A Comparison of the Maximum Simulated Likelihood and Composite Marginal Likelihood Estimation Approaches in the Context of the Multivariate Ordered Response Model System

This paper compares the performance of the maximum-simulated likelihood (MSL) approach with the composite marginal likelihood (CML) approach in multivariate ordered-response situations. The ability of the two approaches to recover model parameters in simulated data sets is examined, as is the efficiency of estimated parameters and computational cost. Overall, the simulation results demonstrate the ability of the Composite Marginal Likelihood (CML) approach to recover the parameters very well in a 5-6 dimensional ordered-response choice model context. In addition, the CML recovers parameters as well as the MSL estimation approach in the simulation contexts used in the current study, while also doing so at a substantially reduced computational cost. Further, any reduction in the efficiency of the CML approach relative to the MSL approach is in the range of non-existent to small. When taken together with its conceptual and implementation simplicity, the CML approach appears to be a promising approach for the estimation of not only the multivariate ordered-response model considered here, but also for other analytically-intractable econometric models.