Estimating parameter of biresponse ordinal logistic regression model using the Berndt-Hall-Hall-Hausman (BHHH) iteration

This study focuses on the estimation of parameters in a biresponse ordinal logistic regression model using Maximum Likelihood Estimation (MLE) and the Berndt-Hall-Hall-Hausman (BHHH) numerical iteration method. Biresponse ordinal logistic regression is particularly useful where there are two correlated ordinal response variables, a common occurrence in fields such as healthcare and social sciences. The traditional univariate models often fail to capture the correlations and interactions between the multiple ordinal outcomes, potentially leading to biased results and incorrect inferences. The MLE method is employed to estimate the model parameters by maximizing the likelihood function, ensuring the best possible fit to the observed data. After analysis using the MLE method, the results of the first partial derivative of the ln likelihood function against the parameter estimator of the Biresponse Ordinal Logistic Regression (BOLR) model are not in close form. To overcome this, numerical optimization is carried out using BHHH iteration, where the BHHH iteration only uses the first partial derivative, not the second partial derivative.