lme {lme4} | R Documentation

## Fit linear mixed-effects models

### Description

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.

### Usage

    lme(formula, data, random, correlation, weights, subset,
        method, na.action, control, model, x)

### Arguments

`formula` | 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.
`data` | an optional data frame containing the variables named in `formula`, `random`, `correlation`, `weights`, and `subset`. By default the variables are taken from the environment from which `lme` is called.
`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` 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 `formula(object)`), 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 `pdMat` 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 `pdMat-class` documentation for a description of the available `pdMat` classes. Defaults to a formula consisting of the right hand side of `formula`.
`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`, corresponding to no within-group correlations.
`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 documentation on `varClasses` for a description of the available `varFunc` classes. Defaults to `NULL`, corresponding to homocesdatic within-group errors.
`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 the row names to be included. All observations are included by default.
`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.
`model, x` | logicals. If `TRUE` the corresponding components of the fit (the model frame, the model matrices) are returned.

### Details

Many of the options are not yet implemented.

### Value

An lme object.

### Examples

    data(bdf)
    fm <- lme(langPOST ~ IQ.ver.cen + avg.IQ.ver.cen, data = bdf,
              random = ~ IQ.ver.cen | schoolNR)
    summary(fm)

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