Submitted to: Columbian Journal of Statistics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/8/2008
Publication Date: 6/1/2009
Citation: Hooks, T., Marx, D.B., Kachman, S.D., Pedersen, J.F. 2009. Revista Columbiana de Estadstica. Columbian Journal of Statistics 32:17-31. Interpretive Summary: A linear mathematical model normally defines the particular experimental design used by scientists. To determine which design is more appropriate, an optimality criterion is developed for models that include random effects (effects whose levels are not predetermined, but are chosen randomly from a large number of possible levels, for example blocks). There are also instances when experiments include treatments that may also be considered random, for example large germplasm screening experiments. This criterion allows for either fixed (the levels of the treatment are predetermined and only those levels are of interest to the researcher) or random treatment effects as well as fixed or random nuisance parameters (effects which are not of interest, but are included in the model, for example blocks and covariates). A general formula is presented for which all previously published optimality criteria are special cases. This research allows scientists to better design and conduct experiments.
Technical Abstract: In the context of linear models, an optimality criterion is developed for models that include random effects. Traditional information-based criteria are premised on all model effects being regarded as fixed. When treatments and/or nuisance parameters are assumed to be random effects, an appropriate optimality criterion can be developed under the same conditions. This paper introduces such a criterion, and this criterion also allows for the inclusion of fixed and/or random nuisance parameters in the model and for the presence of a general covariance structure. Also, a general formula is presented for which all previously published optimality criteria are special cases.