A Probit-based Joint Discrete-continuous Model System: Analyzing the Relationship between Timing and Duration of Maintenance Activities

This paper presents a probit-based discrete-continuous modeling methodology to analyze relationships between discrete and continuous choice dimensions often encountered in activity-travel behaviour research. The probit-based approach allows one to adopt a flexible multivariate normally distributed error covariance structure that overcomes the limitations associated with other discrete-continuous modeling methods that rely on two-step limited information techniques or restrictive distributional transformations. The paper presents the detailed formulation of the modeling methodology and demonstrates its applicability through an analysis of the relationship between the timing (scheduling) and duration of household maintenance activities that include shopping and personal business activity episodes. A new non-nested test developed by the authors is used to compare alternative model structures and identify the nature of the joint relationship between the timing and duration of maintenance activities. Models are estimated separately for commuter and non-commuter samples drawn from the 2000 Switzerland Microcensus of Travel. Model estimation results show that error covariances are significant for commuter models of maintenance activity timing and duration. Non-nested model comparisons indicate that the model specification where time-of-day choice affects activity duration offers a statistically superior goodness-of-fit in comparison to the model specification where activity duration affects time-of-day choice. These findings lend credence to the notion that the joint relationship between timing and duration adopted in activity-based model systems should be one in which the activity schedule or agenda drives activity time allocation or duration.