intervals.lme {nlme} | R Documentation

## Confidence Intervals on lme Parameters

### 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.

### Value

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.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### See Also

`lme`, `print.intervals.lme`, `pdNatural`

### Examples

    data(Orthodont)
    fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject)
    intervals(fm1)

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