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 = 0.95,
which = c("all", "var-cov", "fixed"), ...)
```

### 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)

JosÃ© Pinheiro 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.

`lme`, `intervals`, `print.intervals.lme`, `pdNatural`
```fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject)