A typical problem in mapping quantitative trait loci (QTLs) comes from missing QTL genotype. A routine method for parameter estimation involving missing data is the mixture model maximum likelihood method. We developed an alternative QTL mapping method that describes a mixture of several distributions by a single model with a heterogeneous residual variance. The two methods produce similar results, but the heterogeneous residual variance method is computationally much faster than the mixture model approach. In addition, the new method can automatically generate sampling variances of the estimated parameters. We derive the new method in the context of QTL mapping for binary traits in a F2 population. Using the heterogeneous residual variance model, we identified a QTL on chromosome IV that controls Marek's disease susceptibility in chickens. The QTL alone explains 7.2% of the total disease variation.