A psychologist reports that authoritative parents tend to have well-behaved children. before we conclude that parenting style influences children's personality, what should we check?

Before we conclude that an authoritative parenting style alone influences children's behavior we need to factor in variables such as a child's genetics, socialization, peers, teachers, school environments, etc, and the influence these variables have on his or her behavior. It is unfounded and erroneous to assume that authoritative parents are the sole factor responsible for well-behaved children.