[R] Basic LME

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Apr 8 18:09:59 CEST 2003

aov() can also be used with an Error() term, when it is not just a 
front-end to lm and does fits random effects.  (As the help page for 
aov says.)

On Tue, 8 Apr 2003, Paul, David  A wrote:

> I'm certainly no expert, but I believe that aov( ) is simply a
> front-end to the lm( ) function, which fits fixed-effects linear
> models.  As you may know, it is possible to write any ANOVA model
> as a regression model with appropriate use of indicator variables
> for the various levels of treatments.
> So, aov( ) does not, in general, yield results that are comparable
> to those generated by lme( ).  You have specified the same _fixed_
> effect ( ~ Age ) in both aov( ) and lme( ) which is why they
> give you the same parameter estimates for this covariate.

Not really.  The error structure is different, but that may not matter
if there is the right nesting/balance in the design. After all `randomized 
block designs' are random effects normally analysed as fixed effects, and 
the results are the same.

> When you perform anova( ) to compare the two lme( ) models, you
> are performing a likelihood ratio test.  This is not generally
> the same as the F-test/t-test used to evaluate the marginal 
> significance of a fixed-effect term in a linear model, which explains 
> the difference between the p-values.

(and those lme fits were by ML rather than the default REML used earlier).
In general there are other differences due to the different assumptions 
about error structures, and when there are likelihood-ratio tests would
generally be preferred.

> Best,
>   david paul
> -----Original Message-----
> From: Martin Hoyle [mailto:plxmh at nottingham.ac.uk] 
> Sent: Tuesday, April 08, 2003 10:09 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Basic LME
> Hello R Users,
> I am investigating the basic use of the LME function, using the following
> example;
> Response is Weight, covariate is Age, random factor is Genotype
> model.lme <- lme (Weight~Age, random=~ 1|Genotype)
> After summary(model.lme), I find that the estimate of Age is 0.098 with
> p=0.758.
> I am comparing the above model with the AOV function;
> model.aov <- aov (Weight~Age + Genotype)
> I find that the estimate of Age is also 0.098, and p=0.758 as in the LME
> model above.
> So, my questions are;
> 1: I expected that the LME model would be a better way to analyse this data
> compared to the AOV model, since Genotype is a random factor. However, I
> obtain the same parameter estimate and p value for Age. Please can someone
> tell me why?
> 2: When using LME, when I am after a p value for the covariate Age, is it
> better to do the following;
> Model.lme2 <- lme (Weight~Age, random=~ 1|Genotype, method="ML") Model.lme3
> <- lme (Weight~1, random=~ 1|Genotype, method="ML") Anova(Model.lme2,
> Model.lme3)
> Giving likelihood ratio=0.102, with p=0.749, which is slightly different to
> the p values of 0.758 above.
> Thanks for your attention,
> Martin.
> Martin Hoyle,
> School of Life and Environmental Sciences,
> University of Nottingham,
> University Park,
> Nottingham,
> NG7 2RD,
> UK
> Webpage: http://myprofile.cos.com/martinhoyle
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Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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