[R-sig-ME] cloglog logistic regression interpretation

Ben Bolker bbolker at gmail.com
Wed Jan 7 20:09:45 CET 2015

Javier Atalah <Javier.Atalah at ...> writes:

> Hi,

> Could someone advise me on how to interpret the estimates from a
  logistic regression using a cloglog link?
> I have fitted the following model in lme4:
> glm(cbind (dead, live) ~ time + factor(temp) * biomass, data=mussel,
  family='binomial' (link=cloglog))

This is not actually a mixed model -- you're using glm(), not glmer().
Even if you were using glmer(), this question is not specifically related
to mixed models, it's a more general, GLM-related question.
 Asking in a more general statistics forum such as CrossValidated
(http://stats.stackexchange.com) would be more appropriate (I took
a quick look there and didn't find anything exactly answering your 

> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -4.970 0.428 -11.61 3.64E-31
> time 0.015 0.001 12.15 5.81E-34
> temp19 2.845 0.235 12.1 1.00E-33
> biomassL -0.654 0.148 -4.42 9.73E-06
> temp19:biomassL 0.484 0.194 2.49 1.27E-02

> Is it correct to say, for example, the estimate of time is 0.015
> Thus  1 - (EXP (-EXP (-0.015))) = 0.627

> That means the probability of mortality is 
> increasing 62.7% per unit increase of time if all other
> variables were held constant?

  You can't quite do this.  What you know is that the *log-hazard*
increases by 0.015 per time unit, so the hazard (probability of
mortality per unit time) is multiplied by exp(0.015) = 1.015113
\approx 1.5% per passing time unit.

  Good luck (this looks like a good CV question, but don't
forget to read http://stats.stackexchange.com/help/how-to-ask )

  Ben Bolker

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