# GLMM summary and multcomp differences

Thanks for taking the time to read my question. I am using R to run a GLMM because I have taken repeated measurements on 100 individuals. The explanatory variable it is a proportion so I am using binomial family. The final model after a model selection is:

1. treat: categorical variable with 4 levels
2. place: categorical variable with 6 levels
3. fdate: categorical variable with 13 levels
4. fid: categorical variable with 100 levels

M <- glmer(y ~ treatment + place + fdate + (1|fid), data = table, family = binomial(logit), glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))

The single term deletions tell me that are all significant
Model:
y ~ treatment + place + fdate6 + (1 | fid)
Df    AIC    LRT   Pr(Chi)
<none>      828.25
treatment 848.87 26.620 7.071e-06 ***
place 830.27 12.014    0.0346 *
fdate6   12 851.13 46.881 4.887e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Summary output

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial  ( logit )
Formula: y ~ treatment + place + fdate + (1 | fid)
Data: table
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

AIC      BIC   logLik deviance df.resid
828.3    942.0   -392.1    784.3     1278

Scaled residuals:
Min      1Q  Median      3Q     Max
-1.9511 -0.1789  0.0000  0.0000  5.0429

Random effects:
Groups Name        Variance Std.Dev.
fid (Intercept) 0.1935   0.4399
Number of obs: 1300, groups:  fgpsid, 100

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)      -1.17329    0.31499  -3.725 0.000195 ***
treatme02        -0.45551    0.26314  -1.731 0.083438 .
treatme03        -1.63531    0.31361  -5.215 1.84e-07 ***
treatme04        -0.64832    0.30000  -2.161 0.030690 *
place02          -0.57500    0.24866  -2.312 0.020757 *
place03          -0.24367    0.38401  -0.635 0.525731
place04          -0.48586    0.36544  -1.330 0.183675
place05          -0.92812    0.41933  -2.213 0.026874 *
place06           0.37485    0.49016   0.765 0.444412
fdate62           1.23421    0.26453   4.666 3.08e-06 ***
fdate63           0.97002    0.27035   3.588 0.000333 ***
fdate64           1.12241    0.30254   3.710 0.000207 ***
fdate65           0.71227    0.43558   1.635 0.102005
fdate66          -0.12241    0.66440  -0.184 0.853819
fdate67           0.09972    0.80556   0.124 0.901484
fdate68           2.19890    0.59646   3.687 0.000227 ***
fdate69           0.50455    0.56520   0.893 0.372024
fdate610          0.92899    0.42959   2.162 0.030581 *
fdate611          0.51314    0.56166   0.914 0.360920
fdate612         -0.16656    0.43301  -0.385 0.700492
fdate613          0.93091    0.31163   2.987 0.002815 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


My next question is regarding the levels of the fixed categorical variables. When I use the multcomp function my output is not significant. Is there something here that am I doing wrong? Which of these results should be reported in my manuscript? I do not understand why my variables are reported as significant in the summary, but not significant with I conduct pairwise comparisons.

> test02 <- glht(M, linfct = mcp(place= "Tukey"))
> summary(test02)
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: glmer(formula = y ~ treatment + place + fdate6 + (1 | fgpsid),
data = table, family = binomial(logit), control = glmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 2e+05)))

Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
place01 - place02 == 0      -0.57500    0.24866  -2.312    0.176
place03 - place02 == 0      -0.24367    0.38401  -0.635    0.987
place03 - place02 == 0      -0.48586    0.36544  -1.330    0.753
place04 - place02 == 0      -0.92812    0.41933  -2.213    0.217
place05 - place02 == 0       0.37485    0.49016   0.765    0.971
place06 - place01 == 0       0.33133    0.36982   0.896    0.943
place03 - place01 == 0       0.08914    0.32802   0.272    1.000
place04 - place01 == 0      -0.35313    0.40192  -0.879    0.947
place05 - place01 == 0       0.94985    0.43239   2.197    0.224
place03 - place06 == 0      -0.24219    0.41090  -0.589    0.991
place04 - place06 == 0      -0.68446    0.47250  -1.449    0.679
place05 - place06 == 0       0.61852    0.55486   1.115    0.865
place04 - place03 == 0      -0.44227    0.45707  -0.968    0.922
place05 - place03 == 0       0.86071    0.49542   1.737    0.486
place05 - place04 == 0       1.30298    0.57876   2.251    0.201
(Adjusted p values reported -- single-step method)

• Can't comment on the multcomp thing, but you should generally report all your results (possibly in a supplementary material) - note what is significant but don't hide the non-significant results. Also it is not clear why are you doing model selection in the first place (inference? interpretation? decision making?), knowing your final goal might help people answer the question. Commented Aug 3, 2018 at 9:20
• Thanks you for you answers @Martin Modrák. My goal is to know the effect of the treatment on the response variable and if there are differences between the treatment. During the data explotarion I saw differences on places on the response variable but I would like to know if there differences between them. The reason of model selection was to select the variable which could explain what happen on my system. Commented Aug 3, 2018 at 9:39

1) What should you report: The model selection process you have run tells you that place should be important, but you didn't observe a significant contribution of individual places. That's IMHO totally OK and probably just means you have too little measurements per place. I wouldn't worry about it - it is important that you controlled for place as that might have an impact on your estimates of treatment - which are (I guess) of primary interest.