A flexible multiple discrete-continuous probit (MDCP) model: application to analysis of expenditure patterns of domestic tourists in India

Traditional multiple discrete-continuous (MDC) choice models impose tight linkages between consumers' discrete choice and the continuous consumption decisions due to the use of a single utility parameter driving both the decision to choose and the extent of choice. Recently, Bhat (Trans Res Part B Methodol 110:261-279, 2018) proposed a flexible MDCEV model that employs a utility function with separate parameters to determine the discrete choice and continuous consumption values. However, the flexible MDCEV model assumes an independent and identically distributed (IID) error structure across the discrete and continuous baseline utilities. In this paper, we formulate a flexible non-IID multiple discrete-continuous probit (MDCP) model that employs a multivariate normal stochastic distribution to allow for a more general variance-covariance structure. In doing so, we revisit Bhat (Trans Res Part B: Methodol 109: 238-256, 2018) flexible utility functional form and highlight that the stochastic conditions he used to derive the likelihood function are not always consistent with utility maximization. We offer an alternate interpretation of the model as representing a two-step decision-making process, where the consumers first decide which goods to choose and then decide the extent of allocation to each good. We demonstrate an application of the proposed flexible MDCP model to analyze households' expenditure patterns on their domestic tourism trips in India. Our results indicate that, if the analyst is willing to compromise on the strict utility-maximizing aspect of behavior, while also enriching the behavioral dimension through the relaxation of the tie between the discrete and continuous consumption decisions, the preferred model would be the flexible non-IID MDCP model. On the other hand, if the analyst wants the model to be strictly grounded on utility-maximizing behavior (which may also have benefits by way of welfare measure computations), and is willing to assume a very tight tie between the discrete and continuous consumption decision processes, the preferred model would be the non-IID traditional MDCP model.