1Winona State University, Department of Mathematics and Statistics, Winona, United States. Assistant professor. Email: THooks@winona.edu
2University of Nebraska, Department of Statistics, Lincoln, United States. Professor. Email: DMarx1@unl.edu
3University of Nebraska, Department of Statistics, Lincoln, United States. Professor. Email: SKachman1@unl.edu
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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.
Key words: Optimal design, Information matrix, Nuisance parameter, Covariance structure, Mixed model.
En el contexto de modelos lineales, los criterios de optimalidad se cons- truyen para los modelos que incluyen efectos aleatorios. Tradicionalmente los criterios basados en la información asumen que todos los efectos en el modelo se consideran fijos. Cuando los parámetros, tratamientos o molestias son considerados efectos aleatorios, un criterio adecuado de optimalidad se puede desarrollar en las mismas condiciones. En este trabajo se introduce ese criterio, que permite la inclusión en el modelo de parámetros que representan molestias fijas o al azar, además de una estructura general de covarianza. También, se presenta una fórmula general para la cual en todos los casos publicados anteriormente, los criterios de optimalidad son casos especiales.
Palabras clave: diseño óptimo, matrix informativa, parametros molestos, estructura de covarianza, modelo mixto.
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@ARTICLE{RCEv32n1a02,
AUTHOR = {Hooks, Tisha and Marx, David and Kachman, Stephen and Pedersen, Jeffrey},
TITLE = {{Optimality Criteria for Models with Random Effects}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2009},
volume = {32},
number = {1},
pages = {17-31}
}