Model Quasipoisson interpretation and validation

Question

I am currently doing my Master thesis with evaluating my results in R. I am stuck on my analysis of my glm with quasipoisson. I am analysing influencing variables on the dormouse abundance in 2 types of forests (W = forests along the highway and WK for forests far away from roads) I get the following model output:

Since I am not very good in statistics, I have problems interpreting my result here.

1. Was does the intercept exactly mean?
2. how can I form the regression function and how would it look like?
3. Can I say that e.g. with an increase of cover open, the dormouse abundance increases at a rate of 7.555275 (=estimate)?
4. Can I validate my data using the McFadden Pseudo-R2 (pR2 function in my model output) to evaluate how good my model is and how much it explains of the variation?

I hope someone can help me here since I've been stuck on this for 2 weeks now.. Thanks a lot :)

Answer 1

This reference explains quite nicely what is being modelled in a quasi-Poisson regression: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1141&context=usdeptcommercepub.

In particular, you will see that the log mean value of your response variable, Nr_Nests, is modelled as a linear combination of the predictor variables:

log(mean of Nr_Nests) = beta0 + beta1*LocationWK + beta2*Cover_open + etc.  (1) 

Equivalently, the mean value of Nr_Nests is the exponentiated value of this linear combination:

mean of Nr_Nests = exp(beta0 + beta1*LocationWK + beta2*Cover_open + etc.)  (2)

Thus, the intercept beta0 represents the log mean number of nests when all predictor variables in your model are equal to zero (whatever that means in your context). For instance, LocationWK = 0 for forests along the highway, etc. If you exponentiate the intercept, then exp(beta0) represents mean number of nests when all predictor variables in your model are equal to zero. In practice, beta0 is unknown and estimated from the data. So the estimated value of beta0 is 2.5. For the intercept to be interpretable, your numeric predictor variables should be centered about their mean value, for example.

The regression function looks like (1) or (2), with (2) providing a more natural interpretation.

Can you explain what each of your predictor variables mean?

You should evaluate how well your data satisfy the underlying model assumption. See http://www.flutterbys.com.au/stats/tut/tut10.6a.html for some clues.