Gengler, N  
Tijani, A  
Wiggans, George 
Submitted to: Journal of Dairy Science
Publication Type: Peer reviewed journal Publication Acceptance Date: 1/7/2000 Publication Date: N/A Citation: Interpretive Summary: The random regression models that have been proposed for statistical analysis of testday yields of dairy animals are computationally demanding, and few computing algorithms have existed that can simplify the calculations. An alternative algorithm for solving random regression test day models was developed to allow use of those models for extremely large data sets such as the U.S. database for dairy records. The algorithm also facilitates the integration of 305day lactation records when no testday records are available and simplifies the development of an index for lactation performance that includes genetic differences in lactation curve (persistency) and genetic effects of parity (maturity rate). In addition to the relative simplicity of the method developed, it allows several other statistical techniques to be applied: 1) a simplification of computations by making use of recent advances in solving algorithms that allow missing values; 2) a transformation to limit the number of regressions and create variables with biological meanings such as total yield, persistency, and maturity rate; 3) more complicated parameter structures than those usually considered in random regression models (for example, additional random effects such as interaction of herd and sire); and 4) accommodation of additional traits such as lactation yields for cows without testday records. The use of this computing algorithm will allow the development of genetic evaluations for dairy animals that are more accurate because they are based on yields recorded on test day and, therefore, better accounting of environmental effects can be made. Technical Abstract: An alternative algorithm for solving random regression testday models was developed to allow use of those models with extremely large data sets such as the US database for dairy records. Equations were solved in 2 iterative steps: 1) estimation or update of regression coefficients based on test day yields for a given lactation and 2) estimation of fixed and random effects on those coefficients. Solutions were shown to be theoretically equivalent to traditional solutions for this class of random regression model. Besides the relative simplicity of the proposed method, it allows several other techniques to be applied in the 2nd step: 1) canonical transformation to simplify computations (uncorrelated regressions) by making use of recent advances in solution algorithms that allow missing values; 2) transformation to limit the number of regressions and to create variates with biological meanings such as lactation yield or persistency; 3) more complicated (co)variance structures than those usually considered in random regression models (e.g., additional random effects such as the interaction of herd and sire); and 4) accommodation of data from 305day records when no test day records are available. In a test computation with 176,495 testday yields for milk, fat, and protein from 22,943 1st lactation Holstein cows, a canonical transformation was applied, and the biological variates of 305day yield and persistency were estimated. After 5 rounds of iteration using a sequential solution scheme for the 2step algorithm, maximum relative differences from previous genetic solutions were <10% of corresponding genetic standard deviations; correlations of genetic regression solutions with solutions from traditional random regression were >.98 for 305day yield and >.99 for persistency.
