A comparison of two models for the use of leisure time

In this paper, we make a comparison for two discrete-continuous models for multiple choices in time-use analysis. The random utility-based framework using Kuhn-Tucker conditions for likelihood maximization under non-negativity constraints was firstly proposed by Wales and Woodland (1982) and it has been prevalently applied to many areas in modeling simultaneous multiple choices. Kim et al. (2002) further develop the model by introducing a translated nonlinear utility function to allow for diminishing marginal returns in consumer demand analysis. The sparkling utility form has then been given various discussions and extensions by Kim and other researchers. Among them, Bhat (2005) builds a new model, referred as the multiple discrete-continuous extreme value (MDCEV) model and applies the model to time-use analysis under the transportation context. The most significant difference between the two lies in the error term, which has a log-normal distribution in Kim's model and an extreme value distribution in Bhat's model. In this paper, we raise the important question of how to make a choice between the two models. Using model formulations and simulations, we provide some observations and hints to answer this question. The findings should be useful to practitioners working with multiple discrete choice data.