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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