Estimation of Variance and Covariance Components

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Abstract
Three methods are descr. for estimating variance and covariance components in mixed models (random and fixed effects) in which the data are non-orthogonal. Such situations arise most frequently in expts. designed to estimate genetic variances where a time component introduces fixed effects,and differences, for example, in litter sizes produce non-orthogonality. Method I ignores non-orthogonality and equates computed mean squares to their expectations. This leads to biased estimates if some effects are fixed or correlated. Method II "corrects" the mean squares for the fixed effects and equates the resulting values to expectations. Only correlation will introduce a bias here. Method III is the exact solution of the least squares equations, a tedious process for non-orthogonal data. Its use is feasible only when non-orthogonality is planned, as for example in an incomplete block expt.

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