Mixed model in the context of "Charles Roy Henderson"

Play Trivia Questions online!

or

Skip to study material about Mixed model in the context of "Charles Roy Henderson"

Ad spacer

>>>PUT SHARE BUTTONS HERE<<<

👉 Mixed model in the context of Charles Roy Henderson

Charles Roy Henderson ((1911-04-01)April 1, 1911 – (1989-03-14)March 14, 1989) was an American statistician and a pioneer in animal breeding — the application of quantitative methods for the genetic evaluation of domestic livestock. This is critically important because it allows farmers and geneticists to predict whether a crop or animal will have a desired trait, and to what extent the trait will be expressed. He developed mixed model equations to obtain best linear unbiased predictions of breeding values and, in general, any random effect. He invented three methods for the estimation of variance components in unbalanced settings of mixed models, and invented a method for constructing the inverse of Wright's numerator relationship matrix based on a simple list of pedigree information. He, with his Ph.D. student Shayle R. Searle, greatly extended the use of matrix notation in statistics. His methods are widely used by the domestic livestock industry throughout the world and are a cornerstone of linear model theory.

Henderson obtained his B.Sc., M.Sc.(nutrition) and Ph.D.(breeding) degrees at Iowa State University, where he was a student of Professor L. N. Hazel. Henderson joined the faculty of the Department of Animal Science at Cornell University in 1948 and headed the Animal Breeding division for nearly 30 years until he retired in 1976. After retiring from Cornell, he was a visiting professor at the University of Guelph and University of Illinois until his death. He completed his book in 1984 at the University of Guelph.

↓ Explore More Topics
In this Dossier

Mixed model in the context of Best linear unbiased prediction

In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" (or "prediction") seems not to have been used until 1962. "Best linear unbiased predictions" (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) (see Gauss–Markov theorem) of fixed effects. The distinction arises because it is conventional to talk about estimating fixed effects but about predicting random effects, but the two terms are otherwise equivalent. (This is a bit strange since the random effects have already been "realized"; they already exist. The use of the term "prediction" may be because in the field of animal breeding in which Henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring (Robinson page 28)). However, the equations for the "fixed" effects and for the random effects are different.

In practice, it is often the case that the parameters associated with the random effect(s) term(s) are unknown; these parameters are the variances of the random effects and residuals. Typically the parameters are estimated and plugged into the predictor, leading to the empirical best linear unbiased predictor (EBLUP). Notice that by simply plugging in the estimated parameter into the predictor, additional variability is unaccounted for, leading to overly optimistic prediction variances for the EBLUP.

↑ Return to Menu