Data on individuals of immigrant origin are used in the epidemiological approach in comparative development for understanding the determinants of cultural traits, and the effects of genetic factors. A widespread presumption in the literature is that this approach is exposed to attenuation bias. We discuss three dimensions of unobserved heterogeneity that are typically overlooked and which can confound the estimation and counteract the attenuation bias. Focusing on the United States, a key context in this literature, we highlight the heterogeneity among natives reporting different foreign ancestries with respect to the average time elapsed since ancestral migration, their spatial concentration, and their attachment to their ancestral identity. These dimensions of heterogeneity vary smoothly across space, oftentimes mirroring the general trend of the variables of interest in this literature, creating a threat to identification. We propose proxies that can be controlled for by the researcher as a bias-reducing strategy.