Variance components/major locus likelihood approximation for quantitative, polychotomous, and multivariate data

Pearson Philos Trans R Soc Lond [A 200:1-66, 1903], Mendell and Elston Biometrics 30:41-57, 1974, and Rice et al. Biometrics 35:451-459, 1979 approximated the likelihood of the multifactorial model on a dichotomous phenotype by a procedure of successive univariate computation and conditioning. Hasstedt Pap: Pedigree Analysis Package, Rev. 3. 1989 and Demenais Am J Hum Genet 49:773-785, 1991 extended the algorithm to include a major locus. Here I extend the algorithm to polychotomous, quantitative, and multivariate phenotypes, add a major locus to the model, and describe and evaluate the accuracy of an approximation of the resulting variance components/major locus model.