Name of Model

ML

Firth

Normal

Cauchy 1

Cauchy 2

TrueCoef

Propensity score

estimation

(1st step)

Method

(Logistic regression)

(Bayesian Logistic regression)

maximum likelihood

Firth’s penalized likelihood

Bayes MCMC

Prior

-

Normal

(0, 10,000)

Cauchy

(0, 2.5)

Cauchy (0, 2.5)

Normal (γ_n, 6.25)

Causal effect

estimation

(2nd step)

Method

(Logistic regression)

(Bayesian Logistic regression)

maximum likelihood

Bayes MCMC

Prior

-

Normal

(0, 10,000)

Normal

(0, 10,000)

Cauchy

(0, 2.5)

Normal (γ_n, 6.25)