lme(fixed, data, random, correlation, weights, subset, method, na.action, control)
lmList
object, or a
groupedData
object.
In the first case, a two-sided formula object describing the
fixed-effects part of the model, with the response on the left of a ~
operator and the terms, separated by
+
operators, on the right.
For the other two cases see the help files for
lme.lmList
and
lme.groupedData
.
fixed
,
random
,
correlation
,
weights
,
and
subset
.
By default the variables are taken from the environment
from which
lme
is called.
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 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
.
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.
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
,
corresponding to homoskedastic within-group errors.
data
that should be used in the fit.
This can be a logical vector,
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.
"REML"
the model is fit
by maximizing the restricted log-likelihood.
If
"ML"
the log-likelihood is maximized.
Defaults to
"REML"
.
NA
s.
The default action (
na.fail
)
causes
lme
to print an error message
and terminate if there are any incomplete observations.
lmeControl
.
Defaults to an empty list.
lme
representing the linear mixed-effects model fit.
Generic functions such as
print
,
plot
and
summary
have methods to show the results of the fit.
See
lmeObject
for the components of the fit.
The functions
resid
,
coef
,
fitted
,
fixed.effects
,
and
random.effects
can be used to extract some of its components.
Bates, D. M. and Pinheiro, J. C. (1998). Computational methods for multilevel models. Available in PostScript or PDF formats at http://nlme.stat.wisc.edu.
Box, G. E. P., Jenkins, G. M., and Reinsel G. C. (1994). Time Series Analysis: Forecasting and Control (3rd Edition). San Francisco: Holden-Day.
Davidian, M. and Giltinan, D. M. (1995). Nonlinear Mixed Effects Models for Repeated Measurement Data. London: Chapman and Hall.
Laird, N. M. and Ware, J. H. (1982). Random-Effects Models for Longitudinal Data. Biometrics, 38, 963-974.
Lindstrom, M. J. and Bates, D. M. (1988). Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data. Journal of the American Statistical Association, 83, 1014-1022.
Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996). SAS Systems for Mixed Models. Cary, North Carolina: SAS Institute, Inc.
Pinheiro, J. C. and Bates., D. M. (1996). Unconstrained Parametrizations for Variance-Covariance Matrices. Statistics and Computing, 6, 289-296.
Venables, W. N. and Ripley, B. D. (1999). Modern Applied Statistics with S-PLUS (3rd Edition). New York: Springer-Verlag.
The computational methods are described in Bates and Pinheiro (1998),
and follow on the general framework of Lindstrom and Bates (1988).
The model formulation is described in Laird and Ware (1982).
The variance-covariance parametrizations are described
in Pinheiro and Bates (1996).
The different correlation structures available for the
correlation
argument are described
in Box, Jenkins, and Reinsel (1994),
Littel, Milliken, Stroup, and Wolfinger (1996),
and Venables and Ripley (1997).
The use of variance functions for linear and nonlinear mixed effects models
is presented in detail in Davidian and Giltinan (1995).
fm1 <- lme(distance ~ age, data=Orthodont) # random is ~ age fm2 <- lme(distance ~ age + Sex, data=Orthodont, random = ~ 1)