Development of International Conversion Equations Using Robust Regression Methodology

¹ Department of Dairy Science, University of Wisconsin, Madison 53706
² Department of Industrial Engineering, University of Wisconsin, Madison 53706

International comparisons of dairy sires for production, type, health, and management traits often rely on regression-based conversion equations. Conversion equations are generally calculated using least squares regression, a procedure that is highly susceptible to outlier data points. Outliers can correspond to sires with unusually high or low estimated breeding values in the importing country, but they can also result from errors (e.g., in data collection or data entry) or biases (e.g., from preferential treatment) in the data. Because conversion equations are often calculated using data from a small number of sires, a single outlier can have a large influence on the resulting regression equation. Robust regression procedures can provide protection against outliers and high leverage points by decreasing the weight given to specific data values that are in disagreement with the majority of the sample. In this study, robust regression techniques were used to develop conversion equations for production, type, and health traits with data from the US, Great Britain, Italy, and South Africa. Relative accuracy of the least squares and robust estimators was measured as the standard deviation of converted breeding values across repeated samples of the data; this measure was of the ability of each method to provide consistent estimates in small data sets that might or might not have contained outliers. Performance of the least median squares and least trimmed squares estimators was consistently poorer than least squares. Conversions calculated using M-type estimators were similar to conversions calculated using least squares, perhaps because of a lack of gross errors in the data. Based on this study, it appeared that robust regression estimators did not provide a significant increase in accuracy of international conversion equations relative to least squares regression.

Key Words: international conversions • linear regression • robust methods

Submitted on October 26, 1998
Accepted on May 3, 1999