[R] Repeated measures by lme and aov give different results

[Andrew Robinson]

Vicki,

take a look at P. 47 of the book by Pinheiro and Bates, if you have a copy
(if not, get one!)  They show the analysis of a split-plot design using
lme there.

Here, both aov and lme are estimating two levels of variation. The key
difference is that with aov the Ring-level variation is not being included
in the test of all the terms, whereas with lme it is being included.  If
you want to eliminate it from the tests, which will replicate the aov
analysis, then you need to include it as a fixed effect.

To pinpoint the question: in the simplest case of a randomized complete
block design,   we need to ask whether or not the block-level variation
should be included in the error sum of squares.  aov() excludes it, lme()
includes it unless Block is included as a fixed effect. Whether or not you
want to exclude it depends on what you think about the design and where
the variation is coming from.  The traditional RCB excludes it, but
whether or not you should depends on the circumstances.

Cheers

Andrew

On Wed, November 15, 2006 8:59 am, Vicki Allison wrote:
> I am analyzing data from an experiment with two factors: Carbon (+/-)
> and O3 (+/-), with 4 replicates of each treatment, and 4 harvests over a
> year.  The treatments are assigned in a block design to individual
> Rings.
>
> I have approaches this as a repeated measures design.  Fixed factors
> are Carbon, O3 and Harvest, with Ring assigned as a random variable.  I
> have performed repeated measures analysis on this data set two different
> ways: one utilizing lme (as described in Crawley, 2002), and the second
> using aov (based on Baron and Li, 2006).  Using lme I get very
> conservative p-values, while aov gives me significant p-values,
> consistent with those I obtain performing this analysis in SYSTAT.  Can
> anyone explain how these models differ, and which is more appropriate to
> the experimental design I have described?  The code I use, and the
> output obtained follow:
>
> 1  lme model
>
> library(nlme)
> M5 <-lme(ln_tot_lgth ~ Carbon*O3*Harv., random = ~-1|Ring)
> anova(M5, type="marginal")
>
> # Output
>                 numDF denDF   F-value p-value
> (Intercept)         1    44 176.59692  <.0001
> Carbon              1    12   0.42187  0.5282
> O3                  1    12   0.06507  0.8030
> Harv.               1    44  17.15861  0.0002
> Carbon:O3           1    12   0.23747  0.6348
> Carbon:Harv.        1    44   0.85829  0.3593
> O3:Harv.            1    44   0.04524  0.8325
> Carbon:O3:Harv.     1    44   0.05645  0.8133
>> plot(M5)
>
>
> 2  aov model
>
> M6<-aov(ln_tot_lgth ~ O3*Harv.*Carbon + Error (Ring/Carbon+O3))
> summary(M6)
> plot(M6)
>
> # Output
> Error: Ring
>           Df  Sum Sq Mean Sq F value  Pr(>F)
> O3         1 1.76999 1.76999  8.2645 0.01396 *
> Carbon     1 0.64766 0.64766  3.0241 0.10760
> O3:Carbon  1 0.15777 0.15777  0.7366 0.40756
> Residuals 12 2.57002 0.21417
>
> Error: Within
>                 Df Sum Sq Mean Sq F value   Pr(>F)
> Harv.            1 33.541  33.541 84.0109 9.14e-12 ***
> O3:Harv.         1  0.001   0.001  0.0036   0.9524
> Harv.:Carbon     1  0.414   0.414  1.0362   0.3143
> O3:Harv.:Carbon  1  0.020   0.020  0.0508   0.8226
> Residuals       44 17.567   0.399
>
>
> *** Note change of location***
>
> Victoria Allison
> Landcare Research
> Private Bag 92170
> Auckland 1142
> New Zealand
> Phone: +64 9 574 4164
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> WARNING: This email and any attachments may be confidential ...{{dropped}}
>
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>


Andrew Robinson
Senior Lecturer in Statistics                       Tel: +61-3-8344-9763
Department of Mathematics and Statistics            Fax: +61-3-8344 4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson at ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au