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The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models
Authors:Chandra R Bhat
Institution:The University of Texas at Austin, Department of Civil, Architectural and Environmental Engineering, 1 University Station, C1761, Austin, TX 78712-0278, United States
Abstract:The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provides a “blueprint” for the MACML estimation for a wide variety of MNP models.
Keywords:Multinomial probit  Mixed models  Composite marginal likelihood  Discrete choice models  Spatial econometrics  Panel data
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