A New Estimation Approach to Integrate Latent Psychological Constructs in Choice Modeling
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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.