[Alejandro Torres]

Dear Clyde, I am here to ask you some help again please. In N°14 you said:

"Logistic regression coefficients with magnitudes like 9 and 10 just don't happen in the real world. Those are equivalent to odds ratios of the order of magnitude of 10,000! When I see results like that, I know something is very, very wrong. Usually the problem is in the data. Take religdiver as an example, with a coefficient of 19. That's just not possible. That's an odds ratio of 18,000,000."
May I ask you how do you calculate the odds ratio magnitude please? Are there any paper that you could recomend me to read for interpreting coefficient considering different types of regressions? Thank you very much for your help.
Best regards,
Alejandro

[Clyde Schechter]

In a logistic regression: odds ratio = exp(coefficient)

In a Poisson or nbreg regression: probability ratio = exp(coefficient)

I should dd a clarification to what you quoted. These are odds ratios associated with a unit difference in the variable whose coefficient we are talking about. So, these large coefficients are simply not credible as applied to indicator (dummy, 0/1) variables. They are also not credible as applied to continuous variables that are scaled in the usual way. The only place where coefficients like 9, 10, or 19 are credible is if they are coefficients of continuous variables that are scaled in units that give them extremely small values. For example, if we were using human height as a variable and we measured it in kilometers or miles, the numbers would be extremely small, and a unit difference would be far outside the possible.

So the bottom line in these models is that if you have a variable for which a unit difference between values is possible, or even close to possible, logistic or poisson/nbreg coefficients greater than 4 in magnitude (so > 4 or < -4) are suspect, greater than 6 in magnitude are extremely suspect, and greater than 8 are essentially impossible in the real world. (And I'm really being rather conservative in these judgments.)

[Alejandro Torres]

The answer is absolutely clear, I really appreciate it. Thank you so much !!