Parameters estimation and hypothesis testing of bivariate probit models with BHHH iteration

There are many cases with categorical data, the bivariate probit model is the model used in the case that two categorical response variables are correlated. The predictor variables are discrete and continuous variables. This paper focuses to discuss about theory and parameters estimation of bivariate probit model. The parameter estimation method used is Maximum Likelihood Estimation (MLE), but the results obtained don't produce a closed form, so the solution must use numerical iteration. The numerical iteration method used in this study is the BHHH (Berndt, Hall, Hall, Hausman) iteration method. The test statistic used for simultaneous testing is the Likelihood Ratio Test (LRT). The model was tested simultaneously to test whether all predictor variables had a significant effect on the response variable or at least one predictor variable had a significant effect on the response variable. Partial test was conducted to test the significance of each predictor variables on the response variables. The goodness of the model uses the Akaike Information Criterion (AIC) value.