No abstract

As a continuous generalization of the multinomial logit (MNL) model, the continuous logit (CL) model can be used for continuous response variables (e.g., departure time and activity duration). However, the existing CL model requires the calculation of numerical integrals to obtain the choice probabilities; it thus takes a long time to estimate the model parameters, particularly when the sample size is large. In this paper, we formulate the finite-mixture CL (FMCL) model as a new continuous choice model by combining the finite-mixture method and the CL model, in which the continuous distributional function of the finite mixture is embedded in the CL model. As a result, the individual choice probability can be obtained directly by computing the probability density of the continuous distribution function; this avoids calculation of the integral but still obeys the random utility maximization (RUM) principle. Simulation experiments are conducted to demonstrate the capability of the model. In an empirical study, the proposed model is applied for non-commuters’ shopping activity start time using the expectation-maximization (EM) algorithm based on Shanghai Household Travel Survey data. The results show that the FMCL model developed in this paper can greatly reduce the model estimation time (10,048 observations requiring only 3 min) of the CL model, and the model also has a more intuitive interpretation of model coefficients, directly reflecting variable effects on time-of-day choice. These two advantages can greatly enhance the practical value of the proposed modeling method.

In China, a developing country, the car ownership level is much lower than that in developed countries, but transportation policies have been implemented to discourage car ownership and mitigate traffic congestion. However, car ownership (considered as car availability in this paper, meaning that an individual has access to a household private car) may influence travelers’ well-being. To highlight the interrelation between car ownership and travelers’ well-being, this paper develops a probit-based discrete-continuous model to analyze the relationship between car ownership and the duration of commuters’ three major non-work outdoor activities (Act1: shopping and dining; Act2: leisure and entertainment; and Act3: visiting relatives or friends) in Xiaoshan District, Hangzhou, China. Empirical results indicate strong effects of individual and household socio-demographics, built environment attributes, and work-related characteristics on the car ownership decision and the duration of three non-work activities. The analysis shows positive correlations in unobserved factors between the car ownership decision and the duration of Acts1–3, indicating a mutually promotive relationship. Similarly, negative correlations among the duration of Acts1–3 show that non-work activities’ duration is mutually substitutive. These findings will help to better understand commuters’ car ownership decisions and non-work outdoor activity behavior restricted by fixed work schedules in developing countries, which can, in turn, better evaluate the impact of transportation policies (such as car ownership restriction) on travel demand as well as well-being, and provide decision support for the formulation of transportation policies.

This paper developed a mixed multinomial probit (MMNP) model with alternative error specification and random coefficients (for both generic variables and personal attributes) to accommodate flexible covariance structure and taste variation. The MMNP model can be efficiently estimated with analytic approximations of multivariate normal cumulative distribution functions, which avoid defects of simulation-based integration in the mixed multinomial logit (MMNL) model. The integral dimension of the MMNL model increases as random coefficients increase, but it only depends on the number of available alternatives in the MMNP model. Simulation experiments and empirical analysis of Shanghai commuters’ mode choice behavior were undertaken to examine the performance of MMNP models. Both simulation results and empirical results show that MMNP models can well accommodate flexible covariance structures and taste variation reflected through random coefficients being associated with both generic and personal variables. Empirical results indicate that the MMNP model performs better than traditional discrete choice models, such as the multinomial logit, the cross-nested logit, MMNL, and multinomial probit models. Random coefficients of “in-vehicle time of car” and “number of companions” indicate taste heterogeneity and the identifiability of random coefficients associated with both generic and personal attributes. Pairwise positive correlations between car/taxi, bus/metro, and bus/bus and metro are to be expected. However, the positive correlation between the car and metro modes may be unique to the Chinese city, Shanghai, because of the developed metro system. Unequal error variances reflect heterogeneities in unspecified factors in commute modes’ utilities. The MMNP model will offer an alternative efficient way to accommodate taste heterogeneity and flexible error covariance structure in discrete choice models. Compared with the MMNL model, the MMNP model can accommodate more random coefficients without increasing computational complexity.