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We discuss the development of predictive choice models that go beyond the random utility model in its narrowest formulation. Such approaches incorporate several elements of cognitive process that have been identified as important to the choice process, including strong dependence on history and context, perception formation, and latent constraints. A flexible and practical hybrid choice model is presented that integrates many types of discrete choice modeling methods, draws on different types of data, and allows for flexible disturbances and explicit modeling of latent psychological explanatory variables, heterogeneity, and latent segmentation. Both progress and challenges related to the development of the hybrid choice model are presented.