cloglog logistic regression interpretation

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 
question).

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