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I'm performing a GLM, the response variable is number of individuals, and response variables are 1)habitat (4 levels) and 2)season (4 levels). I need some help since I know the summary() shows p-values but not for the first (alphabetical) level of factor. I mean, I don't know how to interpret that the Intercept has a significant p-value. I can't reach a biological explanation for this model. Hope you can help me...

Call:
glm(formula = individuals ~ habitat + season, family = poisson(link = "log"), 
data = data)

Deviance Residuals: 
 Min        1Q    Median        3Q       Max  
-2.85859  -0.51541  -0.08508   0.36497   2.29058  

Coefficients:
                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)            1.6774     0.1624  10.331  < 2e-16 ***
habitatDeciduous       0.1340     0.1696   0.790  0.42950    
habitatSemiDeciduous   0.2102     0.1675   1.255  0.20933    
habitatWetland        -0.1861     0.2039  -0.912  0.36151    
seasondry2018         -0.1138     0.1510  -0.753  0.45123    
seasonwet2016         -0.2699     0.1576  -1.713  0.08677 .  
seasonwet2017         -0.4383     0.1656  -2.647  0.00813 ** 

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 78.487  on 63  degrees of freedom
Residual deviance: 64.556  on 57  degrees of freedom
AIC: 287.77
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  • $\begingroup$ Can you clarify in your response the names of all of your habitat categories and all of your season categories? $\endgroup$ – Isabella Ghement Sep 18 '18 at 1:29
  • $\begingroup$ I don't think that's really necessary to the question. $\endgroup$ – Ingolifs Sep 18 '18 at 9:09
  • $\begingroup$ @Ingolifs: How can you fully interpret the intercept of a model if you don't know what the reference categories are for the factors included in the model? Having said that, if you feel that information is not necessary, you can go ahead and provide the desired interpretation. Prior to answering, I find it fair to ask for the information I think it is necessary for me to provide a helpful and specific answer. $\endgroup$ – Isabella Ghement Sep 22 '18 at 19:55
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I would quite like to know the proper answer to this too.

In the meantime, you can use the relevel() function. Pick one of the 'non-default' factors, perhaps the ones with the least significance (habitatDeciduous and seasondry2018) and make them the default factor, by typing in something like:

data$habitat <- relevel(data$habitat,"Deciduous") 

and rerunning the glm. You'll get different numbers out of the new model and the two models aren't really comparable with each other, but you will be able to get an idea of how significant the 'missing' factor is.

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