# lme

##### 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.

- Keywords
- models

##### Usage

```
lme(fixed, data, random, correlation, weights, subset, method,
na.action, control)
```

##### Arguments

- fixed
- 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 - data
- an optional data frame containing the variables named in
`fixed`

,`random`

,`correlation`

,`weights`

, and`subset`

. By default the variables are taken from the environment from which`l`

- random
- 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`g1/.../gm`

the grouping structure (`m`

m - correlation
- an optional
`corStruct`

object describing the within-group correlation structure. See the documentation of`corClasses`

for a description of the available`corStruct`

classes. Defaults to`NULL`

, cor - weights
- an optional
`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 do - subset
- 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 th - method
- a character string. If
`"REML"`

the model is fit by maximizing the restricted log-likelihood. If`"ML"`

the log-likelihood is maximized. Defaults to`"REML"`

. - na.action
- a function that indicates what should happen when the
data contain
`NA`

s. The default action (`na.fail`

) causes`lme`

to print an error message and terminate if there are any incomplete observations. - control
- a list of control values for the estimation algorithm to
replace the default values returned by the function
`lmeControl`

. Defaults to an empty list.

##### Value

- 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.

##### References

The computational methods are described in Bates, D.M. and Pinheiro
(1998) and follow on the general framework of Lindstrom, M.J. and Bates,
D.M. (1988). The model formulation is described in Laird, N.M. and Ware,
J.H. (1982). The variance-covariance parametrizations are described in

Bates, D.M. and Pinheiro, J.C. (1998) "Computational methods for multilevel models" available in PostScript or PDF formats at http://franz.stat.wisc.edu/pub/NLME/ 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.

Venables, W.N. and Ripley, B.D. (1997) "Modern Applied Statistics with S-plus", 2nd Edition, Springer-Verlag.

##### See Also

`lmeControl`

, `lme.lmList`

,
`lme.groupedData`

, `lmeObject`

,
`lmList`

, `reStruct`

, `reStruct`

,
`varFunc`

, `pdClasses`

,
`corClasses`

, `varClasses`

##### Examples

`library(nlme)`

```
data(Orthodont)
fm1 <- lme(distance ~ age, data = Orthodont) # random is ~ age
fm2 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
summary(fm1)
summary(fm2)
```

*Documentation reproduced from package nlme, version 3.1-1, License: GPL version 2 or later*