A simple algebraic demonstration of the validity of DeFries-Fulker analysis in unselected samples with multiple kinship levels

A simple proof is presented supporting the validity of DF analysis in broader settings using scalar algebra to show that parameter estimates ofh2 andc2 are unbiased in unselected settings with multiple (more than two) kinship levels.

Abstract

DeFries and Fulker's (Behav. Genet. 15, 467-473, 1985) regression procedure (DF analysis) to estimate c2 and h2 was originally applied to selected twin data. Since then, DF analysis has been applied more broadly in unselected data and with multiple (nontwin) kinship levels. Theoretical work based on the matrix algebra of variance-covariance matrices has shown that estimates of c2 and h2 are unbiased in selected two-group settings. In this article, a simple proof is presented supporting the validity of DF analysis in broader settings. We use scalar algebra to show that parameter estimates of h2 and c2 are unbiased in unselected settings with multiple (more than two) kinship levels. Caveats are offered, and other DF analysis problems are identified.