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

[Daniel Malter]

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
-------------------------

-----Ursprüngliche Nachricht-----
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 want to get the omnibus significance tests for each factor and the
interaction. 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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