Abstract
In the mixed model, the behavior of linear functions of the fixed and random effects is examined. It is found that inclusion of certain functions of random effects can lead to estimators which are equivalent to those under a fixed effects model and are inconsistent with the inherent structure of the mixed model. Three examples are presented which illustrate the behavior of linear functions of the fixed and random effects. These functions represent the broad, narrow and intermediate inference spaces as introduced by McLean, Sanders and Stroup (1991). Which random effects should be included in the model is discussed. Random effects representing experimental error units are candidates for inclusion in estimable functions. Inclusion of experimental unit effects in estimable functions can lead to misleading results.
Keywords
mixed model, inference space, predictable functions, estimability, covariance structure, fixed effects structure, shrinkage estimators
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Blouin, David C.
(1992).
"WHEN SHOULD RANDOM EFFECTS BE INCLUDED IN ESTIMABLE FUNCTIONS AND WHEN THEY SHOULD NOT?,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1406
WHEN SHOULD RANDOM EFFECTS BE INCLUDED IN ESTIMABLE FUNCTIONS AND WHEN THEY SHOULD NOT?
In the mixed model, the behavior of linear functions of the fixed and random effects is examined. It is found that inclusion of certain functions of random effects can lead to estimators which are equivalent to those under a fixed effects model and are inconsistent with the inherent structure of the mixed model. Three examples are presented which illustrate the behavior of linear functions of the fixed and random effects. These functions represent the broad, narrow and intermediate inference spaces as introduced by McLean, Sanders and Stroup (1991). Which random effects should be included in the model is discussed. Random effects representing experimental error units are candidates for inclusion in estimable functions. Inclusion of experimental unit effects in estimable functions can lead to misleading results.
