dispcrepancy between aov F test and tukey contrasts results with mixed effects model
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 ?ster 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 ?ster 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