Comparison of two methods to approximate reliabilities of breeding values from test day model

INTRODUCTION Reliability or its square root, accuracy, is often reported by breeding organizations and required by Interbull along with estimated breeding values. In theory, reliability is calculated as a function of genetic variance and elements of the inverse of the coefficient matrix of the mixed model equations that are used to estimate breeding values. In practice, approximation methods are used due to heavy computational load in calculation of the inverse. Jamrozik et al. (2000) presented an approximation method, named JSJ method hereinafter, that accounts both observation and relationship information. Liu et al. (2002), and Tier and Meyer (2004) have presented recently new methods with comparisons to true reliability and the JSJ method. According to Liu, the JSJ method severely overestimated reliabilities of bulls with first lactation test day records only. However, Tier and Meyer (2004) found R-squared values above 97.4% between the true reliability and the JSJ method. The application was for beef cattle where reliabilities for weight of breeding values estimated by a random regression model were calculated. Both Liu et al. (2002) and Tier and Meyer (2004) presented approximation methods that were better than the JSJ method, although both methods were quite different. Aim of this paper is to compare reliabilities by the JSJ method and the approximation method by Misztal and Wiggans (1988) to true reliabilities. Dairy cattle data with test day records and random regression test day model are used.