"Quasi-REML" correlation estimates between production and health traits inthe presence of selection and confounding: A simulation study

Performance of the "quasi REML" method for estimating correlations between a continuous trait and a categorical trait, and between two categorical tra its, was studied with Monte Carlo simulations. Three continuous, correlated traits were simulated for identical populations and three scenarios with e ither no selection, selection for one moderately heritable trait (Trait 1, h(2) = .25), and selection for the same trait plus confounding between sire s and management groups. The "true" environmental correlations between Trai ts 2 (h(2) = .10) and 3 (h(2) = .05) were always of the same absolute size (.20), but further data scenarios were generated by setting the sign of env ironmental correlation to either positive or negative. Observations for Tra its 2 and 3 were then reassigned to binomial categories to simulate health or reproductive traits with incidences of 15 and 5%, respectively. Genetic correlations (r(g12), r(g13), and r(g23)) and environmental correlations (r (e12), r(e13), and r(e23)) were estimated for the underlying continuous sca le (REML) and the visible categorical scales ("quasi-REML") with linear mul tiple-trait sire and animal models. Contrary to theory, practically all "qu asi REML" genetic correlations were underestimated to some extent with the sire and animal models. Selection inflated this negative bias for sire mode l estimates, and the sign of r(e23) noticeably affected rg23 estimates for the animal model,with greater bias and SD for estimates when the "true" r(e 23) was positive. Transformed "quasi-REML" environmental correlations betwe en a continuous and a categorical trait were estimated with good efficiency and little bias, and corresponding correlations between two categorical tr ails were systematically overestimated. Confounding between sires and conte mporary groups negatively affected all correlation estimates on the underly ing and the visible scales, especially for sire model "quasi-REML" estimate s of genetic correlation. Selection, data structure, and the (co)variance s tructure influences how well correlations involving categorical traits are estimated with "quasi-REML" methods.