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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.29 no.1 Bogotá Jan./June 2006
1Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Profesora temporal. E-mail: dcfrancos@unal.edu.co
2Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Profesor asistente. E-mail: oomelom@unal.edu.co
Se propone una metodología para la estimación de información faltante en modelos mixtos de medias de celda que permite la disminución de la correlaci ón entre la información observada y la información estimada, basada en el método propuesto por Melo & Melo (2005). éste se fundamenta en los métodos de estimación vía máxima verosimilitud, expuesto en Searle (1971), y de covariable, propuesto por Bartlett (1937). Después de realizar la imputaci ón de la información, se plantea una manera de llevar a cabo el análisis de varianza en modelos sin interacción, mediante pruebas ponderadas para los efectos fijos y aleatorios involucrados en el modelo.
Palabras clave: Modelo de medias de celda, modelo mixto, información faltante, estimación e imputación, distribución de formas cuadráticas.
We propose a methodology to estimate missing information in mixed cell means models. This methodology improves on that Melo & Melo (2005), which is based on the methods of maximum likelihood estimation and covariate proposed by Bartlett (1937), and reduces the correlation between the observed and estimated information. Once the imputation of the missing information is done, we suggest a way to perform the analysis of variance in models without interaction, by generating a weighted test for the fixed and random effects involved in the model.
Key words: Cell means model, Mixed model, Missing information, Estimation and imputation, Distribution of quadratic forms.
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Referencias
1. Allan, F. & Wishart, J. (1930), "A Method of Estimating the Yield of a Missing Plot in Field Experiments", J. Agric. Sci. 20, 399406. [ Links ]
2. Barroso, L. P., Bussab,W. O. & Knott, M. (1998), "Best Linear Unbiased Predictor in the Mixed Model with Incomplete Data", Communications in Statistics 21, 121129. [ Links ]
3. Bartlett, M. S. (1937), "Some Examples of Statistical Methods of Research in Agriculture and Applied Biology", Journal of the Royal Statistical Society 4(2), 137183. [ Links ]
4. Corbeil, R. R. & Searle, S. R. (1976), "Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model", Technometrics 18, 3138. [ Links ]
5. Dodge, Y. (1985), Analysis of Experiments with Missing Data, John Wiley & Sons, New York. [ Links ]
6. Fisher, R. A. (1935), The Design of Experiments, Oliver & Boyd, Edinburgh. [ Links ]
7. Franco, D. C. (2005), Metodología para la estimación de información faltante, imputación y estadísticos de prueba en modelos mixtos a dos vías de clasificaci ón, Tesis de maestría, Universidad Nacional de Colombia, Departamento de Estadística, Bogotá D. C. [ Links ]
8. Gallo, J. & Khuri, A. I. (1990), "Exact Test for the Random and Fixed Effects in an Unbalanced Mixed Two Way Cross-Classification Model", Biometrics 46, 10871095. [ Links ]
9. Harville, D. A. & Carriquiry, A. L. (1992), "Classical an Bayesian Prediction as Applied to an Unbalanced Mixed Linear Model", Biometrics 48, 9871003. [ Links ]
10. Henderson, C. R. (1952), Estimation of Variance and Covariance Components, Cornell University. North Carolina Summer Statistics Conference. [ Links ]
11. Hocking, R. R. (1996), Methods and Applications of Linear Models, John Wiley & Sons, New York. [ Links ]
12. Lindstrom, M. J. & Bates, D. M. (1988), "Newton Raphson and EM Algorithms for Linear Mixed Effects Models for Repeated Measures Data", Journal of the American Statistical Association 83, 10141022. [ Links ]
13. Little, R. & Rubin, D. (2002), Statistical Analysis with Missing Data, John Wiley & Sons, New York. [ Links ]
14. Melo, O. O. & Melo, S. E. (2005), Metodología para la estimación de datos faltantes en modelos mixtos de medias de celdas, in "Modelamiento Estadístico. Memorias del XV Simposio de Estadística", Universidad Nacional de Colombia. Departamento de Estadística, Bogotá. [ Links ]
15. Milliken, G. & Johnson, D. (1984), Analysis of Messy Data Designed Experiments, Vol. I , Van Nostrand Reinhold, New York. [ Links ]
16. Murray, L. W. & Smith, D. W. (1985), "Estimability, Testability, and Connectedness in the Cell Means Models", Communications in Statistics 14, 18891917. [ Links ]
17. Searle, S. R. (1971), Linear Models, John Wiley & Sons, New York. [ Links ]
18. Searle, S. R., Casella, G. & McCulloch, C. (1992), Variance Components, John Wiley & Sons, New York. [ Links ]
19. Sheffé, H. (1959), The Analysis of Variance, Wiley. [ Links ]
20. Thomsen, I. (1975), "Testing Hyphoteses in Unbalanced Variance Components Models for Two-Way Layouts", Annals of Statistics 3, 257265. [ Links ]
21. Yates, F. (1933), "The Analysis of Replicate Experiments When the Field Results are Incomplete", Emp. Journ. Exp. Agric. (1). [ Links ]