Prof. Chandra Bhat

Dpt of Civil, Architectural and Environmental Engineering, University of Texas at Austin

April 14, 2010, 11:15, Room GC B3 424 (click here for the map)

Composite Marginal Likelihood Estimation of Mixed Discrete Response Choice Models

<p>The likelihood functions of many discrete ordered and unordered-response choice models entail the evaluation of analytically-intractable integrals. For instance, the use of a mixing mechanism to relax the independent and identically distributed (IID) error term distribution in the multinomial logit model is well documented in the discrete choice literature on unordered multinomial response models. In such an approach, the error term vector is effectively decomposed into an IID component vector and another vector of jointly distributed random coefficients that lends the non-IID structure. It is typical (though not always the case) to consider the joint distribution of the random coefficients to be normally distributed. A particular advantage of the mixing approach is that it can be used for both cross-sectional choice data as well as panel data without any substantial conceptual and coding difference. However, such mixed models also lead to intractable likelihood function expressions. Except in the case when the integration involves only 1-2 dimensions, maximum simulated likelihood (MSL) techniques are usually employed to estimate these models. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and literally infeasible as the number of dimensions of integration rises. Besides, the accuracy of simulation techniques is known to degrade rapidly at medium-to-high dimensions, and the simulation noise increases substantially. This leads to convergence problems during estimation. In addition, such simulation-based approaches become impractical in terms of computation time, or even infeasible, as the number of mixing dimensions grows. </p><p> In this paper, we introduce a maximum composite marginal likelihood (CML) estimation approach for multinomial ordered-response and unordered-response models. The CML approach can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler simulation-free procedure relative to simulation techniques, and has the advantage of reproducibility of the results. This new CML estimation approach for mixed cross-sectional/panel ordered and unordered multinomial models does not have the convergence and stability problems that can plague simulation-based techniques, while at the same time leading to substantial computational efficiency. Simulated datasets are used to empirically compare the performance of the maximum simulated likelihood (MSL) approach and the maximum CML approach introduced here, in terms of ability to recover model parameters, estimator efficiency, and computation time. The presentation will also discuss the CML estimation for a wide variety of cross-sectional and panel discrete choice model structures, some of which, to our knowledge, have not appeared in the econometric literature. </p>