This generic function fits a linear mixed-effects model in the formulation described in Laird and Ware (1982) but allowing for nested random effects. The within-group errors are allowed to be correlated and/or have unequal variances.
This page describes the formula method;
are documented separately.
lme(fixed, data, random, correlation, weights, subset, method, na.action, control, contrasts = NULL, keep.data = TRUE)
# S3 method for formula lme(fixed, data, random, correlation, weights, subset, method, na.action, control, contrasts = NULL, keep.data = TRUE)
# S3 method for lme update(object, fixed., ..., evaluate = TRUE)
An object of class
"lme" representing the linear mixed-effects
model fit. Generic functions such as
summary have methods to show the results of the fit. See
lmeObject for the components of the fit. The functions
random.effects can be used to extract some of its components.
an object inheriting from class
a fitted linear mixed-effects model.
a two-sided linear 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, an
"lmList" object, or a
There is limited support for formulae such as
resp ~ 1 and
resp ~ 0, and less prior to version 3.1-112.
Changes to the fixed-effects formula -- see
update.formula for details.
an optional data frame containing the variables named in
subset. By default the variables are taken from the
environment from which
lme is called.
optionally, any of the following: (i) a one-sided formula
of the form
~ x1 + ... + xn | g1/.../gm, with
x1 + ... + xn
specifying the model for the random effects and
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
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
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
pdClasses for a description of the available
pdMat classes. Defaults to a formula consisting of the right
hand side of
corStruct object describing the
within-group correlation structure. See the documentation of
corClasses for a description of the available
classes. Defaults to
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
corresponding to fixed variance weights. See the documentation on
varClasses for a description of the available
classes. Defaults to
NULL, corresponding to homoscedastic
an optional expression indicating the subset of the rows of
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.
a character string. If
"REML" the model is fit by
maximizing the restricted log-likelihood. If
log-likelihood is maximized. Defaults to
a function that indicates what should happen when the
NAs. The default action (
lme to print an error message and terminate if there are any
a list of control values for the estimation algorithm to
replace the default values returned by the function
Defaults to an empty list.
an optional list. See the
logical: should the
data argument (if supplied
and a data frame) be saved as part of the model object?
some methods for this generic require additional arguments. None are used in this method.
TRUE evaluate the new call else return the call.
José Pinheiro and Douglas Bates email@example.com
offset terms in
fixed are an error since 3.1-157
(2022-03): previously they were silently ignored.
The computational methods follow 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), Littell et al (1996), and Venables and
Ripley (2002). The use of variance functions for linear and nonlinear
mixed effects models is presented in detail in Davidian and Giltinan
Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994). Time Series Analysis: Forecasting and Control, 3rd Edition, Holden--Day.
Davidian, M. and Giltinan, D.M. (1995). Nonlinear Mixed Effects Models for Repeated Measurement Data, Chapman and Hall. tools:::Rd_expr_doi("10.1201/9780203745502").
Laird, N.M. and Ware, J.H. (1982). Random-Effects Models for Longitudinal Data. Biometrics 38, 963--974. tools:::Rd_expr_doi("10.2307/2529876").
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. tools:::Rd_expr_doi("10.2307/2290128").
Littell, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D. (1996). SAS Systems for Mixed Models, SAS Institute.
Pinheiro, J.C. and Bates., D.M. (1996). Unconstrained Parametrizations for Variance-Covariance Matrices. Statistics and Computing 6, 289--296. tools:::Rd_expr_doi("10.1007/BF00140873").
Pinheiro, J.C., and Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS, Springer. tools:::Rd_expr_doi("10.1007/b98882").
Venables, W.N. and Ripley, B.D. (2002). Modern Applied Statistics with S, 4th Edition, Springer-Verlag. tools:::Rd_expr_doi("10.1007/978-0-387-21706-2").