Linear Mixed-Effects Models
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.
The methods lme.lmList
and lme.groupedData
are documented separately.
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)
object |
an object inheriting from class |
fixed |
a two-sided linear formula object describing the
fixed-effects part of the model, with the response on the left of a
There is limited support for formulae such as |
fixed. |
Changes to the fixed-effects formula – see
|
data |
an optional data frame containing the variables named in
|
random |
optionally, any of the following: (i) a one-sided formula
of the form |
correlation |
an optional |
weights |
an optional |
subset |
an optional expression indicating the subset of the rows of
|
method |
a character string. If |
na.action |
a function that indicates what should happen when the
data contain |
control |
a list of control values for the estimation algorithm to
replace the default values returned by the function |
contrasts |
an optional list. See the |
keep.data |
logical: should the |
... |
some methods for this generic require additional arguments. None are used in this method. |
evaluate |
If |
An object of class "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.
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.
José Pinheiro and Douglas Bates bates@stat.wisc.edu
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
(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.
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.
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.
fm1 <- lme(distance ~ age, data = Orthodont) # random is ~ age fm2 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1) summary(fm1) summary(fm2)
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