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The proposed framework uses a multinomial probit kernel for the event\u2010type choice model and introduces unobserved heterogeneity in both the count and discrete\u2010choice components. Additionally, this paper establishes important new results regarding the distribution of the maximum of multivariate normally distributed variables, which form the basis to embed the multinomial probit model within a joint modeling system for multivariate count data. The model is applied to analyzing out\u2010of\u2010home non\u2010work episodes pursued by workers, using data from the National Household Travel Survey. 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