A statistical filtering procedure to improve the accuracy of estimating population parameters in feed composition databases

Abstract

Accurate estimates of mean nutrient composition of feeds, nutrient variance (i.e., standard deviation), and covariance (i.e., correlation) are needed to develop a more quantitative approach of formulating diets to reduce risk and optimize safety factors. Commercial feed-testing laboratories have large databases of composition values for many feeds, but because of potentially misidentified feeds or poorly defined feed names, these databases are possibly contaminated by incorrect results and could generate inaccurate statistics. The objectives of this research were to (1) design a procedure (also known as a mathematical filter) that generates accurate estimates of the first 2 moments [i.e., the mean and (co)variance] of the nutrient distributions for the largest subpopulation within a feed in the presence of outliers and multiple subpopulations, and (2) use the procedure to generate feed composition tables with accurate means, variances, and correlations. Feed composition data (>1,300,000 samples) were collected from 2 major US commercial laboratories. A combination of a univariate step and 2 multivariate steps (principal components analysis and cluster analysis) were used to filter the data. On average, 13.5% of the total samples of a particular feed population were removed, of which the multivariate steps removed the majority (66% of removed samples). For some feeds, inaccurate identification (e.g., corn gluten feed samples included in the corn gluten meal population) was a primary reason for outliers, whereas for other feeds, subpopulations of a broader population were identified (e.g., immature alfalfa silage within a broad population of alfalfa silage). Application of the procedure did not usually affect the mean concentration of nutrients but greatly reduced the standard deviation and often changed the correlation estimates among nutrients. More accurate estimates of the variation of feeds and how they tend to vary will improve the economic evaluation of feeds and risk assessment of diets, and provide the ability to implement stochastic programming.