Using non-normal SEM to resolve the ACDE model in the classical twin design.

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.

[Scheffé-type paired comparison models for examining correlations between individual preferences for alternatives].

It is difficult to estimate and examine correlations between individual preferences for alternatives using the present Scheffé-type paired comparison models. In this paper, we propose two models that address individual preferences for alternatives. One is a simple model that makes it possible to estimate correlations between individual preferences. The other is an improved model that makes it possible to extract independent components from those correlations. Paired comparison data were collected in a survey about preferences for several new product names. Analysis of this data shows that the proposed models enabled the estimation not only of average preferences for alternatives, but also correlations between individual preferences and loading matrices for independent components. The effectiveness of the proposed methods was confirmed by the interpretations of those estimates.