
         
md.ind <- GEE.var.md(formula,id="subject",family=poisson,
        data_alt,corstr="independence")
        
fg.ind <- GEE.var.fg(formula,id="subject",family=poisson,data_alt,
                      corstr="independence",b=0.75) 
mbn.ind <- GEE.var.mbn(formula,id="subject",family=poisson,data_alt,
                      corstr="independence",d=2,r=1)                
wl.ind <- GEE.var.wl(formula,id="subject",family=poisson,
             data_alt,corstr="independence")