Original Research

Behavior Genetics

, Volume 41, Issue 2, pp 329-339

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Using Non-Normal SEM to Resolve the ACDE Model in the Classical Twin Design

  • Koken OzakiAffiliated withResearch Organization of Information and Systems, The Institute of Statistical Mathematics Email author 
  • , Hideki ToyodaAffiliated withWaseda University
  • , Norikazu IwamaAffiliated withWaseda UniversityJapan Society for the Promotion of Science
  • , Saori KuboAffiliated withWaseda University
  • , Juko AndoAffiliated withKeio University


One of the biggest problems in classical twin studies is that it cannot estimate additive genetic (A), non-additive genetic (D), shared environmental (C), and non-shared environmental (E) effects, simultaneously, because the model, referred to as the ACDE model, has negative degrees of freedom when using Structural Equation Modeling (SEM). Therefore, instead of the ACDE model, the ACE model or the ADE model is actually used. However, using the ACE or ADE models almost always leads to biased estimates. In the present paper, the univariate ACDE model is developed using non-normal Structural Equation Modeling (nnSEM). In SEM, (1st- and) 2nd-order moments, namely, (means and) covariances are used as information. However, nnSEM uses higher-order moments as well as (1st- and) 2nd-order moments. nnSEM has a number of advantages over SEM. One of which is that nnSEM can specify models that cannot be specified using SEM because of the negative degrees of freedom. Simulation studies have shown that the proposed method can decrease the biases. There are other factors that have possible effects on phenotypes, such as higher-order epistasis. Since the proposed method cannot estimate these effects, further research on developing a more exhaustive model is needed.


Biases in estimators Higher-order moments Model identification nnSEM Non-normality Univariate ACDE model