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The focus of this thesis is to develop methods to address research challenges related to correlation patterns in discrete choice models. In the context of correlations within alternatives, we extend the novel methodology of the multiple indicator solution (MIS) to deal with endogeneity, and show, through its theoretical derivation, that it is applicable when there are interactions between observed and unobserved variables. In the context of correlations between alternatives, we discuss the importance of using models that can capture them, such as cross nested logit models. We show, through real world examples, that ignoring these correlation patterns can have severe impacts on the obtained demand indicators, and that this can lead to wrong decisions by practitioners. We also address the challenge of using revealed preference data, where the attributes of the non-chosen alternatives are unavailable, and propose a solution based on multiple imputations of their empirical distributions. In the thesis, we also contribute to the existing literature by gaining a better understanding of private motorized modes, in terms of modal split and purchases of new cars. Related to modal split, we use a mode choice case study in low density areas of Switzerland. We find that ignoring the car-loving attitude of individuals leads to incorrect value of time estimates and elasticities, which might have severe implications in the pricing schemes of public transportation, for example. Related to the purchase of new cars, we use data from new car acquisitions in France in 2014, and focus on hybrid and electric vehicles. We find elasticities to price that are in line with the literature, and willingness to pay values in line with the market conditions. We also study the impact of different future policy scenarios and find that the sales of new electric vehicles could reach around 1% as a result of a major technological innovation that would render electric vehicles less expensive. In the last part of the thesis, we propose the discrete-continuous maximum likelihood (DCML) framework, which consists in estimating discrete and continuous parameters simultaneously. This innovative idea, opens the door to new research avenues, where decisions that were usually taken by the analyst can now be data driven. As an illustration, we show that correlations between alternatives can be identified at the estimation level, and do not need to be assumed by the analyst. The DCML framework consists in a mixed integer linear program (MILP) in which the log-likelihood estimator is linearized. This linearization might be useful to estimate parameters of other discrete choice models for which the log-likelihood function is not concave (and therefore global optimality is not insured by the optimization algorithms), since for an MILP, a global optimum is guaranteed. We use a simple mode choice case study for the proof-of-concept of the DCML framework, and use it to investigate its strengths and limitations. The preliminary results presented in the thesis seem very promising. To summarize, we develop methods to deal with correlations in discrete choice models that are relevant to real world problems, and show their applicability by using transportation examples. The contributions are therefore both theoretical and applied. The new methods proposed open the door to new research directions in the discrete choice field.