Specify a Mixed Models to be fit with Generalized Estimating Equations
DESCRIPTION:
Createa a ranDesign object for random effect Z*b where Z is a
covariate matrix of {1, z2, z2, ..., zn} and b is a vactor of
random-effects parameters coming from
a normal distribution (0, D), where D is a diagonal matrix.
a one-sided formula of the form ~z1+...zn specifying the
model for the random effects.
OPTIONAL ARGUMENTS:
variance
a character string specifing the variance structure of random variables. Presently, it
is set to
"independent" only.
fixed
a numeric vector if the variance of random effects are fixed, or NULL if
the variance of random effects need to be estimated. The default is set to NULL.
method
a character string, either
"LS" for least square method or
"moment" for
moment method, specifying the method to estimate the scale parameters and
variances of random effects. The default is set to
"LS".
VALUE:
an object of class
ranDesign is returned
which includes the following components:
`terms'
a
terms object constructed from the formula.
`variance'
a character string of
"independent"
telling the variance structure
of random variables.
`fixed'
a numeric vector for fixed variance of random effects or
NULL
if the
variance of random effects need to be estimated.
`method'
a character string telling the estimation method for scale and variances of random effects.
SIDE EFFECTS:
For mixed models, GEE methods work on the marginal mean and variance.
The marginal mean might have an extra offset added or multiplied
to the linear predictor of the conditional mean.
The marginal variance consists of a set of variance components.
GEE is not a likelihood method.
Except Gaussian case,
applying GEE methods to mixed models might
not result in the same fit as applying with the
glme
.
See Zeger, Liang and Albert (1988) for more details.
Currently, this function is applicable only to
log, logit and probit links for Poisson and binomial data with limited
structure of variance components, e.g. independent variance components.
The best way to check its validity is through a simulation study.
REFERENCES:
Zeger, Linag and Albert (1988).
Models for longitudinal data: a generalized estimating
equation approach. Biometrics, 44, 1049-1060.