It is plausible that distance, quality, and hospital charges all influence which hospital patients (and their referring physicians) choose. Several researchers have estimated conditional choice models that explicitly incorporate the existence of competing hospitals. To be useful for hospital administrators, health planners and insurers, however, estimates must be made for specific types of patients and include entire market areas. Data sets meeting these requirements have many combinations of hospitals and locations with zero patients. This raises computational difficulties with the linear estimation techniques used previously. In this paper, we use data on patients undergoing cardiac catheterization in several market areas to assess alternative estimation techniques. First, we estimate the conditional choice model with the two techniques used previously to transform the non-linear choice model. These involve using as a reference (1) a single hospital, or (2) the geometric mean of all the hospitals in the market. When there are many zeros, these techniques require extensive adjustments to the data which may lead to biased estimators. We then compare these results with maximum likelihood estimates. The latter results are substantively and significantly different from those using traditional techniques. More importantly, the linear estimates are much more sensitive to the proportion of zeros. We thus conclude that maximum likelihood estimates are preferable when there are many zeros.