genZcor: genZcor

Description

constructs the design matrix for the correlation structures: independence, echangeable, ar1 and unstructured The user will need this function only as a basis to construct a user defined correlation structure: use genZcor to get the design matrix Z for the unstructured correlation and define the specific correlation structure by linear combinations of the columns of Z.

Usage

genZcor(clusz, waves, corstrv)

Value

The design matrix for the correlation structure.

Arguments

clusz: integer vector giving the number of observations in each cluster.
waves: integer vector, obervations in the same cluster with values of wave i and j have the correlation \(latex\).
corstrv: correlation structures: 1=independence, 2=exchangeable, 3=ar1, 4=unstructured.

Author

Jun Yan jyan.stat@gmail.com

Examples

Run this code


# example to construct a Toeplitz correlation structure
#    sigma_ij=sigma_|i-j|

# data set with 5 clusters and maximally 4 observations (visits) per cluster
gendat <- function() {
       id <- gl(5, 4, 20)
       visit <- rep(1:4, 5)
       y <- rnorm(id)
       dat <- data.frame(y, id, visit)[c(-2,-9),]
}

set.seed(88)
dat <- gendat()

# generating the design matrix for the unstructured correlation
zcor <- genZcor(clusz = table(dat$id), waves = dat$visit, corstrv=4)

# defining the Toeplitz structure 
zcor.toep     <- matrix(NA, nrow(zcor), 3)
zcor.toep[,1] <- apply(zcor[,c(1, 4, 6)], 1, sum)
zcor.toep[,2] <- apply(zcor[,c(2, 5)], 1, sum)
zcor.toep[,3] <- zcor[,3]

zfit1 <- geese(y ~ 1,id = id, data = dat,
                   corstr = "userdefined", zcor = zcor.toep)


zfit2 <- geeglm(y ~ 1,id = id, data = dat,
                   corstr = "userdefined", zcor = zcor.toep)