# How to interpret the output of Generalised Linear Mixed Model using glmer in R with a categorical fixed variable?

I have computed GLMM using glmer in R. My response variable is species richness and my explanatory variable is grazing treatment (with three categories: cattle, sheep and ungrazed). In the model I have included site as a fixed variable and also a new object with the same number of variations as I have to attempt to account for underdispersal (obs):

model2<-glmer(VegRichness~Grazing+(1|Site)+(1|obs),family="poisson",data=veg.rich)


My output is below and the questions I have about it are:

How do I interpret the fixed effects section? Cattle grazing seems to be missing in the oputput, is this because it is somehow incorporated into the intercept?

> summary(model2)

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]

Family: poisson  ( log )

Formula: VegRichness ~ Grazing + (1 | Site) + (1 | obs)
Data: veg.rich

AIC      BIC   logLik deviance df.resid
178.8    185.2    -84.4    168.8       22

Scaled residuals:

Min..........           1Q............           Median....       3Q.........        Max

-1.4936...      -0.5698.....       -0.1928...      0.4923...   1.3646

Random effects:

Groups  ... Name......        Variance..... Std.Dev.

obs.........      (Intercept).. 0.00000....  0.0000

Site.........     (Intercept).. 0.03596....  0.1896

Number of obs: 27, groups:  obs, 27; Site, 3

Fixed effects:
.......Estimate.... Std. Error..... z value... Pr(>|z|)
(Intercept)............      3.55358.......    0.12309.......  28.869.....  < 2e-16 ***
GrazingSheep......     0.01242......    0.07876........   0.158.......  0.87467
GrazingUngrazed -0.27526.....    0.08503........  -3.237......  0.00121 **

---
Signif. codes:  0 x***x 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr)....GrzngS

GrazingShe......................... -0.322
GrzngUngrzd...................... -0.298...  0.466

• @Sven Hohenstein Great thanks . Is there a way to specify the contrast for 'Grazing'? – Ashley Jul 8 '15 at 12:59
• If you are not specifically interested in a particular contrast, you could also do all comparisons for the factor Grazing: library(multcomp) summary(glht(model2, mcp(Grazing="Tukey"))) Unfortunately, I cannot comment yet, otherwise I wouldn't have pasted this as an answer but rather as a comment. – Stefan Nov 5 '15 at 16:42

Since you didn't specify the type of contrast for Grazing, R creates treatment contrasts by default. The first level, Cattle is the reference category. The remaining the levels are compared with the reference category.
• The fixed effect GrazingSheep is the difference in the dependent variable between Sheep and Cattle.
• The fixed effect GrazingUngrazed is the difference in the dependent variable between Ungrazed and Cattle.
Finally, the intercept represents the mean value of the dependent variable where Grazing = Cattle.
• @Ashley Have a look at the help page of ?contrasts. – Sven Hohenstein Jul 8 '15 at 13:15