# [S] Type I error in linear mixed effects model in S

Chul Ahn (chulahn@heart.med.uth.tmc.edu)
Thu, 28 May 1998 13:16:29 -0500

I performed a simulation study using the lme (linear mixed effects routine)
of S-plus. The simulated data set is based on the split-plot design, which
is widely used in clinical trials. The form of the data is given below.

However, the type I error is too large in lme. I did not examine the power
of the lme routine since I was really suprised to see the large type I
error. Maybe, I made a mistake in the model statement of lme.
I ran 500 data sets using the following form of data.

dsn subject group scr1 scr2 scr3 scr4 scr5 scr6 scr7 scr8
scr9
1 1 1 26.0 25.0 24.0 25.7 27.1 26.3 22.8 29.0
31.0
1 2 1 25.0 23.5 23.1 24.5 26.8 27.1 25.9 28.1
28.8
...
1 50 1 29.0 28.8 25.3 26.7 29.0 24.6 26.7 27.2
27.0
1 1 2 31.0 24.3 24.8 25.0 26.3 27.1 25.6 26.3
24.9
...
1 50 2 24.5 23.6 25.8 26.3 27.4 25.4 26.5 27.1
28.0
...
500 50 2 25.2 25.7 25.8 25.3 24.0 26.1 26.1 24.9
25.8

Here dsn=1 means the data set #1 and dsn=500 means the data set #500. scr1
is the measure at time 1, scri is the measure at time i. The data is a
balanced data without any missing values.

For simulation, I converted the above data set into the standard form in
page 284 of S-plus4 statistics guide.
(scr1-- scr9 were converted into the variable score. A newly created
variable 'time' takes the values 1 through 9.)

I used the following S-Plus lme model statements, which are almost
identical to the models in page 292 of S-Plus4.

(1)
S>lme(fixed=score ~time*group, random= ~time, cluster= ~subject, data=data)

The empirical type I error of the group effect is 31.8% and the empirical
type I error of the interaction effect time*group is 9.6%.

(2) I added the baseline measure (scr1) as a covariate into the model.
S>lme(fixed=score ~time*group+scr1, random= ~time, cluster= ~subject,
data=data)

The empirical type I error of the group effect is 8.8% and the empirical
type I error of the interaction effect time*group is 27.6%.

I think the empirical type I errors are too high. Would you please give me
the suggestions of the model formulation statements? If my model
formulation statements are correct, I think we have to be really careful in
the use of the lme programs in S-Plus. We calculated the empirical type I
errors using other programs. Some are pretty good. The others are not good.
However, they are much better than the empirical type I errors of lme.