Development of Integrated Choice and Latent Variable (ICLV) Models Using Matrix-Based Analytic Approximation and Automatic Differentiation Methods on TensorFlow Platform

Abstract

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.