# intervals.lme {nlme}

### Description

Approximate confidence intervals for the parameters in the linear mixed-effects model represented by `object`

are obtained, using a normal approximation to the distribution of the (restricted) maximum likelihood estimators (the estimators are assumed to have a normal distribution centered at the true parameter values and with covariance matrix equal to the negative inverse Hessian matrix of the (restricted) log-likelihood evaluated at the estimated parameters). Confidence intervals are obtained in an unconstrained scale first, using the normal approximation, and, if necessary, transformed to the constrained scale. The `pdNatural`

parametrization is used for general positive-definite matrices.

### Usage

## S3 method for class 'lme': intervals((object, level, which, ...))

### Arguments

- object
- an object inheriting from class
`"lme"`

, representing a fitted linear mixed-effects model. - level
- an optional numeric value with the confidence level for the intervals. Defaults to 0.95.
- which
- an optional character string specifying the subset of parameters for which to construct the confidence intervals. Possible values are
`"all"`

for all parameters,`"var-cov"`

for the variance-covariance parameters only, and`"fixed"`

for the fixed effects only. Defaults to`"all"`

. - ...
- some methods for this generic require additional arguments. None are used in this method.

### Values

a list with components given by data frames with rows corresponding to parameters and columns `lower`

, `est.`

, and `upper`

representing respectively lower confidence limits, the estimated values, and upper confidence limits for the parameters. Possible components are:

- fixed
- fixed effects, only present when
`which`

is not equal to`"var-cov"`

. - reStruct
- random effects variance-covariance parameters, only present when
`which`

is not equal to`"fixed"`

. - corStruct
- within-group correlation parameters, only present when
`which`

is not equal to`"fixed"`

and a correlation structure is used in`object`

. - varFunc
- within-group variance function parameters, only present when
`which`

is not equal to`"fixed"`

and a variance function structure is used in`object`

. - sigma
- within-group standard deviation.

### References

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.

Documentation reproduced from package nlme, version 3.1-127. License: GPL (>= 2)