[R-sig-ME] [R] dispcrepancy between aov F test and tukey contrasts results with mixed effects model
lbaril at montana.edu
lbaril at montana.edu
Wed Mar 18 17:48:26 CET 2009
Unforunately, the data are highly unbalanced. I have 2 to 3 sites per
stand, but observations within a stand range from 4 to 16 so my variances
in each site will not be similar and so using site averages would not work
in this case, right? Note that at the stand scale, I have roughly equal
observations. Often in ecology balanced designs are not possible
(although if I'd known this would be an issue I would have made more of an
effort towards balance), so it seems as though there ought to be a
solution or others who have experienced this. I have spent a fair bit of
time researching this issue, but it seems like all the advice points to
what I tried originally - which obviously did not work correctly given my
data. Is there potentially another solution?
> lbaril at montana.edu wrote:
>> Thanks Peter for the advice and quick response. I just want to clarify
what you suggest. I should average values within a site then do a
one-way
>> anova to test for differnces between sites based on the 2 to 3 new samples
>> per stand type -- and not use random effects for site? Or, because
I've
>> reduced the data I've 'corrected' the problem with the glht multiple
comparisons and can use the p-values from that summary if I include
site
>> as a random effect? Thanks again for your advice.
>
> This is tricky to say in a few lines, but the basic idea of a random
effects model is that the site averages vary more than they should
according to within-site variability. In the balanced case (equal number
of observations per site), it turns out that the mixed-effects analysis
is _equivalent_ to modeling the site averages. This is not ignoring the
random effects of site; rather, it is coalescing it with the residual
since the variance of a site average is v_site + 1/k v_res where k is
the number of within-site observations.
>
> In the unbalanced case it is not strictly correct to analyze averages,
because thy have different variances. However, the differences can be
slight (when the k's are similar or v_site dominates in the above
formula).
>
> A side effect of looking at averages is that you are fitting a plain lm
model rather than lme and that glht in that case knows how to handle the
degrees of freedom adjustment. (Assuming that the averages are normally
distributed, which is as always dubious; but presumably, it is better
than not correcting at all.)
>
>
>>> 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
>>>> ______________________________________________
>>>> 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.
>>> --
>>> 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
>>> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
>>> ______________________________________________
>>> 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.
>> Lisa Baril
>> Masters Candidate
>> Department of Ecology
>> Montana State University - Bozeman
>> 406.994.2670
>> ______________________________________________
>> 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.
>
>
> --
> 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
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
>
>
>
Lisa Baril
Masters Candidate
Department of Ecology
Montana State University - Bozeman
406.994.2670
More information about the R-sig-mixed-models
mailing list