GLM Poisson regression with Firth Adjustment and comparison with R

[#1]

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.

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. 

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? 

Regards,

Ceg1

[#2]

The likelihood ratio test (LRT) is not based on the standard error. It is based on the chi-square associated with adding this term to the model.

The estimate of the intercept, -17.6756, is within the stated confidence interval, -178.3917 to -9.458.

The R function uses a Z test assuming normal errors and known variance. JMP is using the LRT, which provides better coverage.