[R-sig-ME] glmer.nb - interaction interpretation

[Cueva, Jorge]

Dear all
I hope to get support for interpreting a model. First, I am assessing the natural regeneration in a dry forest. The design has 12 clusters and each cluster includes 3 open and 3 fenced plots (a total of 36 open plots and 36 fenced plots), the open plots are separate from the excluded plots by only 20 meters. I want to know if livestock grazing affects the abundance of regeneration, for this we collected excrements of animals, but a single sample of excrements affects both the open and the fence plot.

Of all the models tested, the best was:
glmer.nb(Ind ~ 1 + Equine * Treat + SPrec + Cattle + (1|Cluster), data = BaseOb2, family=poisson, verbose=FALSE, glmerControl(optimizer="bobyqa", optCtrl = list(maxfun = 2e5)))

Ind = number of individuals
Equine = weight of equines excrements (horses + donkeys)
Treat = treatment (open and exclusion plots)
SPrec = seasonal precipitation
Cattle = weight of cattle excrements
Cluster = cluster was used as random predictor because the samples were nested in the cluster.

My issue is when I want to interpret the effect of the predictors. Here are the results

Fixed effects:
                                              Estimate              Std. Error             z value                  Pr(>|z|)
(Intercept)                          3.170153             0.246584             12.856                  < 2e-16 ***
Equine                                 0.926521             0.233079             3.975                     7.03e-05 ***
Treatopen                          -0.009898            0.068965             -0.144                   0.885875
SPrec                                    0.390747             0.078133             5.001                     5.70e-07 ***
Cattle                                   -0.365988            0.184748             -1.981                   0.047589 *
Equine:Treatopen            -0.989678            0.274040             -3.611                   0.000305 ***

It can be seen that the independent effect of Equine is significantly positive and that of Treatopen non-significantly negative. Interpretation of these would be easy, but my issue is the Equine:Treatopen interaction. Why is the effect of Equine first positive and then in the interaction negative? What does that mean?

Very grateful in advance.

Jorge Cueva Ortiz
PhD Candidate
Technical University of Munich
01631327886


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