# intervals.lme: Confidence Intervals on lme Parameters In nlme: Linear and Nonlinear Mixed Effects Models

## 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

 ```1 2 3``` ```## 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)

José Pinheiro and Douglas Bates [email protected]

## References

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

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

## Examples

 ```1 2``` ```fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject) intervals(fm1) ```

### Example output

```Approximate 95% confidence intervals

Fixed effects:
lower       est.      upper
(Intercept) 15.2183224 16.7611111 18.3038999
age          0.5183867  0.6601852  0.8019837
attr(,"label")
[1] "Fixed effects:"

Random Effects:
Level: Subject
lower       est.     upper
sd((Intercept))       0.9463689  2.3270341 5.7219626
sd(age)               0.1023206  0.2264278 0.5010679
cor((Intercept),age) -0.9385866 -0.6093329 0.3007315

Within-group standard error:
lower     est.    upper
1.084697 1.310040 1.582197
```

nlme documentation built on April 7, 2018, 5:03 p.m.