Hi Pravin,
the reason you get this warning is a theoretical one: When you use
REML you transform your response variable y to y*=t(A)%*%y, in order
not to having to estimate the fixed-effects beta. Thus the choice of A
depends each time on the fixed-effects design matrix X. if you have
two models with different fixed-effects and fit them by REML each one
has its own Y* and thus when you use anova.lme you compare two models
with different response variable (not meaningful). On the other hand
if you use ML instead of REML then you don't transform Y and you just
need to test nested models. However, it is known that ML gives biased
results for the variance components since it doesn't take into account
that you also estimate beta.
For references you could look at
@Article{harville:77,
author = {D. Harville},
journal = {Journal of the American Statistical Association},
pages = {320--340},
title = {Maximum likelihood approaches to variance
component estimation and to related problems},
volume = {72},
year = {1977}
}
I hope this helps.
Best,
Dimitris
----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/396887
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat/
http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm
----- Original Message -----
From: "Pravin" <jadhavpr@vcu.edu>
To: <s-news@lists.biostat.wustl.edu>
Sent: Tuesday, September 28, 2004 8:42 PM
Subject: [S] LME- Comparing likelihood of two models
Dear all,
I seek input on the following issue: I have two competing models
that I was
hoping to compare based on the likelihood. I used REML method and
upon
performing anova(fiitedobject1,fittedobject2), the following
*warning*
message was obtained.
...Likelihood comparisons are not meaningful for objects fit using
restricted maximum likelihood and with different fixed effects...
It is true that my models differ only with respect to a single fixed
effect
parameter.
I would like to know some references that address the underlying
reason. I
did perform internet search and looked at Mixed-effects modeling in
S and
S-Plus by Pinheiro and Bates but haven't understood the issue
completely.
There is some mention of it in the book while explaining the
estimation
methods. Are there any other references?
Thanks,
Pravin
Pravin Jadhav
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