The statistical model for the analysis of twin-family data of Williams and Iyer is examined. The model uses a large number of redundant parameters. It does not lead to quantitative predictions for new relationships. It allows for epistasis but not dominance. It makes assumptions about assortative mating which are inconsistent with any biologically plausible mechanism. It assumes that the environmental correlation between parent and offspring is due to the direct effect of the parental genotypes, not phenotypes, on offspring environment. Other models which avoid these problems are more appropriate for the analysis of extended twin-family data.