lme  R Documentation 
This generic function fits a linear mixedeffects model in the formulation described in Laird and Ware (1982) but allowing for nested random effects. The withingroup errors are allowed to be correlated and/or have unequal variances.
This page describes the formula method;
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 'formula'
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 twosided linear formula object describing the
fixedeffects part of the model, with the response on the left of a
There is limited support for formulae such as 
fixed. 
Changes to the fixedeffects formula – see

data 
an optional data frame containing the variables named in

random 
optionally, any of the following: (i) a onesided 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 
offset
terms in fixed
are an error since 3.1157
(202203): previously they were silently ignored.
An object of class "lme"
representing the linear mixedeffects
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 variancecovariance 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/9780203745502")}.
Laird, N.M. and Ware, J.H. (1982). RandomEffects Models for Longitudinal Data. Biometrics 38, 963–974. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2529876")}.
Lindstrom, M.J. and Bates, D.M. (1988). NewtonRaphson and EM Algorithms for Linear MixedEffects Models for RepeatedMeasures Data. Journal of the American Statistical Association 83, 1014–1022. \Sexpr[results=rd]{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 VarianceCovariance Matrices. Statistics and Computing 6, 289–296. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF00140873")}.
Pinheiro, J.C., and Bates, D.M. (2000). MixedEffects Models in S and SPLUS, Springer. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/b98882")}.
Venables, W.N. and Ripley, B.D. (2002). Modern Applied Statistics with S, 4th Edition, SpringerVerlag. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/9780387217062")}.
corClasses
,
lme.lmList
,
lme.groupedData
,
lmeControl
,
lmeObject
,
lmeStruct
,
lmList
,
pdClasses
,
plot.lme
,
predict.lme
,
qqnorm.lme
,
residuals.lme
,
reStruct
,
simulate.lme
,
summary.lme
,
varClasses
,
varFunc
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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