Page Banner

United States Department of Agriculture

Agricultural Research Service

Title: Iterative Solution of Random Regression Models by Sequential Estimation of Regressions and Effects on Regressions

Authors
item Gengler, N - GLEMBLOUX AGRIC UNIV
item Tijani, A - GEMBLOUX AGRIC UNIV
item Wiggans, George

Submitted to: Interbull Annual Meeting Proceedings
Publication Type: Proceedings
Publication Acceptance Date: March 18, 1999
Publication Date: N/A

Interpretive Summary: The random regression models that have been proposed for statistical analysis of test-day 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 305-day lactation records when no test-day 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 test-day 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 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 integration of data from 305-day records when no test-day records are available and simplifies development of an index for lactation performance that includes genetic differences in lactation curve (persistency) and genetic effects of parity (maturity rate). Equations are solved in two 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 regular solutions for this class of random regression model. In a test computation with 57,034 first-lactation test- day milk yields from 7173 Holstein cows, correlations between solutions from the two solution methods were all >0.98 after only two iterations on the two steps. In addition to the relative simplicity of the proposed method, it allows several other techniques to be applied in the second step: 1) a canonical transformation to simplify computations (uncorrelated regressions) by making use of recent advances in solving algorithms that allow missing values; 2) a transformation to limit the number of regressions and create variates with biological meanings such as total yield, persistency, and maturity rate; 3) more complicated (co)variance structures than those usually considered in random regression models (e.g., additional random effects such as interaction of herd and sire); and 4) accommodation of additional traits for cows without test-day records.

Last Modified: 10/23/2014
Footer Content Back to Top of Page