Modification of negative eigenvalues to create positive definite matrices and approximation of standard errors of correlation estimates.

Abstract

Current methods of estimating covariance matrices (REML and Bayesian methods) for multiple trait methods, provide estimated matrices that are always positive definite (pd), if the starting matrices are pd. Starting matrices are often derived from the literature, from different sources of information and may not necessarily be pd (i.e. all eigenvalues are positive). An easy approach is to use a diagonal starting matrix, in which all diagonals are positive. Alternatively, one may use a phenotypic covariance matrix reduced by some constant, or a procedure where o ff-diagonals are gradually reduced until the matrix is pd. Whichever approach is used, the starting matrix needs to be checked to ensure that it is pd.