Bayesian Inference of Interaction Effects in Item-Level Hierarchical Twin Data

Abstract

Behavior geneticists are interested in the relative importance of genetic and environmental influences in the origins of individual differences in a trait (phenotype). Considerable effort has been devoted to analyses including interactions between these different sources, such as gene-environment interactions. To measure the phenotype, usually, a questionnaire is presented to monozygotic (MZ) and dizygotic (DZ) twins and the resulting sum-scores are used as proxy measures for the phenotype in the genetic model. However, earlier research has shown that using sum-scores can lead to the spurious finding of interactions and, instead, an approach based on raw item data should be adopted. This can be done by simultaneously estimating the genetic twin model and an item response theory (IRT) measurement model. Due to the hierarchical nature of twin data, this is difficult to implement in the frequentist framework. As an alternative, we can adopt the Bayesian framework and use off-the-shelf MCMC methods. This chapter contains an overview of this methodology, including different parametrizations of interaction terms. To illustrate the methodology, the depression scores of 364 MZ twin pairs and 585 DZ twin pairs are analyzed to investigate if depression is etiologically different in older (>60 years) twins.