The multiple regression methodology proposed by DeFries and Fulker (DF; 1985, 1988) for the analysis of twin data is compared with maximum-likelihood estimation of genetic and environmental parameters from covariance structure. Expectations for the regression coefficients from submodels omitting the h2 and c2 terms are derived. Model comparisons similar to those conducted using maximum-likelihood estimation procedures are illustrated using multiple regression. Submodels of the augmented DF model are shown to yield parameter estimates highly similar to those obtained from the traditional latent variable model. While maximum-likelihood estimation of covariance structure may be the optimal statistical method of estimating genetic and environmental parameters, the model-fitting approach we propose is a useful extension to the highly flexible and conceptually simple DF methodology.