Browsing by Subject "multinomial probit"

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Introducing Non-Normality of Latent Psychological Constructs in Choice Modeling with an Application to Bicyclist Route Choice
(2014-07-25) Bhat, Chandra R.; Dubey, Subodh K.; Nagel, Kai
In the current paper, we propose the use of a multivariate skew-normal (MSN) distribution function for the latent psychological constructs within the context of an integrated choice and latent variable (ICLV) model system. The multivariate skew-normal (MSN) distribution that we use is tractable, parsimonious in parameters that regulate the distribution and its skewness, and includes the normal distribution as a special interior point case (this allows for testing with the traditional ICLV model). Our procedure to accommodate non-normality in the psychological constructs exploits the latent factor structure of the ICLV model, and is a flexible, yet very efficient approach (through dimension-reduction) to accommodate a multivariate non-normal structure across all indicator and outcome variables in a multivari8ate system through the specification of a much lower-dimensional multivariate skew-normal distribution for the structural errors. Taste variations (i.e., heterogeneity in sensitivity to response variables) can also be introduced efficiently and in a non-normal fashion through interactions of explanatory variables with the latent variables. The resulting skew normal ICLV (SN-ICLV) model we develop is suitable for estimation using Bhat’s (2011) maximum approximate composite marginal likelihood (MACML) inference approach. The proposed SN-ICLV model is applied to model bicyclists’ route choice behavior using a web-based survey of Texas bicyclists. The results reveal evidence for non-normality in the latent constructs. From a substantive point of view, the results suggest that the most unattractive features of a bicycle route are long travel times (for commuters), heavy motorized traffic volume, absence of a continuous bicycle facility, and high parking occupancy rates and long lengths of parking zones along the route.
The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models
(Elsevier, 2011) Bhat, Chandra R.
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 provide s a “blueprint” for the MACML estimation for a wide variety of MNP models.
A New Approach to Specify and Estimate Non-Normally Mixed Multinomial Probit Models
(Elsevier, 2012) Bhat, Chandra R.; Sidharthan, Raghuprasad
The current paper proposes the use of the multivariate skew-normal distribution function to accommodate non-normal mixing in cross-sectional and panel multinomial probit (MNP) models. The combination of skew-normal mixing and the MNP kernel lends itself nicely to estimation using Bhat’s (2011) maximum approximate composite marginal likelihood (MACML) approach. Simulation results for the cross-sectional case show that our proposed approach does well in recovering the underlying parameters, and also highlights the pitfalls of ignoring non-normality of the continuous mixing distribution when such non-normality is present. At the same time, the proposed model obviates the need to assume a pre-specified parametric distribution for the mixing, and allows the estimation of a very flexible, but still parsimonious, mixing distribution form.
A New Econometric Approach to Multivariate Count Data Modeling
(2013-01) Bhat, Chandra R.; Paleti, Rajesh; Castro, Marisol
In the current paper, we propose a modeling framework to explicitly link a count data model with an event type multinomial choice model. The proposed framework uses a multinomial probit kernel for the event type choice model and introduces unobserved heterogeneity in both the count and discrete choice components. Additionally, this paper establishes several new results regarding the distribution of the maximum of multivariate normally distributed variables, which form the basis to embed the multinomial probit model within a joint modeling system for multivariate count data. The model is applied for analyzing out-of-home non-work episodes pursued by workers, using data from the National Household Travel Survey.
A New Estimation Approach to Integrate Latent Psychological Constructs in Choice Modeling
(2013-07) Bhat, Chandra R.; Dubey, Subodh K.
In the current paper, we propose a new multinomial probit-based model formulation for integrated choice and latent variable (ICLV) models, which, as we show in the paper, has several important advantages relative to the traditional logit kernel-based ICLV formulation. Combining this MNP-based ICLV model formulation with Bhat’s maximum approximate composite marginal likelihood (MACML) inference approach resolves the specification and estimation challenges that are typically encountered with the traditional ICLV formulation estimated using simulation approaches. Our proposed approach can provide very substantial computational time advantages, because the dimensionality of integration in the log-likelihood function is independent of the number of latent variables. Further, our proposed approach easily accommodates ordinal indicators for the latent variables, as well as combinations of ordinal and continuous response indicators. The approach can be extended in a relatively straightforward fashion to also include nominal indicator variables. A simulation exercise in the virtual context of travel mode choice shows that the MACML inference approach is very effective at recovering parameters. The time for convergence is of the order of 30 minutes to 80 minutes for sample sizes ranging from 500 observations to 2000 observations, in contrast to much longer times for convergence experienced in typical ICLV model estimations.