With the rapid increase of motorization in China, transitions have taken place in regards to traditional private transportation modes. This paper aims to understand four types of vehicle ownership within a household, including automobile, motorcycle, electric bicycle and human-powered bicycle. This study presents a cross-sectional multivariate ordered probit model, with a composite marginal likelihood estimation approach that accommodates the effects of explanatory variables, and capturing the dependence among the propensity to household vehicle ownership. The sample data are obtained from the residents’ household travel survey of Xiaoshan District, Hangzhou, in 2015, which can analyze the significant effects of sociodemographic attributes and built environment attributes. Interestingly, the major findings suggest that: (1) The households with higher income tend to own more automobiles, yet the effect is not obvious with a small value of elasticity, which is similar to developed countries. (2) The household education level, which takes a positive effect on automobile ownership, is a more elastic factor than income. (3) The higher population density contributes to less ownership of automobiles and motorcycles, due to traffic congestions and parking challenges. (4) There is a large substitutive relation between automobile and electric bicycle/motorcycle, and the vehicle ownership of electric bicycle/motorcycle and bicycle are mutually promoted, while motorcycle and electric-bicycle are mutually substituted.

This study further explores the multinomial probit-based integrated choice and latent variable (ICLV) models. The LDLT matrix-based analytic approximation methods, including Mendell and Elston (ME) method, bivariate ME (BME) method, and two-variate bivariate screening (TVBS) method, were adapted to calculate the multivariate cumulative normal distribution (MVNCD) function in the ICLV model because of the better performances in accuracy and computational time. Integrated with the composite marginal likelihood (CML) estimation approach, the ICLV model based on high-dimensional integration can be estimated accurately within a reasonable time. In this study, some three-alternative and four-alternative ICLV models are simulated to examine their abilities to recover model parameters. It is found that the parameter estimates and standard error estimates are acceptable for both models and the computational time is expected to decrease using tensor data structures on the TensorFlow platform. For the four-alternative ICLV models, the TVBS method has the highest level of accuracy. The BME method is also a good alternative to TVBS if computational time is of great concern. The application of the automatic differentiation (AD) technique in the model can free researchers from coding analytical gradients of log-likelihood functions and thereby greatly reduce the workload of researchers.