Log-linear models for linked loci

A clarification is given of the difference between a multiplicative model (Haber, 1984, Biometrics 40, 189-198) and an additive model (Weir, 1979, Biometrics 35, 235-254) for association between genes at two loci. Although the parametrization of Haber contains both intergametic and intragametic linkage disequilibrium terms, there are problems in separating these terms when the two types of double heterozygote cannot be distinguished. An alternative formulation that contains the sum and product of these terms also contains measures of association between three or four genes at two loci, and a reexamination of data discussed by Haber shows that the inclusion of trigenic disequilibria can significantly improve the fit of the model.