We determine the power of variance component linkage analysis in the case of discrete, dichotomous traits analyzed under a classical liability threshold model. For simplicity we consider randomly ascertained samples and an additive model of variation incorporating a qtl, residual additive genetic factors, and individual-specific random environmental effects. We derive an expression for the power of variance component linkage analysis in arbitrary relative pairs, and compare the power of discrete and quantitative trait linkage analysis in the specific case of sibpairs. The predicted sample sizes required in linkage analysis of sibpairs are confirmed by analysis of simulated data. Unlike the affected-sibpair method, the power of discrete trait variance component analysis increases with trait prevalence. The relative efficiency of a discrete trait for linkage analysis increases with population trait prevalence, but does not exceed about 40% and is typically much less.