Fishing for pleiotropic QTLs in a polygenic sea

The application of factor analysis to human genetics has the potential to discover the coordinated control of multiple traits by common environment, common polygenes, or a single major gene. Classical factor analysis explains the covariation among the components of a random vector by approximating the vector by a linear transformation of a small number of uncorrelated factors. In the current paper we show how factor analysis dovetails with the classical variance decompositions of biometrical genetics. To explore the relationships between related quantitative variables, and avoid complicated positive definiteness constraints, we employ Cholesky and factor analytic decompositions. We derive an ECM algorithm and a competing quasi-Newton algorithm for estimating parameters by maximum likelihood and propose tactics for selecting initial parameter values. We also show how parameter asymptotic standard errors under these parameterizations propagate to asymptotic standard errors of the underlying variance components. Our genetic analysis program Mendel, which now incorporates the program Fisher, has performed well on a variety of data sets. We illustrate our methods, algorithms, and models on two data sets: a bivariate quantitative genetic example using total finger ridge count data and a multivariate linkage example using insulin resistance data.