Working Papers

Modeling and Forecasting the Evolution of Preferences over Time: A Hidden Markov Model of Travel Behavior

El Zarwi, Vij and Walker

Abstract: Preferences, as denoted by taste parameters and consideration sets, may evolve over time in response tochanges in demographic and situational variables, psychological, sociological and biological constructs,and available alternatives and their attributes. However, existing representations typically overlook theinfluence of past experiences on present preferences. This study develops a hidden Markov model with adiscrete choice kernel for modeling and forecasting the evolution of individual preferences over time. Thehidden states denote different latent preferences, and the evolutionary path is hypothesized to be a firstorderMarkov process such that an individual’s preferences during a particular time period are dependenton their preferences during the previous time period. The framework is applied to study the evolution ofmodal preferences, or modality styles, over time, in response to a major change in the publictransportation system. Empirical findings reveal two complementary narratives. At the population level,there are significant shifts in the distribution of individuals across modality styles before and after thechange in the system, but the distribution is relatively stable in the periods after the change. At theindividual level, greater instability in preferences is observed, much after the change, despite accountingfor the inertial influence of past preferences. A comparison between the proposed dynamic frameworkand comparable static frameworks reveals corresponding differences in aggregate forecasts for differentpolicy scenarios, demonstrating the value of the proposed framework for both individual and populationlevelpolicy analysis.

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Moving past random taste heterogeneity in discrete choice models: Multivariate nonparametric finite mixture distributions

Vij, A.

Abstract: This study develops an expectation maximization algorithm for the estimation of mixed logit models withmultivariate nonparametric finite mixture distributions, where the support of the distribution is specified as ahigh-dimensional grid over the coefficient space, with equal or unequal intervals between successive pointsalong the same dimension, and the location of each point on the grid and the probability mass at that point aremodel parameters that need to be estimated. The framework does not require the analyst to specify the shape ofthe distribution prior to model estimation, but can approximate any multivariate probability distributionfunction to any arbitrary degree of accuracy. The estimation algorithm can feasibly estimate behaviorallymeaningful models with multivariate distributions over high-dimensional coefficient spaces with hundreds ofmass points. Multiple synthetic datasets and a case study on travel mode choice behavior are used todemonstrate the value of the model framework and estimation algorithm. The literature on discrete choicemodels is replete with ways to incorporate random taste heterogeneity. By proposing a fully flexible andcomputationally tractable approach, this study aims to bring to a close the question of how best to includerandom taste heterogeneity within existing representations of decision-making.

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