# Re: [R] degrees of freedom in lme

From: Doran, Harold <HDoran_at_air.org>
Date: Mon, 25 Jun 2007 13:15:32 -0400

> -----Original Message-----
> From: r-help-bounces_at_stat.math.ethz.ch
> [mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of
> Jean-Baptiste Ferdy
> Sent: Monday, June 25, 2007 12:26 PM
> To: r-help_at_stat.math.ethz.ch
> Subject: [R] degrees of freedom in lme
>
> Dear all,
>
> I am starting to use the lme package (and plan to teach a
> course based on it next semester...). To understand what lme
> is doing precisely, I used balanced datasets described in
> Pinheiro and Bates and tried to compare the lme outputs to
> that of aov. Here is what I obtained:
>
> > data(Machines)
> > summary(aov(score~Machine+Error(Worker/Machine),data=Machines))
> Error: Worker
> Df Sum Sq Mean Sq F value Pr(>F) Residuals 5
> 1241.89 248.38
>
> Error: Worker:Machine
> Df Sum Sq Mean Sq F value Pr(>F)
> Machine 2 1755.26 877.63 20.576 0.0002855 ***
> Residuals 10 426.53 42.65
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Within
> Df Sum Sq Mean Sq F value Pr(>F)
> Residuals 36 33.287 0.925
> >
> anova(lme(fixed=score~Machine,random=~1|Worker/Machine,data=Machines))
> numDF denDF F-value p-value
> (Intercept) 1 36 773.5709 <.0001
> Machine 2 10 20.5762 3e-04
>
> No problem here: the results are essentially the same, which
> is expected. Now I turn to an ANCOVA with a random grouping factor.
>
> > data(Orthodont)
> > OrthoFem <- Orthodont[Orthodont\$Sex=="Female",];
> > summary(aov(distance~age+Error(Subject/age),data=OrthoFem))
> Error: Subject
> Df Sum Sq Mean Sq F value Pr(>F) Residuals 10
> 177.227 17.723
>
> Error: Subject:age
> Df Sum Sq Mean Sq F value Pr(>F)
> age 1 50.592 50.592 52.452 2.783e-05 ***
> Residuals 10 9.645 0.965
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Within
> Df Sum Sq Mean Sq F value Pr(>F) Residuals 22 9.8250 0.4466
> > anova(lme(fixed=distance~age,random=~1+age|Subject,data=OrthoFem))
> numDF denDF F-value p-value
> (Intercept) 1 32 1269.7764 <.0001
> age 1 32 52.4517 <.0001
>
> This time the F values are (almost) identical, the numerator
> degrees of freedom are the same, but the denominator degrees
> of freedom are very different (10 for aov vs. 32 for lme). I
> understand that there is an issue with the estimation of that
> number, but I would naively expect the number given by lme to
> be close to that provided by aov is the case of a balanced
> dataset. That's obviously not true in the case of an
> ANCOVA... But why?? And how should I interpret the F-test
> given by anova.lme?
>
> --
> Jean-Baptiste Ferdy
> Institut des Sciences de l'Évolution de Montpellier CNRS UMR
> 5554 Université Montpellier 2
> 34 095 Montpellier cedex 05
> tel. +33 (0)4 67 14 42 27
> fax  +33 (0)4 67 14 36 22
>
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