[R] summary.lme and anova question
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu Aug 21 11:52:14 CEST 2008
On Thu, 21 Aug 2008, Christoph Scherber wrote:
> Dear all,
>
> Thanks to Brian Ripley for pointing this out. If I understand it correctly,
> this would mean that looking at the parameter estimates, standard errors and
> P-values in summary.lme only makes sense if no interaction terms are present?
You can look at the highest-order interaction terms, only. Even then you
need to be careful if there is more than one of them.
> My conclusion would then be that it is better to rely on the anova.lme()
> output when assessing the significance of terms in the model (rather than
> looking at the P-values from summary.lme).
It is better to do a stepwise model selection (assuming you want to select
a model for explanatory purposes). The anova() methods for lm() and lme()
use a particular order than may or may not be appropriate.
> Is that correct? Because in most books (e.g. Crawley, "The R book"), the P
> values from summary.lme are used to assess the significance of terms.
I don't know about 'most books' -- maybe make that 'some books by
Professors of Biology'? It certainly is not done in MASS for example, and
there were some cogent reasons why I referred you to MASS chapter 6 where
Bill Venables tackled some of these misconceptions.
In these days when it is easy to fit different models, I would say that is
the way to do model selection. And often it is best to interpret models
via their predictions: if you know how to interpret coefficients via what
effect they have on predictions you are less likely to go wrong. E.g. in
your case the 'CO2' parameter is the difference in mean response between
the two levels of CO2 *at the reference level of DROUGHT and TEMP*, unless
you changed the contrasts.
>
> Best wishes,
> Christoph
>
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> Prof Brian Ripley schrieb:
>> Please read the help for anova.lme, and note the 'type' argument. You are
>> comparing apples and oranges here (exactly as if you did this for a linear
>> model fit).
>>
>> Because you have a three-way interaction in your model, looking at the
>> (marginal) t-tests for any other coefficient than the third-order
>> interaction violates the marginality principle. And the third-order
>> interaction seems to be important.
>>
>> On Thu, 21 Aug 2008, Christoph Scherber wrote:
>>
>>> Dear all,
>>>
>>> When analyzing data from a climate change experiment using linear
>>> mixed-effects models, I recently
>>> came across a situation where:
>>>
>>> - the summary(model) showed a significant difference between the levels of
>>> a two-level factor,
>>> - while the anova(model) showed no significance for that factor (see
>>> below).
>>>
>>> My question now is: Is the anova.lme() approach correct for that model?
>>> And why does the F-test for CO2 yield a non-significant P-value, while the
>>> t-test in the summary.lme() is significant?
>>
>> CO2 on its own explains little, but allowing different CO2 effects within
>> the levels of DROUGHT seems important.
>>
>> A good book on fitiing linear models (e.g. MASS chapter 6) will explain
>> this to you.
>>
>>> Many thanks for your help!
>>>
>>> Best wishes
>>> Christoph
>>>
>>> ######################################################
>>>
>>> mod11=lme(log(ind1+1) ~ CO2*DROUGHT*TEMP,
>>> random=~1|B/C,na.action=na.exclude)
>>>
>>> summary(mod11)
>>> Linear mixed-effects model fit by REML
>>> Data: NULL
>>> AIC BIC logLik
>>> 97.3077 115.6069 -37.65385
>>>
>>> Random effects:
>>> Formula: ~1 | B
>>> (Intercept)
>>> StdDev: 1.303146e-05
>>>
>>> Formula: ~1 | C %in% B
>>> (Intercept) Residual
>>> StdDev: 0.2466839 0.4846578
>>>
>>> Fixed effects: log(ind1 + 1) ~ CO2 * DROUGHT * TEMP
>>> Value Std.Error DF t-value p-value
>>> (Intercept) 1.9981490 0.2220158 29 9.000030 0.0000
>>> CO2 -1.0308687 0.3139778 5 -3.283254 0.0219
>>> DROUGHT -0.9715216 0.2798173 29 -3.471986 0.0016
>>> TEMP -0.5592615 0.2954130 29 -1.893151 0.0684
>>> CO2:DROUGHT 1.2196261 0.3957214 29 3.082032 0.0045
>>> CO2:TEMP 0.9791044 0.4068987 29 2.406261 0.0227
>>> DROUGHT:TEMP 0.6413038 0.4068987 29 1.576077 0.1259
>>> CO2:DROUGHT:TEMP -1.1448624 0.5675932 29 -2.017047 0.0530
>>> Correlation:
>>> (Intr) CO2 DROUGHT TEMP CO2:DROUGHT CO2:TE DROUGHT:
>>> CO2 -0.707 DROUGHT -0.630 0.446
>>> TEMP -0.597 0.422 0.474 CO2:DROUGHT 0.446
>>> -0.630 -0.707 -0.335 CO2:TEMP 0.433
>>> -0.613 -0.344 -0.726 0.486 DROUGHT:TEMP 0.433
>>> -0.306 -0.688 -0.726 0.486 0.527 CO2:DROUGHT:TEMP -0.311
>>> 0.439 0.493 0.520 -0.697 -0.717 -0.717
>>> Standardized Within-Group Residuals:
>>> Min Q1 Med Q3 Max
>>> -1.4631313 -0.5715171 -0.2024273 0.4592221 1.9568914
>>>
>>> Number of Observations: 47
>>> Number of Groups:
>>> B C %in% B
>>> 6 12
>>>
>>> ######################################################
>>>
>>> anova(mod11)
>>> numDF denDF F-value p-value
>>> (Intercept) 1 29 162.95719 <.0001
>>> CO2 1 5 1.15108 0.3324
>>> DROUGHT 1 29 5.53240 0.0257
>>> TEMP 1 29 0.04519 0.8331
>>> CO2:DROUGHT 1 29 5.66686 0.0241
>>> CO2:TEMP 1 29 1.88455 0.1803
>>> DROUGHT:TEMP 1 29 0.03481 0.8533
>>> CO2:DROUGHT:TEMP 1 29 4.06848 0.0530
>>>
>>>
>>> ######################################################
>>>
>>> ______________________________________________
>>> R-help at r-project.org 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.
>>>
>>
>
> --
> Dr. rer.nat. Christoph Scherber
> University of Goettingen
> DNPW, Agroecology
> Waldweg 26
> D-37073 Goettingen
> Germany
>
> phone +49 (0)551 39 8807
> fax +49 (0)551 39 8806
>
> Homepage http://www.gwdg.de/~cscherb1
>
> ______________________________________________
> R-help at r-project.org 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.
>
--
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
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