This paper investigates the use of an elicited consideration set in a mathematical model of choice and consideration set formation. It proposes an econometric formulation by allowing unrestricted correlations among alternatives in the consideration set formation and a flexible substitution pattern in the choice model. Data from a stated preference (SP) survey is used where the SP choice tasks were followed by an elicitation of the consideration set while responding to the SP experiments. As opposed to the latent choice set formation approach, the elicited consideration set reduces the computational burden for model estimation. Empirical models reveal the benefit of modeling choice in conjunction with consideration of the set formation. It is evident that overlooking the probabilistic consideration set results in the over-estimation of the effects of key choice attributes, for example, travel time and generalized cost. Estimated correlations among alternatives in the consideration set formation revealed rich patterns of complementary and supplementary relationships among the alternatives that would not be possible to observe otherwise. However, it is also clear that the relationship in the consideration set formation may not be fully translated into substitution patterns in the choice model; that is explained by the error-component mixed logit model.