A Comparative Assessment between the Simultaneous and Sequential Maximum Likelihood Estimation Approaches for the Frank Copula-Based Joint Model of Vehicle Type Ownership and Usage in Metro Manila

Abstract

The copula-based joint discrete-continuous framework is superior to the full information maximum likelihood estimation approach of the bivariate normal distribution function. Using the simultaneous maximum likelihood estimation (MLE) to estimate the copula-based joint model is computationally prohibitive,and sometimes the simultaneous MLE approach does not converge. This paper aims to compare the models developed using the sequential and simultaneous MLE approaches of the Frank copula-based discretecontinuous model. The results implied that the simultaneous MLE of the joint model did not converge, and the problem arose during the model estimation. The estimated percentage shares of the discrete choice component using the sequential MLE approach matched the actual percentage shares. Beyond that, the model was slightly superior to the independencebased joint model in term of Akaike Information Criteria (AIC) but marginally lower in terms of root mean square error (RMSE) and mean relative error (MRE) for the continuous choice component.