I'm using poisson regressions to analyze count data. I have two groups of patients in a clinical trial, and I'm comparing numbers of brain lesions that can be detected on their MRIs at 3 different assessment points. Here is an example of what the frequency tables look like:
I was first looking at lesion frequency over time as a function of group, while having several other covariates in the model. Here is an example of a model I was using: m1 <- glmer(lesions ~ Groupvisit + Agegender + DiseaseDuration + Site + (visit|id), family=poisson, data=visit1_2_3) I am interested in both the Group*visit interaction and the main effect of Group. Because the model was not converging, I started simplifying it, and as a sanity check, I tried running separate poisson regression glms on each visit's data to see if I would get similar results for the Group effect as I get form the mixed effects models. The models produce discrepant findings with the simple glms yielding smaller errors and significant effects of Group. Below are examples of the two types of models using the same data (i.e. fitting the mixed effects model to just a single visits's data).
As you can see, the results are quite different between the two models. I understand that glmer fits the models using maximum likelihood and glm does it using least squares (IWLS), with glmer tending to produce larger error estimates. However not being a quantitative expert, I'm not able to draw any meaningful conclusions from that for the interpretation of my data. I am trying to decide which findings I should report, and I was hoping to get some well-informed opinion or advice on which type of model should be more accurate or valid in my case. Thank you!