The goodness-of-fit of a model to the observed data is summarized by a statistic distributed as chi-square (χ2). By testing the change in model fit (Δχ2) against the change in degrees of freedom (Δdf), we can test whether constraining parameters to zero or constraining them to be equal, significantly worsens the model fit. In this way we can test hypotheses regarding those parameters. Further details of the classical twin design can be found elsewhere (Neale & Cardon, 1992; Posthuma et al. 2003).
