# I have significant differences detected in my glmer model summary but not in my mcp (Tukey) multiple comparisons summary. Why?

I am working on a project looking at ant recruitment to bait in the lab. I want to see which baits ('treatment') the ants recruit to more/less and have multiple measurements for each colony over the course of multiple weeks. I have (hopefully) accounted for varience between colonies and each measurement collection by nesting 'colony' in 'DAT' (days after treatment). My data was overdispersed so I added an observation level random factor to correct for this ('obs'). I am using the lme4 package for the overall glmer model with results below

MODEL

> mod2015<-glmer(numants~Treatment+(1|colony)+(1|DAT)+(1|obs), family=poisson, data=ncl2015)
> summary(mod2015)

Generalized linear mixed model fit by maximum
likelihood (Laplace Approximation) [glmerMod]
Family: poisson  ( log )
Formula:
numants ~ Treatment + (1 | colony) + (1 | DAT) + (1 | obs)
Data: ncl2015

AIC      BIC   logLik deviance df.resid
1281.8   1302.6   -633.9   1267.8      137

Scaled residuals:
Min       1Q   Median       3Q      Max
-2.82084 -0.26069  0.02638  0.15502  0.49829

Random effects:
Groups Name        Variance Std.Dev.
obs    (Intercept) 0.1954   0.4420
colony (Intercept) 0.1519   0.3897
DAT    (Intercept) 0.1275   0.3571
Number of obs: 144, groups:
obs, 144; colony, 24; DAT, 6

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    3.1883     0.2310  13.801   <2e-16 ***
TreatmentHON   0.5283     0.2522   2.095   0.0362 *
TreatmentKB    0.5512     0.2522   2.186   0.0288 *
TreatmentPB    0.1277     0.2528   0.505   0.6136
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) TrtHON TrtmKB
TreatmntHON -0.551
TreatmentKB -0.551  0.504
TreatmentPB -0.549  0.503  0.503


and am using the multcomp package to conduct pairwise comparisons using the glht function with the results below

POST HOC

> mcpncl2015<-glht(mod2015, mcp(Treatment="Tukey"))
> summary(mcpncl2015)

Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Tukey Contrasts

Fit: glmer(formula = numants ~ Treatment + (1 | colony) + (1 | DAT) +
(1 | obs), data = ncl2015, family = poisson)

Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
HON - BUFF == 0  0.52830    0.25223   2.095    0.155
KB - BUFF == 0   0.55117    0.25218   2.186    0.127
PB - BUFF == 0   0.12769    0.25285   0.505    0.958
KB - HON == 0    0.02287    0.25109   0.091    1.000
PB - HON == 0   -0.40061    0.25179  -1.591    0.384
PB - KB == 0    -0.42348    0.25173  -1.682    0.333
(Adjusted p values reported -- single-step method)


PROBLEM As you can see, I get significant differences (p values) when from the over all glmer model summary but those significant differences are not detected when I run the glht function for multiple comparisons using Tukey post hoc test. Can anyone tell me why and how to remedy this? I hope I've explained the issue well enough for help.

• The Tukey test is more stringent than the glmer test. Nov 15 '16 at 2:39
• @DJohnson Glmer is not a test. Nov 15 '16 at 15:37
• @subhashc.davar Thanks. Of course that's correct. I should have said than the test results produced by glmer. Nov 15 '16 at 15:43
• I'm sorry for the delay in commenting. I had issues with merging 2 accounts. I am by no means a statistician so please forgive my ignorance. I was under the impression that the results from glmer (pvalues) show which level of the fixed factor significantly differs from the intercept (in this case, the level BUFF) based on the model. Is this incorrect? If my interpretation IS correct, why does the significant differences not also show in the pairwise comparisons? Nov 21 '16 at 20:54
• @subhashc. Am I correct or incorrect in my interpretation in the above comment? and why would the model indicate significant pvalues (in comparison with the BUFF Treatment as the intercept) while the post hoc test did not? Nov 23 '16 at 20:49