A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP): Modelling framework for episode-level activity participation and time-use analysis

This paper formulates a novel, multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP) to analyze multiple discrete-continuous (MDC) choices at a disaggregate level, including the number of instances different alternatives are chosen and the amount of consumption at each instance of choice. In doing so, the proposed model ensures a logically consistent prediction of multiple choice instances of an alternative. Specifically, the model prevents the prediction of positive allocation to the j^th instance (i.e., a frequency of j episodes) of a good while predicting zero allocation to the (j-1)^th or lower-numbered instances of that alternative. This is achieved by imposing a non-increasing order on the baseline-preference parameters of different choice instances of an alternative. The model results in a conditional likelihood function, where the likelihood arising from the optimality conditions of the utility maximization problem is conditioned on the ordering of baseline marginal utilities. Combining this strategy with independent and identically distributed (IID) Gumbel stochastic terms in the utility functions results in a closed-form likelihood expression that is not much more difficult than that of the MDCEV model. The proposed framework is applied for an empirical analysis of disaggregate, episode-level activity participation and time allocation behavior of non-working adults in Los Angeles, California. The empirical MDCEV-OP model provided better fit and predictive accuracy (in both estimation and validation datasets) for analyzing episode-level activity participation than a disaggregate MDCEV model that does not recognize the logical ordering of episodes. At the same time, the activity-level predictions aggregated from the episode-level predictions of the MDCEV-OP model do not deviate significantly from the predictions of an aggregate MDCEV model. These results highlight the efficacy of the proposed model for analyzing episode-level activity generation and time allocation.