Interpreting results from GLM

Question

I'm trying to understand the results from a glm I ran. I am doing this for multiple different fish species (one at a time), to see how month, average salinity, temperature, discharge, and rainfall impact their abundance. Below is an example from one fish, I have gotten similar results from other species as well.

I used this data https://drive.google.com/file/d/1Swp0rEFeaInGD4kA1h3xZReFNtho6JPz/view?usp=sharing

and this code to run a GLM on one species

glm.full.bin = glm(binom~Month +Salinity +Temperature +Discharge.x +Rainfall.x,
                   data=fish_B_all,family=binomial)
glm.base.bin = glm(binom~Month,data=fish_B_all,family=binomial)

#step to simplify model and get appropriate order
glm.step.bin = step(glm.base.bin,scope=list(upper=glm.full.bin,lower=~Month),direction='forward',
                    trace=1,k=log(nrow(fish_B_all)))

#final model - may choose to reduce based on deviance and cutoff in above step
glm.final.bin  = glm.step.bin
print(summary(glm.final.bin))

#calculate the LSMeans for the proportion of positive trips
lsm.b.glm = emmeans(glm.final.bin,"Month",data=fish_B_all)
LSMeansProp = summary(lsm.b.glm)

#plot model
par(mfrow=c(2,2))
plot(glm.final.bin)

and the plot shows this.. What does this mean when the residuals and qqplot look like this? Do I need to do something to transform my data to correct this?

Answer 1

These diagnostic plots are designed for use with normal models, not binomial ones.

Moreover, when the response values are all 0s and 1s, the diagnostic plots will always look sort of like this. Take residuals versus fitted. The residuals are defined as $Y_i - \hat Y_i$, so all the points in this plot will have coordinates $(\hat Y_i, \; 0-\hat Y_i)$ when $Y_i=0$, and $(\hat Y_i, \;1 - \hat Y_i)$ when $Y_i = 1$. So these points all lie along two lines with slope $-1$ and intercepts $0$ and $1$, respectively. In this particular plot, there is some additional standardization, causing some shifting and curvature, but that does not stop it from showing two distinct curves corresponding to the 0s and the 1s.

Don't worry about it.