Accommodating correlation across days in multiple discrete-continuous models for time use

The MDCEV modelling framework has established itself as the preferred method for modelling time allocation, with data very often collected through travel or activity diaries. However, standard implementations fail to recognise the fact that many of these datasets contain information on multiple days for the same individual, with possible correlations and substitution between days. This paper discusses how the theoretical accommodation of these effects is not straightforward, especially with budget constraints at the day and multi-day level. We rely on additive utility functions where we accommodate correlation between activities at the within-day and between-day level using a mixed MDCEV model, with multivariate random distributions. We illustrate our approach using a well-known time use datasets, confirming our theoretical points and highlighting the benefits of allowing for correlation across days in terms of model fit and behavioural insights.