that contribute to sibling similarity, whereas unique environment subsumes all environmental mechanisms that promote sibling differences . To express similarity for vertical relationships such as parent and offspring, two major variance components are usually identified: genetic variance and vertical environmental transmission variance. Technically, vertical environmental transmission variance includes all environmental mechanisms, even those outside the home, that correlate with parental antisocial behavior and at the same time influence individual differences in offspring antisocial behavior.
Genetic influence is usually quantified by either of two estimates of heritability. Broad sense heritability is the total genetic variance divided by the phenotypic variance; usually, the only population to permit estimation of broad sense heritability is a large series of identical twins raised apart in random environments. Narrow sense heritability is the additive genetic variance divided by the phenotypic variance. The difference between additive genetic variance and total genetic variance is a complicated function of allele frequencies, allelic action, and interaction among difference genetic loci. Precise heritability estimates are seldom possible with human behavioral phenotypes. Narrow sense estimates are usually reported, with little or no empirical data to justify the validity of their assumptions.
One does not inherit behavior as one inherits eye color. Hence, when the behavioral phenotype is dichotomized (e.g., criminal offender versus nonoffender), behavioral genetic analysis is aimed at liability. Liability is a latent, unobserved variable that is at least ordinally related to risk—the higher an individual's score on the liability scale, the greater is the relative probability that the individual will be an offender. The latent variable of liability is analyzed, not the dichotomized phenotype. Hence, it is appropriate to speak of heritability of liability to criminal offending; it is not technically correct to refer to the heritability of criminal offending.
One important specific application of the concept of liability is the multifactorial model. The central assumption of this model is that a large number of factors (many genes, parenting, schooling, peers, etc.) contribute to liability in roughly equal amounts so that some mathematical transformation will be able to scale liability to resemble a multivariate normal distribution within families. In this case, the tetrachoric correlation is the appropriate statistical index used to quantify familial resemblance for liability.