[R] Interpreting NB GLM output - effect sizes?

[Achim Zeileis]

On Tue, 6 Jul 2010, Anna Berthinussen wrote:

> Hi,
>
> I am trying to find out how to interpret the summary output from a neg
> bin GLM?
>
> I have 3 significant variables and I can see whether they have a
> positive or negative effect, but I can't work out how to calculate the
> magnitude of the effect on the mean of the dependent variable. I used
> a log link function so I think I might have to use the antilogs of the
> coefficients but I have no idea how this relates to the dependent
> variable??

The mean equation is

   log(mu) = x'b

so this is similar in interpretation to a semi-logarithmic linear model. 
Absolute changes in x lead to relative changes in the response. In your 
example below, a sloppy formulation would be: If Time increases by one 
unit, the expected mean Pass decreases by 1.6% (if everything else stays 
the same).

A useful discussion of this is for example in "Analysis of Microdata" by 
Winkelmann & Boes (2009, Springer). But of course in many other textbooks 
as well.

Another useful approach is to employ "effects" to visualize the effects, 
e.g.:

   library("effects")
   plot(allEffects(fitted_glm.nb_object), ask = FALSE, rescale = FALSE)

hth,
Z

> Any help would be much appreciated.
>
> My model and output is shown below.
>
> Thanks
>
> Anna
>
> Call:
> glm.nb(formula = Pass ~ Dist + Time + Wind, data = bats, link = "log",
>     init.theta = 0.8510838809)
>
> Deviance Residuals:
>     Min       1Q   Median       3Q      Max
> -2.2784  -0.9967  -0.3594   0.2603   2.2142
>
> Coefficients:
>               Estimate Std. Error z value Pr(>|z|)
> (Intercept)  3.3329718  0.3603909   9.248  < 2e-16 ***
> Dist         0.0008892  0.0002377   3.741 0.000183 ***
> Time        -0.0159068  0.0034665  -4.589 4.46e-06 ***
> Wind        -0.1177475  0.0346301  -3.400 0.000673 ***
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> (Dispersion parameter for Negative Binomial(0.8511) family taken to be 1)
>
>     Null deviance: 134.586  on 79  degrees of freedom
> Residual deviance:  92.725  on 76  degrees of freedom
> AIC: 501.21
>
> Number of Fisher Scoring iterations: 1
>
>
>               Theta:  0.851
>           Std. Err.:  0.164
>
>  2 x log-likelihood:  -491.211
>
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