# [R] confidence interval too small in nlme?

From: Wittner, Ben, Ph.D. <Wittner.Ben_at_mgh.harvard.edu>
Date: Thu, 3 Jan 2008 09:41:39 -0500

Hello,

I am interested in using nlme to model repeated measurements, but I don't seem to get good CIs.

With the code below I tried to generate data sets according to the model given by equations (1.4) and (1.5) on pages 7 and 8 of Pinheiro and Bates 2000 (having chosen values for beta, sigma.b and sigma similar to those estimated in the text).
For each data set I used lme() to fit a model, used intervals() to get a 95% CI for beta, and then checked whether the the CI contained beta. The rate at which the CI did not contain beta was 8%, which was greater than the 5% I was expecting.
This may seem like a small difference, but in the lab in which I work M would more likely be 2 or 3. When I re-ran with M = 3 I got 13% of the CIs not containing beta and when I re-ran with M = 2, I got 21%.

Am I calculating the CIs incorrectly?
Am I interpreting them incorrectly?
Am I doing anything else wrong?

Output of packageDescription('nlme') and version given below the code.

Any help will be greatly appreciated. Thanks very much in advance. -Ben

```#########################################################################
##
##  Code to test intervals() based on equations (1.4) and (1.5) of
```
## Pinheiro and Bates
##

library('nlme')

M <- 6
n <- 3
beta <- 67
sigma.b <- 25
sigma <- 4

Rail <- rep(1:M, each=n)

set.seed(56820)
B <- 10000
num.wrong <- 0
error.fraction <- Ks <- c()
for (K in 1:B) {
travel <- beta + rep(rnorm(M, sd=sigma.b), each=n) + rnorm(M*n, sd=sigma)   fm1Rail.lme <- lme(travel ~ 1, random = ~ 1 | Rail)   CI <- intervals(fm1Rail.lme, which='fixed')\$fixed   if ((CI[1, 'lower'] > beta) || (CI[1, 'upper'] < beta))     num.wrong <- num.wrong + 1
if (K %% 200 == 0) {
error.fraction <- c(error.fraction, num.wrong/K)     Ks <- c(Ks, K)
plot(Ks, error.fraction, type='b',

ylim=range(c(0, 0.05, error.fraction)))     abline(h=0.05, lty=3)
}
}

num.wrong/B

```#########################################################################
##
```

## version information
##

> packageDescription('nlme')

Package: nlme
Version: 3.1-86
Date: 2007-10-04
Priority: recommended
Title: Linear and Nonlinear Mixed Effects Models Author: Jose Pinheiro <Jose.Pinheiro_at_pharma.novartis.com>, Douglas

```        Bates <bates_at_stat.wisc.edu>, Saikat DebRoy
<saikat_at_stat.wisc.edu>, Deepayan Sarkar
<Deepayan.Sarkar_at_R-project.org> the R Core team.
```
Maintainer: R-core <R-core_at_R-project.org> Description: Fit and compare Gaussian linear and nonlinear

mixed-effects models.
Depends: graphics, stats, R (>= 2.4.0)
Imports: lattice
LazyData: yes
Packaged: Thu Oct 4 23:25:21 2007; hornik Built: R 2.6.0; i686-pc-linux-gnu; 2007-12-26 15:48:00; unix

• File: /home/bwittner/R-2.6.0/library/nlme/DESCRIPTION
> version
_ platform i686-pc-linux-gnu arch i686 os linux-gnu system i686, linux-gnu status major 2 minor 6.0 year 2007 month 10 day 03 svn rev 43063 language R version.string R version 2.6.0 (2007-10-03)

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