Separated coefficients estimated in Poisson model

[laszloda]

Hi,

First, thank you very much for the package!

The potential issue I found is the following: I generated a data set with two dummies D1 and D2 and an outcome variable, Y, which is always 0 when D2==1; otherwise Y follows a poisson distribution.

set.seed(123)
n <- 10000

D1 <- rbinom(n, 1, 0.5)  # D1 ~ Bernoulli(0.5)
D2 <- rbinom(n, 1, 0.3)  # D2 ~ Bernoulli(0.3)

Y <- rep(0, n)
lambda_values <- exp(D1)
idx <- which(D2 == 0)
Y[idx] <- rpois(length(idx), lambda_values[idx])

data <- data.frame(D1 = D1, D2 = D2, Y = Y)

I run two estimations feglm(fml=as.formula('Y ~ D1 + D2'), data = data, family = "poisson") and feglm(fml=as.formula('Y ~ D1 | D2'), data = data, family = "poisson").

While in the latter version, fixest recognises that D2 predicts the outcome perfectly (and therefore discards the variable and related observations), the former method gives an, I think, misleading large negative estimate for D2. (The more negative the estimate here, the larger the likelihood function. This I think explains the large negative value here.)

I want to ask as if this an expected response? Is there perhaps an option to run checks for such separations?