[R] Some questions on repeated measures (M)ANOVA & mixed models with lme4

Marco B tymester at gmail.com
Sun May 13 16:22:05 CEST 2007

```Dear R Masters,

I'm an anesthesiology resident trying to make his way through basic
statistics. Recently I have been confronted with longitudinal data in
a treatment vs. control analysis. My dataframe is in the form of:

subj | group | baseline | time | outcome (long)
or
subj | group | baseline | time1 |...| time6 | (wide)

The measured variable is a continuous one. The null hypothesis in this
analysis is that the Group factor does not significantly influence the
outcome variable. A secondary null hypothesis is that the Group x Time
interaction is not significant, either. Visual of the group means
indicates the outcome measure decreases linearly (more or less) over
time from baseline values. The time==1...time==6 intervals are
equally-spaced and we have equal sample sizes for the groups.

I've done a little reading around and found (at least) four possible approaches:

A. Linear mixed model using lme4 with random intercept and slope with
lmer() or lme()

B. Repeated measures ANOVA using aov() with Error() stratification
(found in Baron & Li, 2006), something along the lines of:
aov(outcome ~ group * time + baseline + Error(subj+subj:time))

(from: http://cran.r-project.org/doc/contrib/Baron-rpsych.pdf, p. 41)

C. "Repeated measures" MANOVA as follows (using data in wide format):
response <- cbind(time1,time2,time3,time4,time5,time6)
mlmfit <- lm(response ~ group)
mlmfit1 <- lm(response ~ 1)
mlmfit0 <- lm(response ~ 0)
# Test time*group effect
anova.mlm(mlmfit, mlmfit1, X=~1, test="Spherical")
# Test overall group effect
anova.mlm(mlmfit, mlmfit1, M=~1)
# Test overall time effect
anova.mlm(mlmfit1, mlmfit0, X=~1, test="Spherical")

(taken from http://tolstoy.newcastle.edu.au/R/help/05/11/15744.html)

Now, on with the questions:

1. This is really a curiosity. I find lmer() easier to use than lme(),
but the former does not allow the user to model the correlation
structure of the data. I figure lmer() is presently assuming no
within-group correlation for the data, which I guess is unlikely in my
example. Is there a way to compare directly (maybe in terms of
log-likelihood?) similar models fitted in lme() and lmer()?

2. Baron & Li suggest a painful (at least for me) procedure to obtain
Greenhouse-Geisser or Huyn-Feldt correction for the ANOVA analysis
they propose. Is there a package or function which simplifies the
procedure?

3. I must admit that I don't understand solution C. I can "hack" it to
fit my model, and it seems to work, but I can't seem to grasp the
overall concept, especially regarding the outer and/or inner
projection matrices (M & X). Could anyone point me to a basic
explanation of the procedure?

4. Provided the assumptions for ANOVA hold, or that deviations from
them are not horrible, am I correct in saying that this procedure
would be the most powerful one? How would you choose solution A over
solution B (or viceversa)?

My sincerest gratitude to anyone who will take the time to answer my questions!

Best Regards,

Marco

```