Hi,
I came across a strange results when creating Poisson regression model in JMP and comparing them to R.
I am modelling count (Y variable), using model with intercept and single categorical variable mod ("Before mod"/"Modified"). I am using Log(Time) as my offset variable. My sample size is 60.
When running this model, my Parameters Estimates Std Error are very big (1291), but both parameters are significant.
![Ceg1_3-1687440599801.png Ceg1_3-1687440599801.png](https://community.jmp.com/t5/image/serverpage/image-id/54029i6E60019CA523A4BB/image-size/medium?v=v2&px=400)
Isn't it contradictory, I think that significant parameter, should have low std error?
What is more, Intercept estimate is outside of the Lower and Upper CL. Can those two be a bug? Or such information would be an indication to reject poor model.
Additionally, I run a platform with Firth Adjusted Maximum Likelihood, which significantly reduced std error and returned a valid model.
![Ceg1_1-1687440367789.png Ceg1_1-1687440367789.png](https://community.jmp.com/t5/image/serverpage/image-id/54027i4D9DC68AD4DE89B0/image-size/medium?v=v2&px=400)
But I recreated this model in R, using glm and brglm2 libraries [glmPoisson_firth <- glm(Y ~ mod + offset(Log.Time.), data = data, family = poisson(link = "log"), method = "brglmFit", type = "AS_mean")]. Parameters estimates and standard errors are same, but in contrast to JMP R shows that mod variable is insignificant (R p-value 0.10 vs JMP p-value 0.0062). Can you explain where does the difference come from?
![Ceg1_2-1687440489195.png Ceg1_2-1687440489195.png](https://community.jmp.com/t5/image/serverpage/image-id/54028i02A7CD1CE0A048EC/image-size/medium?v=v2&px=400)
Regards,
Ceg1