The initial condition problem with complete history dependency in learning models for travel choices

:Learning-based models that capture travelers' day-to-day learning processes in repeated travel choices could benefit from ubiquitous sensors such as smartphones, which provide individual-level longitudinal data to help validate and improve such models. However, the common problem of missing initial observations in longitudinal data collection can lead to inconsistent estimates of perceived value of attributes in question, and thus inconsistent parameter estimates. In this paper, the stated problem is addressed by treating the missing observations as latent variables. The proposed method is implemented in practice as maximum simulated likelihood (MSL) correction with two sampling methods in an instance-based learning model for travel choice, and the finite sample bias and efficiency of the estimators are investigated. Monte Carlo experimentation based on synthetic data shows that both the MSL with random sampling (MSLrs) and MSL with importance sampling (MSLis) are effective in correcting for the endogeneity problem in that the percent error and empirical coverage of the estimators are greatly improved after correction. Compared to the MSLrs method, the MSLis method is superior in both effectiveness and computational efficiency. Furthermore, MSLis passes a formal statistical test for the recovery of the population values up to a scale with a large number of missing observations, while MSLrs systematically fails due to the curse of dimensionality. The impacts of sampling size in MSLrs and number of high probability choice sequences in MSLis on the methods' performances are investigated. The methods are applied to an experimental route-choice dataset to demonstrate their empirical application. Hausman-McFadden tests show that the estimators after correction are statistically equal to the estimators of the full dataset without missing observations, confirming that the proposed methods are practical and effective for addressing the stated problem.