Direction of causation between shared and non-shared environmental factors

Determining the direction of causation between two related variables is an interesting and challenging problem. A simple regression model is a frequently used statistical tool to find out whether a dependent variable is significantly predicted by an independent variable; however using a simple regression model cannot determine the direction of causation, because the model fit takes no account of this direction. As an approach to this problem, non-normal structural equation modeling (nnSEM; Shimizu and Kano, J Stat Plan Inference 138:3483-3491, 2008) using higher order moments (third, fourth,...) as well as first and second order moments, can be useful. This method enables us to determine the direction of causation using goodness of fit, even for a simple regression model. In this paper, nnSEM is applied to behavior genetics, in particular, to the genetic simplex model. In this context, nnSEM enables us to determine the direction of causation between C (shared environment) factors and between E (non-shared environment) factors. The efficiency of this method is illustrated by simulation studies and the analysis of real longitudinal twin data.