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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: enter image description here

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 :)

sonnisonja
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1 Answers1

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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.

Isabella Ghement
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  • Hey - thanks for the response. My predictor values mean:
    1. Location WK = forest that is situated far from the highway (i have two categories of locations: W and WK where W are the forests along the highway and WK the ones far from the highway
    2. Cover open: meaning percentage of clearing areas in the forest
    3. Cover single: percentage of single-layered structure in a forest
    4. multi: percentage of multi-layered structures, consisting of shrubs and very dense
     – sonnisonja Jan 08 '19 at 08:27
  • Plant species sum: ist the amount of different plant species in the areas
  • PSY_sum: sum of pinus sylvestris (pine tree species) present in the areas
  • fb_nr_holes: number of holes along the forest border
  • Coverage June and October: this refers to the density / Scarcity of the forest border (= how much light can pass through the vegetation)
    • – sonnisonja Jan 08 '19 at 08:32
  • To evaluate how well my model fits the data, I used the McFadden's R2 (pR2 at the end of the above model). Is this not appropriate? – sonnisonja Jan 08 '19 at 08:41
  • McFadden's pseudo R-squared value for a given model evaluates the proportion of deviance explained by that model compared to an intercept-only model (see http://madalgo.au.dk/fileadmin/madalgo/OA_PDF_s/J202.pdf for example). See here for a possible interpretation for this value: https://stats.stackexchange.com/questions/82105/mcfaddens-pseudo-r2-interpretation/99615#99615. You should still check the assumptions underlying your quasi-Poisson regression model in addition to reporting the McFadden pseudo R-squared value as an overall measure of goodness of fit of your model. – Isabella Ghement Jan 08 '19 at 22:22
  • How Can I Check the assumptions? I also have the problem that some of my Data in the model correlate. Is There a way to deal with this so that i dont get wrong Results? Thanks! – sonnisonja Jan 09 '19 at 06:52