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: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > Jean-Baptiste Ferdy > Sent: Monday, June 25, 2007 12:26 PM > To: r-help@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 > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.