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