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.
lme(fixed, data, random, correlation, weights, subset, method, na.action, control, contrasts = NULL, keep.data = TRUE) ## S3 method for class 'lme': update((object, fixed., ..., evaluate = TRUE))
- an object inheriting from class
lme, representing 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
lmListobject, or a
groupedDataobject. The method functions
lme.groupedDataare documented separately.
- Changes to the fixed-effects formula -- see
- an optional data frame containing the variables named in
subset. By default the variables are taken from the environment from which
- optionally, any of the following: (i) a one-sided formula of the form
~ x1 + ... + xn | g1/.../gm, with
x1 + ... + xnspecifying the model for the random effects and
g1/.../gmthe grouping structure (
mmay 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
pdMatobject with a formula (i.e. a non-
formula(object)), or a list of such formulas or
pdMatobjects. 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
pdMatobjects 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
reStructobject. See the documentation on
pdClassesfor a description of the available
pdMatclasses. Defaults to a formula consisting of the right hand side of
- an optional
corStructobject describing the within-group correlation structure. See the documentation of
corClassesfor a description of the available
corStructclasses. Defaults to
NULL, corresponding to no within-group correlations.
- an optional
varFuncobject 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
varClassesfor a description of the available
varFuncclasses. Defaults to
NULL, corresponding to homoscedastic within-group errors.
- an optional expression indicating the subset of the rows of
datathat 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
"ML"the log-likelihood is maximized. Defaults to
- a function that indicates what should happen when the data contain
NAs. The default action (
lmeto print an error message and terminate if there are any incomplete observations.
- a list of control values for the estimation algorithm to replace the default values returned by the function
lmeControl. Defaults to an empty list.
- an optional list. See the
- logical: should the
dataargument (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.
TRUEevaluate the new call else return the call.
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.
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 Reinse (1994), Littel 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 (1995).
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.
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", SAS Institute.
Pinheiro, J.C. and Bates., D.M. (1996) "Unconstrained Parametrizations 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.
Venables, W.N. and Ripley, B.D. (2002) "Modern Applied Statistics with S", 4th Edition, Springer-Verlag.
The function does not do any scaling internally: the optimization will work best when the response is scaled so its variance is of the order of one.
Documentation reproduced from package nlme, version 3.1-109. License: GPL (>= 2)