The concern of this investigation lies with the development and estimation of models explaining children's intellectual variability. Specifically, attention is directed to: (a) the role of parental status attainments and family environments in the transmission of intellectual advantage-disadvantage across generations; (b) the possibility that children's abilities affect the nature of the environment to which they are exposed; and, (c) the dimensionality of family environment as a prerequisite to (a) and (b). Data on children's ability (males only), family environments, and parental status attainments from 100 families were provided by Dr. Harry Mosychuk, Director of Research with the Edmonton, Canada, Public School Board. Data collection for the present investigation involved contacting these families again and administering an intelligence test to both parents where possible. Visits were made with 72 of the original 100 families and usable parent ability data obtained for 69 of these. These comprised complete data for 55 families, and ability data on one parent only in another 14 families. Ability measures were the Wechsler Intelligence Scales for Children and Adults, respectively. The data provided general support for the existence of a triple advantage (disadvantage). It seems that children of intellectually advantaged parents are themselves advantaged in terms of genetic endowment (although this could not be shown in this investigation), the family environment in which they develop, and in the degree of control they have over this environment. (Author/JM)