[R] degrees of freedom in lme

[Doran, Harold]

This is such a common question that it has a an "FAQ-like" response from Doug Bates. Google "lmer p-values and all that" to find the response. 

> -----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?
> 
> Thanks in advance for your help !
> --
> 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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