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Biased Estimates of Heritability Resulting from Incorrect Methods of Estimating Components of Variance

Department of Experimental Statistics, Louisiana State University, Baton Rouge

ABSTRACT

In any type of statistical analysis the model which underlies the data should include all effects present. VanVleck and Henderson (2) have listed the steps to follow: a) Write the supposed underlying model; b) take expectations of the functions of the data used in estimation, considering the effect of any necessary simplifying assumptions; c) determine what has been estimated and, if possible, equate these expectations to the calculated values. Solve for the unknown quantities.

It will be assumed that a trait such as milk yield in dairy cattle can be expressed by the following model:

Y^ijk1 = µ + Sⁱ + D^ij + C^ijk + E^ijkl

where Y^ijk1 = the l^th record on the k^th cow from the j^th dam and i^th sire

µ = an effect common to all observations

S_i = the effect of the i^th sire

D_ij = the effect of the j^th dam bred to the i^th sire

C_ijk = the effect of the k^th cow from the i^th sire and the j^th dam

E_ijk1 = an effect peculiar to the l^th record of the k^th cow from the j^th dam and i^th sire.