Function to fit a Generalized Estimating Equation Model
Produces an object of class ‘geese’ which is a Generalized Estimating Equation fit of the data.
geese( formula = formula(data), sformula = ~1, id, waves = NULL, data = parent.frame(), subset = NULL, na.action = na.omit, contrasts = NULL, weights = NULL, zcor = NULL, corp = NULL, control = geese.control(...), b = NULL, alpha = NULL, gm = NULL, family = gaussian(), mean.link = NULL, variance = NULL, cor.link = "identity", sca.link = "identity", link.same = TRUE, scale.fix = FALSE, scale.value = 1, corstr = "independence", ... )
formula |
a formula expression as for |
sformula |
a formula expression of the form |
id |
a vector which identifies the clusters. The length of ‘id’ should be the same as the number of observations. Data are assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula. |
waves |
an integer vector which identifies components in
clusters. The length of |
data |
an optional data frame in which to interpret the
variables occurring in the |
subset |
expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default. |
na.action |
a function to filter missing data. For |
contrasts |
a list giving contrasts for some or all of the factors appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels. |
weights |
an optional vector of weights to be used in the
fitting process. The length of |
zcor |
a design matrix for correlation parameters. |
corp |
known parameters such as coordinates used for correlation coefficients. |
control |
a list of iteration and algorithmic constants. See
|
b |
an initial estimate for the mean parameters. |
alpha |
an initial estimate for the correlation parameters. |
gm |
an initial estimate for the scale parameters. |
family |
a description of the error distribution and link
function to be used in the model, as for |
mean.link |
a character string specifying the link function
for the means. The following are allowed: |
variance |
a character string specifying the variance function
in terms of the mean. The following are allowed:
|
cor.link |
a character string specifying the link function for
the correlation coefficients. The following are allowed:
|
sca.link |
a character string specifying the link function for
the scales. The following are allowed: |
link.same |
a logical indicating if all the components in a cluster should use the same link. |
scale.fix |
a logical variable; if true, the scale parameter
is fixed at the value of |
scale.value |
numeric variable giving the value to which the
scale parameter should be fixed; used only if |
corstr |
a character string specifying the correlation
structure. The following are permitted: |
... |
further arguments passed to or from other methods. |
when the correlation structure is fixed, the specification of
Zcor should be a vector of length sum(clusz * (clusz - 1)) /
2.
An object of class "geese" representing the fit.
Jun Yan jyan.stat@gmail.com
Yan, J. and J.P. Fine (2004) Estimating Equations for Association Structures. Statistics in Medicine, 23, 859–880.
data(seizure)
## Diggle, Liang, and Zeger (1994) pp166-168, compare Table 8.10
seiz.l <- reshape(seizure,
varying=list(c("base","y1", "y2", "y3", "y4")),
v.names="y", times=0:4, direction="long")
seiz.l <- seiz.l[order(seiz.l$id, seiz.l$time),]
seiz.l$t <- ifelse(seiz.l$time == 0, 8, 2)
seiz.l$x <- ifelse(seiz.l$time == 0, 0, 1)
m1 <- geese(y ~ offset(log(t)) + x + trt + x:trt, id = id,
data=seiz.l, corstr="exch", family=poisson)
summary(m1)
m2 <- geese(y ~ offset(log(t)) + x + trt + x:trt, id = id,
data = seiz.l, subset = id!=49,
corstr = "exch", family=poisson)
summary(m2)
## Using fixed correlation matrix
cor.fixed <- matrix(c(1, 0.5, 0.25, 0.125, 0.125,
0.5, 1, 0.25, 0.125, 0.125,
0.25, 0.25, 1, 0.5, 0.125,
0.125, 0.125, 0.5, 1, 0.125,
0.125, 0.125, 0.125, 0.125, 1), 5, 5)
cor.fixed
zcor <- rep(cor.fixed[lower.tri(cor.fixed)], 59)
m3 <- geese(y ~ offset(log(t)) + x + trt + x:trt, id = id,
data = seiz.l, family = poisson,
corstr = "fixed", zcor = zcor)
summary(m3)
data(ohio)
fit <- geese(resp ~ age + smoke + age:smoke, id=id, data=ohio,
family=binomial, corstr="exch", scale.fix=TRUE)
summary(fit)
fit.ar1 <- geese(resp ~ age + smoke + age:smoke, id=id, data=ohio,
family=binomial, corstr="ar1", scale.fix=TRUE)
summary(fit.ar1)
###### simulated data
## a function to generate a dataset
gendat <- function() {
id <- gl(50, 4, 200)
visit <- rep(1:4, 50)
x1 <- rbinom(200, 1, 0.6) ## within cluster varying binary covariate
x2 <- runif(200, 0, 1) ## within cluster varying continuous covariate
phi <- 1 + 2 * x1 ## true scale model
## the true correlation coefficient rho for an ar(1)
## correlation structure is 0.667.
rhomat <- 0.667 ^ outer(1:4, 1:4, function(x, y) abs(x - y))
chol.u <- chol(rhomat)
noise <- as.vector(sapply(1:50, function(x) chol.u %*% rnorm(4)))
e <- sqrt(phi) * noise
y <- 1 + 3 * x1 - 2 * x2 + e
dat <- data.frame(y, id, visit, x1, x2)
dat
}
dat <- gendat()
fit <- geese(y ~ x1 + x2, id = id, data = dat, sformula = ~ x1,
corstr = "ar1", jack = TRUE, j1s = TRUE, fij = TRUE)
summary(fit)
#### create user-defined design matrix of unstrctured correlation.
#### in this case, zcor has 4*3/2 = 6 columns, and 50 * 6 = 300 rows
zcor <- genZcor(clusz = rep(4, 50), waves = dat$visit, "unstr")
zfit <- geese(y ~ x1 + x2, id = id, data = dat, sformula = ~ x1,
corstr = "userdefined", zcor = zcor,
jack = TRUE, j1s = TRUE, fij = TRUE)
summary(zfit)
#### Now, suppose that we want the correlation of 1-2, 2-3, and 3-4
#### to be the same. Then zcor should have 4 columns.
z2 <- matrix(NA, 300, 4)
z2[,1] <- zcor[,1] + zcor[,4] + zcor[,6]
z2[,2:4] <- zcor[, c(2, 3, 5)]
summary(geese(y ~ x1 + x2, id = id, data = dat, sformula = ~ x1,
corstr = "userdefined", zcor = z2,
jack = TRUE, j1s = TRUE, fij = TRUE))
#### Next, we introduce non-constant cluster sizes by
#### randomly selecting 60 percent of the data
good <- sort(sample(1:nrow(dat), .6 * nrow(dat)))
mdat <- dat[good,]
summary(geese(y ~ x1 + x2, id = id, data = mdat, waves = visit,
sformula = ~ x1, corstr="ar1",
jack = TRUE, j1s = TRUE, fij = TRUE))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.