R: Confidence Intervals on gls Parameters

intervals.gls {nlme} | R Documentation

## Confidence Intervals on gls Parameters

### Description

Approximate confidence intervals for the parameters in the linear 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.

### Usage

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

### Arguments

`object` | an object inheriting from class `gls`, representing a generalized least squares fitted linear model.
`level` | an optional numeric value for the interval confidence level. 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 `"coef"` for the linear model coefficients 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:

`coef` | linear model coefficients, only present when `which` is not equal to `"var-cov"`.
`corStruct` | correlation parameters, only present when `which` is not equal to `"coef"` and a correlation structure is used in `object`.
`varFunc` | variance function parameters, only present when `which` is not equal to `"coef"` and a variance function structure is used in `object`.
`sigma` | residual standard error.

### Author(s)

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

### References

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

### See Also

`gls`, `intervals`, `print.intervals.gls`

### Examples

    fm1 <- gls(follicles ~ sin(2*pi*Time) + cos(2*pi*Time), Ovary,
               correlation = corAR1(form = ~ 1 | Mare))
    intervals(fm1)

[Package nlme version 3.1-89 Index]