A Modified GEE Variance Estimator Proposed by Wang and Long (2011).

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Description

Calculate the modified GEE variance estimator proposed by Wang and Long (2011).

Usage

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GEE.var.wl(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

a vector which identifies the clusters. The length of id should be the same as the total number of observations. Data is assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula.

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the variance estimator proposed by Wang and Long (2011). Two assumptions need to be satisfied: 1) The conditional variance is correctly specified; 2) A common correlation structure exists across all subjects.

Value

cov.beta

estimate of the variance for beta

cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <mwang@phs.psu.edu>

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

References

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.

Examples

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data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
                   varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
wl.ind <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="independence") ##Independence correlation structure;            
wl.exch <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="exchangeable") ##Exchangeable correlation structure;               
wl.ar1 <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="AR-M") ##AR-1 correlation structure;            
wl.unstr <- GEE.var.wl(formula,id="subject",family=gaussian,
         data_alt,corstr="unstructured") ##Unstructured correlation structure;