[R] Omnibus test for main effects in the face ofaninteraction containing the main effects.
Mark Difford
mark_difford at yahoo.co.uk
Tue Sep 8 09:09:15 CEST 2009
Hi John,
>> 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.
This does not (normally) happen so you are doing something strange.
## From your first posting on this subject
fita<-lme(Post~Time+factor(Group)+factor(Group)*Time,
random=~1|SS,data=blah$alldata)
To begin with, what is blah$alldata? lme() asks for a data frame if the
formula interface is used. This looks like part of a list, or the column of
a data frame.
Have a look at the output below, from a syntactically correct model that has
essentially the same structure as yours. The data set should be loaded with
nlme so you can run it directly to see the result. Sex, with two levels, is
not split in the anova table.
##
str(Orthodont)
anova( lme(distance ~ age * Sex, data = Orthodont, random = ~ 1) )
Surely this is essentially what you are looking for? If Sex is not already a
factor, and it really is better to make it one when you build your data set,
then you can use as.factor as you have done, with the same result.
(Note: age * Sex expands to age + Sex + age:Sex, which equals the messy and
unnecessary age + Sex + age * Sex.)
Regards, Mark.
John Sorkin wrote:
>
> 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
> -------------------------
>
> -----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$alldata)
>
> I wantinteraction. I believe I can get the omnibus test for the
> interaction by
> running the model:
>
> fitb<-lme(Post~Time+factor(Group), random=~1|SS,data=blah$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)
>
> Confidentiality Statement:
> This email message, including any attachments, is for th...{{dropped:16}}
>
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