[19150] in s-news-athena
[S] Linear Mixed Models, Likelihood Ratio, Expected Mean Squares
daemon@ATHENA.MIT.EDU (LeBlond,David)
Wed Sep 8 15:23:00 1999
From: "LeBlond,David" <david.leblond@abbott.com>
To: <s-news@wubios.wustl.edu>
Message-Id: <0055600016594608000002L082*@MHS>
Date: Wed, 8 Sep 1999 14:18:03 -0500
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Can anyone out there address the following issues for me?
please send comments to david.LebLond@abbott.com and accept my eternal
gratitude!!
All issues have to do with the fitting of linear mixed models. In S+ this is
done using the varcomp() function. I use the REML method.
Q1: The log-likelihood that is calculated by S+ and made available in the
varcomp() object does not agree with the output of SAS Proc Mixed. I am
unable to determine the equations used for the calculation of this
log-likelihood. Literature equations do not reproduce the values obtained by
S+ although I can reproduce the value produced by SAS Proc Mixed. Can you
explain specifically the equation used to calculate the in varcomp() REML
log-likelihood, please?
Q2: In deriving tests for fixed effects in linear mixed models, it can be
useful to know the coefficients in the expected mean squares so that proper
method of moment F tests can be constructed. Such coefficients are available
in SAS software through the RANDOM statement in Proc GLM. In order to make
full use of the linear mixed model capability of S+ varcomp(), it would be
desirable to be able to output the coefficients in the expected mean squares
as could be done in SAS. The raov() function in S+ will output coefficients
for a fully random model, but will not accept a model with a fixed effect.
The aov() function does not have the ability to produce the coefficients of
EMS. Is there any way to derive the coefficients of EMS for linear mixed
models using S+ software? If not will such a capability be added to future
revisions?
Q3: In testing for the significance of a random component of a mixed model,
one uses the likelihood ratio test. One fits the full and reduced model
(lacking the random component of interest) and uses the chi-square
distribution of the difference in log-likelihoods for the test. A difficulty
with S+ is that when there is only 1 random component (in addition to pure
error; as in a split plot), it is not possible to obtain the log-likelihood
for the reduced model since varcomp() requires at least one random
component.
The lm() function which can fit a pure fixed effects linear model,
unfortunately will not calculate either the unrestricted or the restricted
log-likelihood. I am not sure how to calculate the appropriate
log-likelihood
in S+ by hand (see Q1). Can you tell me if it is possible to obtain the
appropriate log-likelihood statistic for a pure fixed model in S+ and if so
how? If not, is there a plan to add the capability to fit pure fixed linear
models using maximum likelihood procedures to varcomp()?
Any information you can provide on these 3 issues would be greatly
appreciated!
thank you,
Dave LeBlond
Senior non-clinical Statistician
Pharmaceutical Division
Abbott Laboratories
D436 AP9A-1
Abbott Park, IL 60064
847-935-6031
david.leblond@abbott.com
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