A Note on Jöreskog’s ACDE Twin Model: A Solution, Not the Solution

The classical twin design is used to decompose phenotypic variance into genetic and environmental variance components. In practice, for reasons of identification, either an ADE or an ACE twin model is fitted, i.e., models with three variance components. Jöreskog proposed to use the Moore-Penrose inverse to estimate the four genetic and environmental variance components in the ACDE twin model. We demonstrate that the variance components thus obtained do not equal the true genetic and environmental variance components. Given a ACDE model, resorting to an ADE or ACE model or applying Jöreskog’s method will not produce correct results. However, it is possible that Jöreskog’s method will produce a better approximation to the true variance components under certain configurations of A, D, C, and E variance components.