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I have data on the abundance of beetles I have collected (I have also done this for biomass of beetles and proportion of abundance represented by a particular functional group of beetles, but only include abundance for simplicity in this post).

Beetles were collected over 3 seasons: winter, spring and summer. At 3 sites: RW, RA and CTRL. And at 2 locations within each site: edge and centre.

I have plotted the data in R and performed all the data checks. Then I have conducted a GLM on this data.

What I need help with is understanding the summary output of this GLM.

In the coefficients returned I have the intercept and then the relevant p values for the other variables. However, I was not given p values for RW, centre, or spring. It is my understanding that the intercept is made up of a combination of these 3 un-returned variables.

So what I want to know is are the p-values I have been given showing that they differ significantly from the intercept/baseline which is a combination of these 3 variables rather than from each other e.g. RA differs significantly from RW/centre/spring and not from the other sites.

And then if that's the case, how do I get a p-value for RW if the intercept contains RW (with centre and spring), surely this doesn't make sense as how would RW differ from something that contains RW (with centre and spring)?

Also, how can I tell from the P values if RA differs significantly from CTRL for example, or if winter differs significantly from summer?

Also, if the intercept is made up of the combination of these 3 variables, what does its p value indicate? Why don't I have p values for the other combinations e.g. CTRL, edge, winter?

Thanks in advance for your help but please be mindful that I am an ecologist, not a mathematician. I do not want to understand the math, but to understand how to write about my results in a scientific paper and talk about how the sites, locations and times effects the abundance of the beetles.

Here is my data:

enter image description here

and here is the summary of the glm provided by R:

enter image description here

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  • $\begingroup$ Hello. You can two observations per (site, location, time). Can you explain? Also I notice at least one row "missing": it's (RA, Center, Winter). Is the observation truly missing, or perhaps it's 0 and has been omitted by chance? $\endgroup$
    – dipetkov
    Sep 7 at 18:43
  • $\begingroup$ Your data is over-dispersed: dispersion $\approx$ residual deviance / residual df = 30. This means that the standard errors from the Poisson fit are too small. You should address this issue first before reporting any p-values. Perhaps consider a negative binomial regression instead. $\endgroup$
    – dipetkov
    Sep 8 at 20:10

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The intercept is the predicted value when all the other variables are 0. (I don't know what "a combination of the other variables" means).

Each of the parameter estimates for the categorical variables are in comparison to the reference group for that variable. For the interactions, you won't get output for any of the reference levels in either variable, because an interaction is the product of two variables and the reference group is coded as 0.

I have fount that the easiest way to get a sense of what interactions are doing is to output the predicted values for different combinations of those effects. Since you have 3 sites, 3 seasons and 2 locations, you have 3x3x2 combinations, and you can get the predicted value for each. You can then put them in a table, or make graphs (or both) to look at what is happening.

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