An Expectation-Maximization Algorithm to Estimate the Integrated Choice and Latent Variable Model

As computing capability has grown dramatically, the transport choice model has rigorously included latent variables. However, integrated latent and choice variable (ICLV) models are hampered by a serious problem that is caused by the maximum simulated likelihood method. The method cannot properly reproduce the true coefficients, which is a problem that is often referred to as a lack of empirical identification. In particular, the problem is exacerbated particularly when an ICLV model is calibrated based on cross‐sectional data. An expectation‐maximization (EM) algorithm has been successfully employed to calibrate a random coefficient choice model, but it has never been applied to the calibration of an ICLV model. In this study, an EM algorithm was adapted to calibrate an ICLV model, and it successfully reproduced the true coefficients in the model. The main contribution of adopting an EM algorithm was to simplify the calibration procedure by decomposing the procedure into three well known econometric problems: a weighted linear regression, a weighted discrete choice problem, and a weighted ordinal choice problem. Simulation experiments also confirmed that an EM algorithm is a stable method for averting the problem of lack of empirical identification.