A Modified Purcell Model for the Analysis of Heritability by Socioeconomic Status Interactions

We propose a structural equation model, which we call a modified twin correlation model, for the analysis of pair-level modifiers of biometric analyses continuous phenotypes. The standard model for this type of analysis, which... [ view full abstract ]

We propose a structural equation model, which we call a modified twin correlation model, for the analysis of pair-level modifiers of biometric analyses continuous phenotypes. The standard model for this type of analysis, which was developed by Purcell (2002), expresses biometric modification of ACE variances by modeling paths between standardized ACE variances and a phenotype as quadratic functions of the moderator. Our proposed modifications of this highly successful model are in response to several theoretical and empirical considerations. First, we have commonly observed that phenotypic variance is systematically related to the moderator: in particular, phenotypic variance of cognitive ability is often reduced in high quality environments.  Reductions in phenotypic variance are confounded with changes in ACE components; our model treats changes in phenotypic variance and changes in standardized components separately.  Second, we have recently observed that modification models of ACE components of cognitive ability sometimes lead to estimates outside the permitted parameter space of the classical twin model, especially by predicting DZ twin correlations that are less than half the corresponding MZ correlation.  Our modified model therefore focuses the analysis on changes in the twin correlations themselves, rather than on the ACE components that are derived from them.  Finally, when modeling variances we prefer exponential to quadratic models. Exponential models have the advantage of being monotonic with respect to the modifier, and they are more consistent with similar models for heteroscedasticity in the general analysis of variance literature. Parameters describing the ACE components can be added to the model if they are desired. 

We demonstrate the validity of the model by analyzing simulated data with known parameters.  We then apply it to cognitive ability data from Norwegian conscripts,  longitudinal data from the Louisville Twin Study, and the contemporary TwinLife project in Germany.  Results are compared to those obtained using the classical twin model.

Purcell, S. (2002). Variance components models for gene–environment interaction in twin analysis. Twin research, 5(06), 554-571.