[R] summary.lme and anova question

[Prof Brian Ripley]

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
>
>
> ######################################################
>
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>

-- 
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