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This study presents a joint discrete-discrete copula-based model that simultaneously estimates the determinants of the choice to use a container terminal and of the choice of dwell time. Moreover, this study proposes the treatment of missing information as a latent variable by specifying a hybrid version of the joint copula-based model. Model estimates show the practicality of enriching a dataset with missing information via a robust econometric solution. Results also illustrate the importance of distance, time-of-day, and industry type on the choice of using CTs and on the decision of the dwell time in both import and export container transport.