summary.lme() vs. anova.lme()
On Wed, 17 Nov 2004, Dan Bebber wrote:
I modelled changes in a variable (mconc) over time (d) for individuals
(replicate) given one of three treatments (treatment) using:
mconc.lme <- lme(mconc~treatment*poly(d,2), random=~poly(d,2)|replicate,
data=my.data)
summary(mconc.lme) shows that the linear coefficient of one of the
treatments is significantly different to zero, viz.
Value Std.Error DF t-value p-value
... ... ... ...
...
treatmentf:poly(d, 2)1 1.3058562 0.5072409 315 2.574430 0.0105
But anova(mconc.lme) gives a non-significant result for the treatment*time
interaction, viz.
numDF denDF F-value p-value
(Intercept) 1 315 159.17267 <.0001
treatment 2 39 0.51364 0.6023
poly(d, 2) 2 315 17.43810 <.0001
treatment:poly(d, 2) 4 315 2.01592 0.0920
Pinheiro & Bates (2000) only discusses anova() for single arguments briefly
on p.90.
I would like to know whether these results indicate that the significant
effect found in summary(mconc.lme) is spurious (perhaps due to
multiplicity).
Probably yes (but p values of 9% and 1% are not that different, and in both cases you are looking at a few p values). But since both summary.lme and anova.lme use Wald tests, I would use a LRT, using anova on two fits (and I would use ML fits to get a genuine LRT but that is perhaps being cautious). To Dimitris Rizopoulos: as this is the last term in the sequential anova, it is the correct Wald test.
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