GLM R-plot: linear relationship?

Question

I constructed GLM's to compare a set of variables before constructing GLMM (to model habitat selection). I also wanted to see if there were linear relationships between the response variable and the explanatory variables. I have a response binary variable, which correspond to used or available (1/0) locations of several individuals (which is the reason I will construct GLMM, to include them as a random effect).

First question: since GLMM can handle non-linear variables (correct me if I am wrong), is it important to test linear relationships before constructing GLMMs?

Second question: I plotted one of the models and I don't know how to interpretate the plot. I present the summary and the plot below.

Here is the summary of the model:

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.5364  -0.5364  -0.4028  -0.2793   2.6059  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.42919    0.02177 -111.58   <2e-16 ***
LC2_z       -0.57874    0.02361  -24.51   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19905  on 32669  degrees of freedom
Residual deviance: 19191  on 32668  degrees of freedom
AIC: 19195

Here is the plot:

How do I interpretate this? Is it normal to have these two lines?

Answer 1

I would argue that it makes no sense to say there is a "linear relationship" between a dichotomous response variable and an independent variable. That's one reason we use logistic regression (or other transformations of the response).

Also, perhaps it's just a sort of typo, but variables can't be linear. Did you mean "non-continuous"?

Finally, if you need a mixed model (to deal with dependent data) then any model which does not account for the dependency may be very misleading.