[R-sig-ME] model estimates in glmmTMB

[Stephanie Rivest]

Hi there,

I'm hoping to get some clarification on interpreting the model estimates
from the output of a glmmTMB. I fit a model using this package where my
response was zero-inflated count data. I had multiple continuous and
categorical predictors and a random effect of site.

My question relates to the sign of the model estimates. It is my intuition
that the sign of the model estimates (+ or -) indicates the direction of
effect. Therefore, when back-transforming model estimates to get them on
the scale of the response, I *would not* include the sign in this
calculation.

For example, from the model output below, I would conclude that the
predictor CanopyCover significantly (although only marginally) and
negatively affected my response variable. Back-transforming this estimate
should work if I simply take e^(2.6705) which results in the interpretation
that counts decrease by 14.4 for every 1 unit increase in canopy. Is this
correct? Does the sign actually need to be included when back-transforming?

Conditional model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.1274 0.7162 0.178 0.85882
Grass -0.7919 0.7340 -1.079 0.28060
AllFlowers 1.9984 1.8340 1.090 0.27589
CanopyCover -2.6705 1.3044 -2.047 0.04062 *
avg.bft 3.1577 6.5799 0.480 0.63130
season.bft1 0.6337 0.3705 1.710 0.08719 .
occur.bft1 0.6664 0.2560 2.603 0.00925 **
DisturbanceLevel2 0.2997 0.7239 0.414 0.67883
DisturbanceLevel3 1.5339 0.7170 2.139 0.03240 *
DisturbanceLevel4 0.7870 0.7743 1.016 0.30945

Also, what does it mean if the intercept is negative? For example, in the
output above, the intercept represents the baseline level for my
categorical predictors. For arguments sake, if the intercept was negative
would this represent that at the baseline level, the model is predicting
negative counts?

Any help would be greatly appreciated!

Thanks!
Stephanie Rivest

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[Thomas Merkling]

Hi Stephanie,

First, I think you should try to simplify your model (unless you have
good reasons to keep the non-significant variables in your model), this
will likely influence the other estimates. Also, I wouldn't rely on the
p-values from the summary to assess the significance of your variables.
As for your question about back-transforming to interpret the effect of
a variable, I don't think you can just use exp(estimate)  as the
estimate is part of a model equation involving all the parameters (e.g.
intercept + beta1 * Grass + beta2 * AllFlowers ...) and the estimates
are also influenced by the scale of the response variable. I usually use
the predict function to graphically plot the effect of a given variable.
If you're interested in knowing if a given variable has a stronger
effect than another one, I'd recommend standardising your continuous
variables, so that they are all on the same scale.

A negative intercept would mean that the baseline level is somewhere
between 0 and 1 (but still positive!), as exp(-1) = 0.36.. for example.

Hope that helps,
Thomas