Solved – Interpreting coefficient in GLM with categorical explanatory variables

categorical datacontrastsgeneralized linear modelinterpretationpoisson-regression

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

Best Answer

When independent variables are categorical, one level of each is chosen as a refernce level. By default, R choose the first one in alphabetical order. The other levels are compared to that level.

The intercept is the parameter estimate for when all the other variables are 0 -- in this case, when the other two variables are at the reference level.

You can change the defaults, but R questions are off-topic here.

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