# Rare events modelling - value of coefficients

I am running a logit regression on a dataset with only 2 independent categorical variables, country and device type. Both of these variables can take several values. The dependant variable is binary. The event occurs approximately 0.2% of the time.

For certain countries, the coefficients are significant, but I do not have any positive event for this country. How can this happen ?

I am using the glm procedure in R.

Thank you,

• How confident are you in your rate? Setting a weak prior may add realistic support over the events. Is there a hidden structure to the data you could take advantage of? There is no such things as "significance" though in Bayesian methods. To walk you through the idea, imagine you had an event that happened one every 1000 times, though you did not know that. If you saw 1000 events and nothing happened a triangular prior would create an expected rate of 2 per 1003. It would be an over-estimate, but less than 0 per 1000. – Dave Harris Feb 14 '17 at 3:40
• The only problem is that your prior will determine your coefficient, which is not a good thing. I am assuming you have no way to get more data as this is really a power issue. If you have some way to get reasonable estimates outside the data, then I would put a prior over the parameter space and use a Bayesian form of logistic regression instead. This is far from a perfect solution, but if your goal is accuracy and not testing the truth of a null, its about a close as you can get. The data will hopefully swamp the prior anyway. – Dave Harris Feb 14 '17 at 3:42
• Why are you not simply estimating the contingent probability for being in a joint category, why are you using logistic methods? – Dave Harris Feb 14 '17 at 3:44
• Are you sure your procedure has converged properly and is not giving you warning messages (I would normally expect that with standard logistic regression when some categories have no events)? Or where you using some kind of exact procedure or Firth's penalized likelihood version? Hierarchical models whether Bayesian or not may be another analysis strategy to consider (exploiting that there is presumably some similarity across bars and - if you want to avoid the averaging of samples - across samples from the same bar). – Björn Feb 14 '17 at 7:59