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