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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.1 Bogotá Jan./June 2022 Epub Jan 17, 2023
https://doi.org/10.15446/rce.v45n1.93196
Artículos originales de investigación
Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors
Modelos mixtos para estudios pretest-posttest en poblaciones finitas con error en la respuesta
1 DEPARTAMENTO DE ESTADÍSTICA, FACULTAD DE CIENCIAS, UNIVERSIDAD NACIONAL DE COLOMBIA, BOGOTÁ, COLOMBIA
2 DEPARTAMENTO DE ESTATÍSTICA, INSTITUTO DE MATEMÁTICA E ESTATÍSTICA, UNIVERSIDADE DE SÃO PAULO, SÃO PAULO, BRAZIL
3 DEPARTMENT OF PUBLIC HEALTH, UNIVERSITY OF MASSACHUSETTS, AMHERST, USA
We consider a finite population mixed model that accommodates response errors and show how to obtain optimal estimators of the finite population parameters in a pretest-posttest context. We illustrate the method with the estimation of the difference in gain between two interventions and consider a simulation study to compare the empirical version of the proposed estimator (obtained by replacing variance components with estimates) with the estimator obtained via covariance analysis usually employed in such settings. The results indicate that in many instances, the proposed estimator has a smaller mean squared error than that obtained from the standard analysis of covariance model.
Key words: analysis of covariance; BLUP; optimal estimator; random permutation model
Se considera un modelo mixto para población finita que tiene en cuenta el error de respuesta y que arroja estimadores óptimos de los parámetros de la población finita, para analizar datos de estudios con estructura del tipo pretest-posttest. Se ilustra el método estimando la diferencia en ganancia entre dos intervenciones y se considera un estudio de simulación para comparar la versión empírica del estimador propuesto (obtenido al reemplazar las componentes de varianza con sus estimativas) con el estimador obtenido vía análisis de covarianza, que es usualmente empleado en este tipo de estudios. Los resultados indican que en muchas circunstancias, el estimador propuesto tiene menor error cuadrático medio que el obtenido del análisis estándar usando el modelo de covarianza.
Palabras clave: análisis de covarianza; BLUP; estimador óptimo; modelo de permutación aleatoria
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Received: January 2021; Accepted: November 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
