Fitted several biometrical genetic models to the National Merit Scholarship Qualifying Test (NMSQT) California Psychological Inventory (CPI) data. These models include parameters for an additive genetic effect (D-sub(R)), an among-families environmental effect (E-sub-2), and a within-families environmental effect (E-sub-1). It is shown that the CPI scales do not fit the same model; the heritabilities, calculated from the parameter estimates of the model fit for each scale, are not the same. Most scales fit a model with parameters for the D-sub(R ) and E-sub-1 environmental effects, although the Capacity for Status and Intellectual Efficiency scales require E-sub-2 to achieve fit, and the Responsibility, Achievement via Independence, and Femininity scales require separate-sex E-sub-1 and E-sub-2 parameters. Similar parameter estimates were found for the models' fit to the full sample and the 2 random subsamples, and the heritabilities calculated from these estimates were quite consistent. The applicability of various models for the study of monozygotic and dizygotic twin traits is discussed.