[R] Omnibus test for main effects in the face ofaninteraction containing the main effects.

[John Sorkin]

Daniel,
When Group is entered as a factor, and the factor has two levels, the
ANOVA table gives a p value for each level of the factor. What I am
looking for is the omnibus p value for the factor, i.e. the test that
the factor (with all its levels) improves the prediction of the outcome.

You are correct that normally one could rely on the fact that the model 
Post<-Time+as.factor(Group)+as.factor(Group)*Time
contains the model 
Post<-Time+as.factor(Group)
and compare the two models using anova(model1,model2). However, my model
is has a random effect, the comparison is not so easy. The REML
comparions of nested random effects models is not valid when the fixed
effects are not the same in the models, which is the essence of the
problem in my case. 

In addition to the REML problem if one wants to perform an omnibus test
for Group, one would want to compare nested models, one containing
Group, and the other not containing group. This would suggest comparing
Post<-Time+      as.factor(Group)*Time to
Post<-Time+Group+as.factor(Group)*Time
The quandry here is whether one should or not "allow" the first model as
it is poorly specified - one term of the interaction,
as.factor(Group)*Time, as.factor(Group) does not appear as a main effect
- a no-no in model building. 
John


John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC,
University of Maryland School of Medicine Claude D. Pepper OAIC,
University of Maryland Clinical Nutrition Research Unit, and
Baltimore VA Center Stroke of Excellence

University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524

(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
jsorkin at grecc.umaryland.edu
>>> "Daniel Malter" <daniel at umd.edu> 09/07/09 9:23 PM >>>
John, your question is confusing. After reading it twice, I still cannot
figure out what exactly you want to compare.

Your model "a" is the unrestricted model, and model "b" is a restricted
version of model "a" (i.e., b is a hiearchically reduced version of a,
or
put differently, all coefficients of b are in a with a having additional
coefficients). Thus, it is appropriate to compare the models (also
called
nested models).

Comparing c with a and d with a is also appropriate for the same reason.
However, note that depedent on discipline, it may be highly
unconventional
to fit an interaction without all direct effects of the interacted
variables
(the reason for this being that you may get biased estimates).

What you might consider is:
1. Run an intercept only model
2. Run a model with group and time
3. Run a model with group, time, and the interaction

Then compare 2 to 1, and 3 to 2. This tells you whether including more
variables (hierarchically) makes your model better.

HTH,
Daniel

On a different note, if lme fits with "restricted maximum likelihood," I
think I remember that you cannot compare them. You have to fit them with
"maximum likelihood." I am pointing this out because lmer with
restricted
maximum likelihood by standard, so lme might too.

-------------------------
cuncta stricte discussurus
-------------------------

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Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Im
Auftrag von John Sorkin
Gesendet: Monday, September 07, 2009 4:00 PM
An: r-help at r-project.org
Betreff: [R] Omnibus test for main effects in the face of aninteraction
containing the main effects.

R 2.9.1
Windows XP

UPDATE,
Even my first suggestion
anova(fita,fitb) is probably not appropriate as the fixed effects are
different in the two model, so I don't even know how to perform the
ombnibus
test for the interaction!



I am fitting a random effects ANOVA with two factors Group which has two
levels and Time which has three levels:
 fita<-lme(Post~Time+factor(Group)+factor(Group)*Time,
random=~1|SS,data=blah$alldata)

I wantinteraction. I believe I can get the omnibus test for the interaction by
running the model:

fitb<-lme(Post~Time+factor(Group), random=~1|SS,data=blah$alldata)
followed
by anova(fita,fitb).

How do I get the omnibus test for the main effects i.e. for Time and
factor(Group)? I could drop each from the model, i.e.
fitc<-lme(Post~          factor(Group)+factor(Group)*Time,
random=~1|SS,data=blah$alldata)
fitd<-lme(Post~Time+                        factor(Group)*Time,
random=~1|SS,data=blah$alldata)

and then run
anova(fita,fitc)
anova(fita,fitd)
but I don't like this option as it will have in interaction that
contains a
factor that is not included in the model as a main effect. How then do I
get
the omnibus test for Time and factor(Group)?

Thanks
John




John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

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