Plasma total cholesterol, low-density lipoprotein (LDL), and high-density lipoprotein (HDL) measurements on 402 individuals in 62 randomly selected families from the Columbia Medical Plan population were used to select the "best" model among a series of multifactorial models using the maximum likelihood method described by Lange et al . These models included both genetic and nongenetic components of variance. The most parsimonious model for each trait was selected and examined using a goodness-of-fit statistic designed by Hopper and Mathews  to test the assumptions of this technique. A simple additive genetic model was the most plausible for all three measurements, suggesting a strong role for genetic factors in determining lipid and lipoprotein levels in these data. Goodness-of-fit statistics for these models were examined and showed little evidence of deviation from the assumption of multivariate normality within pedigrees. This approach of selecting the most parsimonious model among a series of competing models and then assessing its goodness-of-fit has many applications in studying familial aggregation of quantitative traits.