Discrete choice models are widely used in studies of recreation demand. They have proven valuable when modeling situations where decision makers face large choice sets and site substitution is important. However, when the choice set faced by the individual becomes very large (on the order of hundreds or thousands of alternatives), computational limitations make estimation with the full choice set intractable. Sampling of alternatives in a conditional logit framework is an effective method to limit computational burdens while still producing consistent estimates. This method is allowed by the existence of the independence of irrelevant alternatives (IIA) assumption. More advanced mixed logit models account for unobserved preference heterogeneity and overcome the behavioral limitations of the IIA assumption, however in doing so, prohibit sampling of alternatives. A method is developed where a latent class (finite mixture) model is estimated via the expectations-maximization algorithm and in doing so, allows consistent sampling of alternatives in a mixed logit model. The method is tested and applied to a recreational demand Wisconsin fishing survey.