Would this be modeled as a mixed effects model or regular logistic regression?

Question

I have data that looks like the following

>df
id  response   Factor  Count1      Count2 
1   0            A       6            1            
1   0            B       5            2            
1   0            C       4            3            
2   1            A       3            4
2   1            C       2            5
2   1            D       1            6

The goal is to see how the Factor and the Count covariates effect the response. My current set up is glm(response~Factor+Count1+Count2,family=binomial(link=logit))

The problem is that I am getting wild residual plots.

I am wondering if i should try running a mixed effects model since I have multiple observations for each id. I also wonder if my ratio of 1s to 0s in the response are to great. I have 11,000 rows and 1,500 are 1s.

Any insight would be helpful. Thanks!

Edit: I just came across this post about each id being drawn from a Bernoulli. It turns out that I was able to find a natural grouping for my ids and make proper proportions from there. My Normal Q-Q plot is not great, but at least they don't have a large gap in them anymore.

Answer 1

A normal Q-Q plot is really not relevant for logistic regression. As the name says, it is for visually inspecting whether the residuals in a model with a normal error term (which logistic regression is not) approximately follow some normal distribution.

If the observations for each ID are related (from a common sense thinking about it perspective, e.g. asking the same patient in consecutive weeks whether he/she feels better, checking whether the same server is up and running etc.), then a random effects version of logistic regression (or generalized linear mixed model) is one way (alternatives are e.g. GEE methods) of taking that into account. Otherwise you claim that observations that are not independent are independent, which can lead to seriously wrong results.