[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 16:27:15 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