International Choice Modelling Conference, International Choice Modelling Conference 2017

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Activity start time and duration: Incorporating hybrid utility-regret decision rules in joint models
Nima Golshani, Ramin Shabanpour, Abolfazl Mohammadian, Joshua Auld

Last modified: 28 March 2017



This paper presents a new discrete-continuous joint modeling framework to explore the relationship between decisions on activity start time and activity duration. We aim to test the hypothesis that dependency structure between discrete and continuous variables not only depends on the connector (e.g. copula) but also depends on the assumed decision rules. To that end, we propose a copula-based joint structure which comprises a hybrid RUM-RRM model as the discrete component to estimate activity start time and a log-linear regression model as the continuous component to estimate activity duration.

Activity start time and duration choices are two key components of activity-travel behavior that directly influence the spatial and temporal distribution of travel demand in transportation systems. Traditionally, these two components have been modeled independently by applying a variety of methodological approaches; however, they are closely intertwined because of the shared factors influencing them and the causal effects that they might have on each other. Hence, in order to represent the realistic decision behavior of people toward these variables, it is necessary to consider them as a joint decision process to capture the unrestricted correlation between their unobserved influencing factors.


The data source used in this paper is the UTRACS survey (1), which is a GPS-based prompted recall activity-travel survey that collected detailed information of respondents’ activity planning and scheduling processes in the Chicago region. Based on the distribution of activities start times during the day, the 24-h day period is split into 6 exhaustive and mutually exclusive time choices, namely nighttime, morning peak-hour, morning off-peak, afternoon off-peak, afternoon peak-hour and evening.


As the first component of this joint structure, a hybrid RRM-RUM model (2) is applied to predict the activity start time decision. The main motivation to adopt the hybrid approach in the context of activity start time modeling is that while travelers prefer the alternative which has the highest utility, they might also incorporate some attribute-level comparisons (rather than alternative-level comparisons) in their evaluation (3,4). Activity duration as the second component of this model is treated as a positive continuous variable and is estimated using a log-linear regression model.

The linkage between these two components depends on the type and the extent of the dependency between their stochastic error terms. The disparity in the distributions of the error terms hardens the joining process; from all the available methods, this study applies the copula approach (5) because it facilitates estimation process without imposing restrictive distribution assumptions on the dependency structures between the errors in the discrete and continuous components.

The performance of the proposed joint model is compared with: (i) a copula-based joint model using RUM (for discrete start time) and log-linear regression model (for continues duration) to assess the potential benefits of adopting hybrid approach, and (ii) independent activity start time and activity duration models to investigate the potential advantages of joint modeling approach. The preliminary analysis of estimation results indicates that the proposed model is statistically superior to its counterparts in terms of goodness-of-fit measures and prediction accuracy. Furthermore, among the available copula functions, Frank copula, which has no limitations in parametrizing the complete range of dependence between the two dependent variables, shows the best joint structure.

The proposed modeling approach is capable of improving the activity planning module of the Agent-based Dynamic Activity Planning and Travel Scheduling (ADAPTS) activity-based framework (6) by replacing the current independent activity start time and activity duration sub-models with the joint hybrid model.


1. Auld, J., Williams, C., Mohammadian, A., Nelson, P., 2009. An automated GPS-based prompted recall survey with learning algorithms. Transp. Lett. 1, 59–79. doi:10.3328/TL.2009.01.01.59-79

2. Chorus, C.G., Rose, J.M., Hensher, D.A., 2013. Regret minimization or utility maximization: It depends on the attribute. Environ. Plan. B Plan. Des. 40, 154–169. doi:10.1068/b38092

3. Chorus, C.G., Arentze, T.A., Timmermans, H.J.P., 2008. A Random Regret-Minimization model of travel choice. Transp. Res. Part B Methodol. 42, 1–18. doi:10.1016/j.trb.2007.05.004

4. Shabanpour, R., Golshani, N., Auld, J., Mohammadian, A. (Kouros), 2017. Dynamics of Time-of-Day Choices in the Agent-Based Dynamic Activity Planning and Travel Simulation ( ADAPTS ) Framework, in: Proceedings of 96th Annual Meeting of Transportation Research Board. Washington, D.C.

5. Bhat, C.R., Eluru, N., 2009. A copula-based approach to accommodate residential self-selection effects in travel behavior modeling. Transp. Res. Part B Methodol. 43, 749–765. doi:10.1016/j.trb.2009.02.001

6. Auld, J., Mohammadian, A., 2012. Activity planning processes in the Agent-based Dynamic Activity Planning and Travel Scheduling (ADAPTS) model. Transp. Res. Part A Policy Pract. 46, 1386–1403. doi:10.1016/j.tra.2012.05.017

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