Abstract
For more than a decade, it has been known that many common behavior genetics models for a single phenotype can be estimated as multilevel models (e.g., van den Oord 2001; Guo and Wang 2002; McArdle and Prescott 2005; Rabe-Hesketh et al. 2007). This paper extends the current knowledge to (1) multiple phenotypes such that the method is completely general to the variance structure hypothesized, and (2) both higher and lower levels of nesting. The multi-phenotype method also allows extended relationships to be considered (see also, Bard et al. 2012; Hadfield and Nakagawa 2010). The extended relationship model can then be continuously expanded to merge with the case typically seen in the molecular genetics analyses of unrelated individuals (e.g., Yang et al. 2011). We use the multilevel form of behavior genetics models to fit a multivariate three level model that allows for (1) child level variation from unique environments and additive genetics, (2) family level variation from additive genetics and common environments, and (3) neighborhood level variation from broader geographic contexts. Finally, we provide R (R Development Core Team 2020) functions and code for multilevel specification of several common behavior genetics models using OpenMx (Neale et al. 2016).
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Notes
The value of “better” was often defined by white, European, male standards at the time.
The correlation coefficient used in this setting differs slightly from the Pearson product-moment correlation, but broadly speaking is still a correlation.
Of course, MLM accounts for many kinds of nesting regardless of the setting: time points within persons, regions within countries, teeth within jaws, and so on. We use the classical example of students nested within classrooms merely as an evocative illustration near the centroid of MLM.
For example, van den Oord (2001, p. 397) estimated a 4-level MLM where the level 3 estimated variance had to be interpreted as \(\sigma^2_3 = a^2/8 + c^2\) where \(a^2\) and \(c^2\) were the additive genetic and common environmental variances, respectively.
The Cholesky decomposition constrains the covariance matrix to be symmetric and positive semi-definite, but places no further limit on its structure.
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Helper function for Cholesky paths
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Hunter, M.D. Multilevel Modeling in Classical Twin and Modern Molecular Behavior Genetics. Behav Genet 51, 301–318 (2021). https://doi.org/10.1007/s10519-021-10045-z
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DOI: https://doi.org/10.1007/s10519-021-10045-z