A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelof Civil, Architectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761, Austin TX 78712-1172 Tel: 512-471-4535, Fax: 512-475-8744Email: bhat@maiLuKxas.edu andKing Abdulaziz University, Jeddah 21589, Saudi ArabiaMarisol CastroThe University of Texas at AustinDepartment of Civil, Arch A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelitectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761. Austin TX 78712-1172 Tel: 512-471-4535, Fax: 512-475-8744Email: m.castro@utA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
exas.eduMubassira KhanThe University of Texas at AustinDepartment of Civil, Architectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model 2013ABSTRACTThis paper develops a blueprint (complete with matrix notation) to apply Bhat's (2011) Maximum Approximate Composite Marginal Likelihood (MACML) inference approach for the estimation of cross-sectional as well as panel multiple discrete-continuous probit (MDCP) models. A simulation exer A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelcise is undertaken to evaluate (he ability of the proposed approach to recover parameters from a cross-sectional MDCP model. The results show that theA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
MACML approach does very' well in recovering parameters, as well as appears to accurately capture the curvature of the Hessian of the log-likelihood A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelre) choice among alternative destination locations and the number of trips to each recreational destination location, using data drawn from the 2004-2005 Michigan statewide household travel survey.Keywords: Multiple discrete-continuous model, maximum approximate composite marginal likelihood, recrea A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modeltion choice.1. INTRODUCTIONConsumers often encounter two inter-related decisions dl d choice instance — which dllerndlive(s) to choose for consumptionA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
from d set of available alternatives, and the amount to consume of the chosen alternatives. Classical discrete choice models, such as the multinomialA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelong a set of available and mutually exclusive alternatives. Ihese models assume that die alternatives are perfect substitutes of one another. However, there are several multiple discrete-continuous (MDC) choice situations where consumers choose to consume multiple alternatives dt the same time, alon A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelg with the continuous dimension of the amount of consumption. Examples of such MDC contexts include, but are not limited to, household vehicle type hoA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
ldings and usage, airline fleet mix and usage, individuals’ choice of recreational destination locations and number of trips to the selected locationsA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelion, and stock selection and investment amount.A variety of modeling approaches have been used in the literature to accommodate MDC choice contexts, including (a) the use of a traditional random utility-based (RUM) single discrete choice models by identifying all combinations or bundles of the “elem A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelental" alternatives and treating each bundle as a “composite” alternative, and (b) the use of multivariate probit (logit) methods (see Manchanda et alA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
., 1999, Baltas, 2004. Edwards and Allenby, 2003, and Bhat and Srinivasan, 2005). However, the first approach leads to an explosion in the number of cA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelriate models rather being based on an explicit utility-maximizing framework for multiple discreteness. Besides, it is difficult to incorporate the continuous dimension of consumption quantity in these approaches. Another approach lor MIX', situations that is moled lirmly in the utility maximization A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelframework assumes a non-linear (but increasing and continuously differentiable) utility structure to accommodate decreasing marginal utility (or satiaA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
tion) with increasing consumption. Consumers are assumed Io maximize this utility subject to a budget constraint. The optimal consumption quantities (A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelfunction with lospcct to the consumption quantities. Researchers from many disciplines have used such a KKT approach, and several additively1separable and non-linear utility structures have been proposed in the literature (see Hanemann, 1978, Wales and Woodland. 1983, Kirn et al., 2002, von Haefen a A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelnd Phaneuf, 2005, Phaneuf and Smith, 2005, Bhat, 2005, 2008, and Kuriyama el al., 2011). Of these, the general utility form proposed by Bhat (2008) suA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
bsumes other non-linear utility forms as special cases, and allows a clear interpretation of model parameters. In this and other more restrictive utilA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelor’s that may impact the utility of each alternative (rhe baseline preference is the marginal utility of each alternative at the point of zero consumption of the alternative). Since the baseline preference has to be positive for the overall utility function to be valid, the baseline preference is pa A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelrameterized as the exponential of a systematic component (capturing the effect of exogenous variables) as well as a stochastic error term. As in tradiA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
tional discrete choice models, the most common distributions used for the stochastic error term are the multivariate normal (see Kim el al., 2002) andA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelCP) model structure, while the second to a closed-form MDC generalized extreme value (or MDCGEV) model structure (the closed-form MDC extreme value or MDCEV model structure is a special case of the MDCGEV model). In all these cases, the analyst can further superimpose a mixing random distribution st A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelructure in the baseline preference to accommodate unobserved taste variations across consumers in the sensitivity to relevant exogenous attributes (suA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
ch as differential sensitivity due to unobserved factors to travel time and travel cost in a recreation destination choice model). All studies to dateA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelicity and correlations across alternatives (due to generic unobserved preferences) in the MDCEV and MDCGEV model structures.In the context of a normal mixing error distribution, the use of a GEV kernel structure leads to a mixing of the normal distribution with a GEV kernel (leading to the mixed MDC A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelGEV model or MMDCGEV structure), while the use of a probit kernel leads back to an MDCP model structure (because of the conjugate nature of the multivA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
ariate normal distribution in terms of addition). The domain of integration (to uncondition out the unobserved mixing elements in the consumption probA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelhant) space. In both2https://khothuvien.cori!these structures, the multidimensional integration does not have a closed-form solution, and so it is usually undertaken using simulation techniques. The MMDCGEV structure is typically estimated using quasi-Monte Carlo simulations in combination with a qu A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modelasi-Newton optimization routine in a maximum simulated likelihood (MSL) inference approach (see Bhat, 2001, 2003). The MDCP structure, on the other haA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
nd, is typically estimated using the Geweke-Hajivassiliou-Keane (GHK) simulator or the Genz-Bretz (GB) simulator that accommodate the orthant integratA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice ModelChandra R. Bhat*The University of Texas at AustinDepartment o A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Modeleen the model form of choice in the economics and transportation fields because simulation techniques to evaluate multidimensional integrals are generally easier when the domain is the entire real space rather than orthant spaces. In any case, the consistency, efficiency, and asymptotic normality of A New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model these MSL-based simulation estimators is critically predicated on the condition that the number of simulation draws rises faster than the square rootA New Estimation Approach for the Multiple Discrete-Continuous Probit (MDCP) Choice Model
of the number of individuals in the estimation sample. Unfortunately, as the number of dimensions of integration increases, the computational cost toGọi ngay
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