Increasing Precision or Reducing Expense in Regression Experiments by Using Information from a Concomitant Variable

Abstract

A method to improve precision of estimates or reduce expense without loss of precision relative to direct regression is presented. The method is potentially useful when observations on the dependent variable are more expensive than observations on some related concomitant variable. It consists of collecting the expensive observations on the dependent variable for a subset of the experimental units only, while observing the concomitant variable for all units. Typically the subset will be considerably smaller than the entire sample. An important application is the prediction of the lean meat percentage of a pig carcass from objective carcass measurements. The actual lean meat content of a carcass may be determined by complete dissection, which is very expensive, or alternatively, by a less accurate but cheaper incomplete dissection method. A practical example will be discussed where carcass dissections were carried out in The Netherlands, mainly according to the standard method of the Research Institute for Animal Production Schoonoord (incomplete dissection) and partly by the EC-reference method (complete dissection). A prediction formula for the EC-reference lean meat percentage with carcass measurements obtained with the Hennessy Grading Probe as explanatory variables was constructed by linear regression. The information contained in both the complete and incomplete dissections was used to estimate the regression coefficients and residual variance.