Imputing missing trip purposes in smartphone-based travel surveys using Bayesian posterior analysis

Smartphone-based travel surveys are gaining popularity for collecting trip diaries, where much of the travel information (i.e. travel modes, purposes) is inferred and the participants are asked to verify or correct the inferred information. While this allows researchers to collect high-resolution mobility data from larger samples with minimal user input, in many cases, the participants do not verify all of their trips, resulting in a considerable amount of untagged or missing data. To better impute missing trip purposes for individuals with partially tagged trips, we propose using posterior analysis within a mixed multinomial logit (MMNL) modelling framework. Posterior analysis leverages Bayes' rule to predict missing data by conditioning on the individual's previously observed trip purposes. Using a two-week-long dataset collected in the UK, we find this approach provides a better predictive performance on a testing dataset in terms of predicting market shares and the probability of choosing the correct alternative when compared to not using posteriors in MMNL or using a standard multinomial logit model. We further investigate the impact of using the imputed trip purposes in a mode choice model. Our findings demonstrate that imputing trip purposes using MMNL with posterior analysis achieves a better model fit and values of travel time compared to mode choice models that use (a) other methods of imputing trip purposes, and (b) ignore trip purpose as an explanatory variable. This highlights the advantages of our imputation strategy, as well as the benefits of incorporating imputed trip purpose data in developing travel behaviour models.