Parameter Estimation in Multivariate Logit models with Many Binary Choices

Abstract

The multivariate choice problem with correlated binary choices is investigated. The Multivariate Logit [MVL] model is a convenient model to describe such choices as it provides a closed-form likelihood function. The disadvantage of the MVL model is that the computation time required for the calculation of choice probabilities increases exponentially with the number of binary choices under consideration. This makes maximum likelihood-based estimation infeasible in case there are many binary choices. To solve this issue we propose three novel estimation methods which are much easier to obtain, show little loss in efficiency and still perform similar to the standard Maximum Likelihood approach in terms of small sample bias. These three methods are based on (i) stratified importance sampling, (ii) composite conditional likelihood, and (iii) generalized method of moments. Monte Carlo results show that the gain in computation time in the Composite Conditional Likelihood estimation approach is large and convincingly outweighs the limited loss in efficiency. This estimation approach makes it feasible to straightforwardly apply the MVL model in practical cases where the number of studied binary choices is large.