On modeling the shared environment

The shared environment is a key component in estimating the heritability of phenotypic traits from familial data. Unlike the genetic components, defined by the kinship parameters, the shared environment stems from complex, latent processes that vary in nature and impact across traits. This concept is intricate, encompassing latent variables and ambiguous interpretations that differ across scientific disciplines. A common approach assumes a 100% correlation for the shared environment among all family members. However, this model has inherent limitations and may fail to capture the dynamics of the conditions that constitute the shared environment within and across traits. This study explores aspects of the shared environment and adopts a more general approach to modeling its correlation structure. We introduce models that represent different dynamic structures, enabling alternative interpretations of shared environmental influence on the transmission of phenotypic traits. A more realistic correlation structure for the shared environment will result in more accurate and precise heritability estimates for a given trait, as well as deeper understanding of its etiology. We demonstrate the performance of our proposed models through simulations and application to data on body mass index and systolic blood pressure from Norwegian health surveys linked to family data.