Identifying shared genetic risk factors for multiple measured traits has been of great interest in studying complex disorders. Marlow's (2003) method for detecting shared gene effects on complex traits has been highly influential in the literature of neurodevelopmental disorders as well as other disorders including obesity and asthma. Although its method has been widely applied and has been recommended as potentially powerful, the validity and power of this method have not been examined either theoretically or by simulation. This paper establishes the validity and quantifies and explains the power of the method. We show the method has correct type 1 error rates regardless of the number of traits in the model, and confirm power increases compared to standard univariate methods across different genetic models. We discover the main source of these power gains is correlations among traits induced by a common major gene effect component. We compare the use of the complete pleiotropy model, as assumed by Marlow, to the use of a more general model allowing additional correlation parameters, and find that even when the true model includes those parameters, the complete pleiotropy model is more powerful as long as traits are moderately correlated by a major gene component. We implement this method and a power calculator in software that can assist in designing studies by using pilot data to calculate required sample sizes and choose traits for further linkage studies. We apply the software to data on reading disability in the Russian language.