[R] dispcrepancy between aov F test and tukey contrasts results with mixed effects model

[Peter Dalgaard]

lbaril at montana.edu wrote:
> Hello,
> 
> I have some conflicting output from an aov summary and tukey contrasts
> with a mixed effects model I was hoping someone could clarify.  I am
> comparing the abundance of a species across three willow stand types. 
> Since I have 2 or 3 sites within a habitat I have included site as a
> random effect in the lme model.  My confusion is that the F test given by
> aov(model) indicates there is no difference between habitats, but the
> tukey contrasts using the multcomp package shows that one pair of habits
> is significantly different from each other.  Why is there a discrepancy? 
> Have I specified my model correctly?  I included the code and output
> below.  Thank you.

Looks like glht() is ignoring degrees of freedom. So what it does is 
wrong but it is not easy to do it right (whatever "right" is in these 
cases). If I understand correctly, what you have is that "stand" is 
strictly coarser than "site", presumably the stands representing each 2, 
2, and 3 sites, with a varying number of replications within each site. 
Since the between-site variation is considered random, you end up with a 
comparison of stands based on essentially only 7 pieces of information. 
(The latter statement requires some qualification, but let's not go 
there to day.)

If you have roughly equal replications within each site, I'd be strongly 
tempted to reduce the analysis to a simple 1-way ANOVA of the site 
averages.

> 
>> co.lme=lme(coye~stand,data=t,random=~1|site)
>> summary (co.lme)
> 
> Linear mixed-effects model fit by REML
>  Data: R
>        AIC      BIC    logLik
>   53.76606 64.56047 -21.88303
> 
> Random effects:
>  Formula: ~1 | site
>         (Intercept)  Residual
> StdDev:   0.3122146 0.2944667
> 
> Fixed effects: coye ~ stand
>                  Value Std.Error DF    t-value p-value
> (Intercept)  0.4936837 0.2305072 60  2.1417277  0.0363
> stand2       0.4853222 0.3003745  4  1.6157240  0.1815
> stand3      -0.3159230 0.3251201  4 -0.9717117  0.3862
>  Correlation:
>        (Intr) stand2
> stand2 -0.767
> stand3 -0.709  0.544
> 
> Standardized Within-Group Residuals:
>        Min         Q1        Med         Q3        Max
> -2.4545673 -0.5495609 -0.3148274  0.7527378  2.5151476
> 
> Number of Observations: 67
> Number of Groups: 7
> 
>> anova(co.lme)
>             numDF denDF   F-value p-value
> (Intercept)     1    60 23.552098  <.0001
> stand           2     4  3.738199  0.1215
> 
>> summary(glht(co.lme,linfct=mcp(stand="Tukey")))
> 
>          Simultaneous Tests for General Linear Hypotheses
> 
> Multiple Comparisons of Means: Tukey Contrasts
> 
> 
> Fit: lme.formula(fixed = coye ~ stand, data = R, random = ~1 | site)
> 
> Linear Hypotheses:
>            Estimate Std. Error z value Pr(>|z|)
> 2 - 1 == 0   0.4853     0.3004   1.616   0.2385
> 3 - 1 == 0  -0.3159     0.3251  -0.972   0.5943
> 3 - 2 == 0  -0.8012     0.2994  -2.676   0.0202 *
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> (Adjusted p values reported -- single-step method)
> 
> 
> 
> Lisa Baril
> Masters Candidate
> Department of Ecology
> Montana State University - Bozeman
> 406.994.2670
> 
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-- 
    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
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