R help - May 2007 - Some questions on repeated measures (M)ANOVA & mixed models with lme4

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

Dear Marco,

You might also take a look at ?Anova (or ?Manova) in the car package; the
last examples are for a repeated-measures ANOVA using both MANOVA and
univariate approaches, the latter with GG and HF corrections.

I hope this helps,
 John

--------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Marco B
> Sent: Sunday, May 13, 2007 10:22 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Some questions on repeated measures (M)ANOVA & 
> mixed modelswith lme4
> 
> 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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Marco B wrote:
> 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?
>   
They're also computed as part of the
anova.mlm(...test="Spherical") route.
> 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?
>   
Something is en route to R News, I hope....
> 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)?
>
>   
Aov, lmer, and anova.mlm with the Spherical option all fit essentially 
the same model, but lmer has less fine control over small-sample 
properties and the effect of departures from the assumptions (partly 
because it needs to deal with unbalanced data).

Lme with an estimated covariance matrix is similar to anova.mlm without 
assuming sphericity. They are often less powerful than the 
sphericity-with-correction alternative, because of the larger number of 
estimated parameters. The balance should shift in "large N, small p"
cases.
> My sincerest gratitude to anyone who will take the time to answer my
questions!
>
> Best Regards,
>
> Marco
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>