Bivariate Probit Model

Bivariate probit modelling jointly estimates two probit equations for two binary outcomes whose latent errors are bivariate normal with correlation rho, using maximum likelihood.

이변량 프로빗 모형은 잠재 오차가 상관 ρ를 가진 이변량 정규분포라고 보고 두 이진 결과의 프로빗 식을 최대우도로 함께 추정하는 방법입니다.

Two yes/no outcomes are likely driven by shared unobserved factors; how do I model them together and test their correlation?

두 예/아니오 결과가 관측되지 않은 공통 요인에 함께 영향을 받는 것 같은데, 둘을 함께 모형화하고 상관을 검정하려면 어떻게 하나요?

The bivariate probit fits two probit equations at once and estimates the correlation rho between their unobserved error terms. A likelihood-ratio test of rho = 0 shows whether separate probits suffice, and the recursive form lets one binary outcome enter the other equation as an endogenous regressor.

When to use Bivariate Probit Model

• Two binary outcomes are observed for the same units and may share unobserved determinants.
• A binary treatment is endogenous for a binary outcome (recursive bivariate probit).
• Joint probabilities of both outcomes are needed.

When to use something else

• The outcomes are unrelated after conditioning on covariates; fit two separate probit regressions.
• There are more than two binary outcomes; use a multivariate probit or a latent class model.

Assumptions and requirements

• The latent errors are bivariate normal.
• Observations are independent.
• The recursive form needs an exclusion restriction for credible identification.

What the analysis reports

• Coefficients of both equations with standard errors
• Error correlation rho with CI, Wald and likelihood-ratio tests
• Predicted versus observed joint and marginal probabilities
• Log-likelihood and AIC

How to report it

The bivariate probit estimated rho = [value], 95% CI [[value], [value]]; the likelihood-ratio test of rho = 0 gave chi2(1) = [value], p = [value].

Related methods

• Probit Regression Model
• Seemingly Unrelated Regression
• Instrumental Variables (2SLS)

Run Bivariate Probit Model on Quorant