family
argument.
glme(fixed, data, random, family, correlation, weights, dispersion, start, subset, method, na.action, control, verbose)
~
operator
and the terms, separated by
+
operators,
on the right, a
glmList
object,
or a
groupedData
object.
The method functions
glme.glmList
and
glme.groupedData
are documented separately.
fixed
,
random
,
correlation
,
weights
,
and
subset
.
By default the variables are taken from the environment
from which
lme
is called.
~x1+...+xn | g1/.../gm
,
with
x1+...+xn
specifying the model for the random effects
and
g1/.../gm
the grouping structure
(
m
may be equal to 1,
in which case no
/
is required).
The random effects formula will be repeated for all levels of grouping,
in the case of multiple levels of grouping;
(ii) a list of one-sided formulas of the form
~x1+...+xn | g
,
with possibly different random effects models for each grouping level.
The order of nesting will be assumed the same as the order
of the elements in the list;
(iii) a one-sided formula of the form
~x1+...+xn
,
or a
pdMat
object with a formula
(i.e. a non-
NULL
value
for
formula(object)
),
or a list of such formulas or
pdMat
objects.
In this case, the grouping structure formula will be derived
from the data used to fit the linear mixed-effects model,
which should inherit from class
groupedData
;
(iv) a named list of formulas or
pdMat
objects as in (iii), with the grouping factors as names.
The order of nesting will be assumed the same as the order
of the order of the elements in the list;
(v) an
reStruct
object.
See the documentation on
pdClasses
for a description of the available
pdMat
classes.
Defaults to a formula consisting of the right hand side
of
fixed
.
gaussian
,
binomial
,
poisson
,
Gamma
,
inverse.gaussian
and
quasi
.
Functions like
binomial
produce a family object,
but can be given without the parentheses.
Family functions can take arguments,
as in
binomial(link=probit)
.
Defaults to
gaussian
.
corStruct
object describing the
within-group correlation structure.
See the documentation of
corClasses
for a description of the available
corStruct
classes.
Defaults to
NULL
,
corresponding to no within-group correlations.
varFunc
object or one-sided formula
describing the within-group heteroscedasticity structure to
be used in addition to the variance function corresponding to
family
.
If given as a formula,
it is used as the argument to
varFixed
,
corresponding to fixed variance weights.
See the documentation on
varClasses
for a description of the available
varFunc
classes.
Defaults to
NULL
,
in which case only the variance function corresponding
to
family
is used.
0
.
mu
,
with starting estimates for the fitted responses.
Defaults to an empty list, in which case the starting estimates
for the fitted responses are obtained using the initialization procedure
in
family
.
data
that should be used in the fit.
This can be a logical vector,
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.
"(RE)PQL"
the model is fit
by maximizing the (restricted) penalized quasi-likelihood.
If
"(RE)MQL"
the (restricted) marginal
quasi-likelihood is maximized. Use
AGQUAD
for adaptive gaussian quadrature
or
LAPLACE
for Laplacian approximation to the
likelihood when fitting the
model. The number of quadrature points can be specified through the
control
formal argument, see below. The default number of
quadrature points is three. When using methods
AGQUAD
or
LAPLACE
, the
family
must be either
binomial
or
poisson
with their canonical links
logit
and
log
, respectively.
Defaults to
"REPQL"
.
See the NOTES section below about using "REPQL" with the poisson or binomial
families.
NA
s.
The default action (
na.fail
) causes
lme
to print an error message
and terminate if there are any incomplete observations.
lmeControl
. If
method=AGQUAD
is used, the number of quadrature points can be specified using
Ngq=n
, where
n
is
a positive integer.
Defaults to an empty list.
TRUE
information on the evolution
of the iterative algorithm is printed.
Default is
FALSE
.
glme
,
also inheriting from class
lme
,
representing the generalized linear mixed-effects model fit.
Generic functions such as
print
,
plot
and
summary
have methods to show the results of the fit.
See
glmeObject
for the components of the fit.
The functions
resid
,
coef
,
fitted
,
fixef
, and
ranef
can be used to extract some of its components.
The computational and estimation methods are
described in Breslow and Clayton (1993) and Pinheiro and Chao (2004).
The variance-covariance parameterizations
and the different correlation structures available
for the
correlation
argument are described
in Pinheiro and Bates (1996, 2000)
and Venables and Ripley (1999).
The PQL approximation of the likelihood for the binomial and poisson
families is generally poor especially with small sample sizes.
The LAPLACE approximation (
method="LAPLACE"
) may be a better
in these situations.
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized mixed models. Journal of the American Statistical Association, 88, 9-25.
Pinheiro, J. C. and Bates., D. M. (1996). Unconstrained parameterizations for variance-covariance matrices. Statistics and Computing, 6, 289-296.
Pinheiro, J. C. and Bates., D. M. (2000). Mixed-effects Models in S and S-PLUS. Springer-Verlag, New York.
Pinheiro, J. C. and Chao, E. C. (2004). Efficient Laplacian and adaptive Gaussian quadrature algorithms for multilevel generalized linear mixed models, Journal of Computational and Graphics Statistics, (submitted).
Venables, W. N. and Ripley, B. D. (1999). Modern Applied Statistics with S-PLUS", 3rd Edition Springer-Verlag, New York.
fm1 <- glme(resp ~ trt, data=Clinic, random = ~1|clinic/trt, family=binomial)