Dynamic Latent Plan Models
Charisma Farheen Choudhury, Moshe Ben-Akiva, Maya Abou Zeid
Abstract
In many situations, individual behavior comes as a result of a conscious planning process. People plan ahead several aspects of their lives: their daily travel behavior, their weekly activity participation patterns, their next job or residential location, and so on. They then select actions to execute their plans. While these plans determine the action choice set and guide the actions, the plans themselves are often unobserved (latent). Further, these plans and actions take place in a dynamic environment where individuals’ goals, resulting in plans, as well as external conditions are subject to change. People may consider several alternatives to come up with a plan, but the actions that they end up executing might be different from what they have initially planned. This evolution in plans could be due to several factors. First, situational constraints or contextual changes might lead one to revise his/her plan. For example, an unusual level of congestion might lead a traveler to revise his/her planned time of travel or route. Second, people’s current plans are influenced by their past experiences so that as their history changes, their plans could change as well. For example, the choice of an action with an unfavorable outcome might lead one to abandon the plan that led to this action in future choice situations. Third, people might eventually adapt to conditions in their environment so that they might exhibit inertia in the choice of their plans and actions. An example of the latter effect is the decision to stay in the same residential location for several years due to adaptation to the surrounding environment and housing conditions. Capturing such evolutions of plans and resulting actions is key to understanding behavioral dynamics.
In this paper, we present the methodology to model the dynamics of choices using a two-layer decision hierarchy (choice of a plan and choice of action conditional on the plan) and its dynamics using the framework of a first-order Hidden Markov Model (HMM) (Baum and Petrie 1966, Baum, 1972). In this model framework, the upper level represents the evolution of the plans and lower level denotes the observed actions. The plan at every time period is determined by the plan at the previous time period (first-order Markov model) and the actions taken in the previous time periods (experience). An action at a given time period is determined only by the plan during the same time period. Also, the dynamics in the observed actions are explained by the dynamics in the underlying latent (unobserved) plans (Hidden Markov Model).
The methodology is demonstrated by modeling the dynamics associated with the driving decisions as the drivers enter a freeway. The model is estimated using disaggregate trajectory data extracted from video observations and validated in a microscopic traffic simulator.
In this paper, we present the methodology to model the dynamics of choices using a two-layer decision hierarchy (choice of a plan and choice of action conditional on the plan) and its dynamics using the framework of a first-order Hidden Markov Model (HMM) (Baum and Petrie 1966, Baum, 1972). In this model framework, the upper level represents the evolution of the plans and lower level denotes the observed actions. The plan at every time period is determined by the plan at the previous time period (first-order Markov model) and the actions taken in the previous time periods (experience). An action at a given time period is determined only by the plan during the same time period. Also, the dynamics in the observed actions are explained by the dynamics in the underlying latent (unobserved) plans (Hidden Markov Model).
The methodology is demonstrated by modeling the dynamics associated with the driving decisions as the drivers enter a freeway. The model is estimated using disaggregate trajectory data extracted from video observations and validated in a microscopic traffic simulator.
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