Correcting estimates of shared environmental variance for range restriction in adoption studies using a truncated multivariate normal model.

A model is presented for the truncated trivariate normal distribution that arises in behavior genetic adoption designs that focus on sibling similarity to estimate shared environmental effects. The model estimates the point of truncation and shared environmentality. Both moment and maximum likelihood estimates are obtained numerically. Simulations indicate that the model and the numerical procedures perform well when they are most needed, that is, when shared environmentality is large, truncation is extensive or both. When applied to published data from the Texas Adoption Project, results indicate that the point of truncation is at about the 63rd percentile of the family environmental quality distribution (i.e., the bottom 63% is missing) and shared environmentality is about 55%. Implications for current views on the importance of shared environment for child developmental outcomes such as antisocial behavior and IQ are discussed.