Hello to all. am hoping someone can help with an issue I am having – all roads have led me to this direction.

I am having trouble running firthlogit on national survey data. I am trying to run a logistic regression command on variables that do not have a really large sample size compared to the all other variables in the dataset. I imagine this is “a rare event regression” would be useful.

My main variables:

Y = binary (0/1) either yes or no (Yes = 39,990 / No = 76,190)
X1 = binary (0/1) either yes or no (Yes = 884 / No = 26, 077)
X2 = binary (0/1) either yes or no (Yes = 1701 / No = 14250)

Covariates:

X3 = categorical (1,2,3,4) a race variable (n = 125,598)
X4 = binary (0/1) either male or female (n = 125,598)
X5 = binary (0/1) either Urban or Rural (n = 125,598)

When I try and run the simple regression (svy: logit y x1 x2) it tells me “x2 !=0 predicts failure perfectly” and it drops the variable. I assume there is collinearity between x2 and x1.

When I run it with firthlogit, it works. However, my standard errors on X2 (the previously omitted variable on regular svy:logit) are really large and not sure if they are accurate.

My main issue is this...

When I throw all the variables in (firthlogit x1 x2 x3 x4 x5) does it take into account the complex survey design? How can I use the svy command with firthlogit? Will relogit work with svy?

I have also tried relogit (relogit y x1 x2) but it tells me “matrix has missing values”

I am hoping someone can provide a solution.

-Cheers
​​​​