Thread: Writing down firth logistic regression equation

1. Writing down firth logistic regression equation

Hi,

This is a really simple question that I'm sort of embarrassed I can't answer - how would you write down a firth logistic regression? Now to clarify, I know how to RUN one in Stata and I know how to interpret the coefficients, but how would you actually write one down, like in a paper? Not sure what the formula is and papers that use firth logistic regression is an extreme rarity in my field.

Also I should mention that I'm having the output transformed into odds ratios.

2. Re: Writing down firth logistic regression equation

I think you are looking for an nice clean way to write out the model equation or formula for the odds ratio, which I don't think are available. It is a bias correction in the likelihood, so I think the two above mention equations remain the same, but the interworkings for coefficient calculation are slightly tweaked.

I am a little like you, in that I know when to use it and I interpret results the same as before but document the use of the correction. The best that I can do is provide the link below and say perhaps some people (unsure?) add a subscript documenting its use (e.g., ORFirth: 2.4 95% CI: 1.2, 3.9), imagine I know Latex and the firth is a subscript.

http://stats.stackexchange.com/quest...tic-regression

PS, We can see if anyone else chimes in, and please update you post if you figure out an acceptable solution.

3. Re: Writing down firth logistic regression equation

Hi,

So would it be OK to write logitFirth(Reward=1)= (and then the actual equation) with Firth obviously written as a subscript? Is that what you mean? Because that I can do :P

Thanks for the help.

4. Re: Writing down firth logistic regression equation

Yeah, that would be my applied approach. Since the Firth approach is a little too complicated to paraphrase in a cute little package, at least in my opinion.

"Actual equation" you mean, say - the model's form. So a bunch of betas with variable terms?

5. Re: Writing down firth logistic regression equation

Yeah, like
logit(reward=1) = B1Treatment1 + B2Treatment2 + B3Age1823 etc (obviously I'd use Beta and subscripts for the numbers but you get the point). I did an experiment with two treatments.

6. Re: Writing down firth logistic regression equation

That is what I would do, as long as you don't need anything in addition.

7. Re: Writing down firth logistic regression equation

Yeah, it's just for the results section to show everyone that I used logistic regression with the firth penalization, the actual code that you'd punch in to replicate the results I have in the appendix.

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