Efecto de datos influyentes en el análisis de diseños factoriales de efectos fijos 3 ω
Main Article Content
Keywords
Diseño factorial, datos influyentes, análisis de varianza, atípicos y sumas de cuadrados.
Resumen
En este trabajo se establece una metodología alternativa para la detección de observaciones influyentes en diseños factoriales de efectos fijos 3^w, a través del planteamiento de la estadística de prueba (Fq) y la caracterización de los efectos de dichas observaciones sobre el análisis, las sumas de cuadrados y los estimadores del modelo que describe el diseño experimental
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Referencias
[1] M. T. Jiménez, “Ajuste de factoriales 2 k con presencia de observaciones influyentes y valores faltantes mediante modelos de regresión,” Master’s thesis, Universidad Nacional de Colombia, Bogotá, 2000.
[2] C. R., “Assessment of Local Influence (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 48, pp. 133–169, 1986.
[3] ——, “Robust Test for the Equality of Variantes,” Technometrics, vol. 19, pp. 15–18, 1977.
[4] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data Via the EM Algorithm (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 39, no. 1, pp. 1–38, 1977.
[5] Thomas W. and R. D. Cook, “Assessing Influence on Regression Coefficients in Generalized Linear Models,” Biometrika, vol. 76, no. 4, pp. 741–749, 1989. [Online]. Available: http://www.jstor.org/stable/2336634
[6] ——, “Assessing Influence on Predictions from Generalized Linear Models,” Technometrics, vol. 32, no. 1, pp. 59–65, 1990. [Online]. Available:http://dx.doi.org/10.2307/1269845
[7] A. J. Lawrence, “Local and Deletion Influence,” in Directions in Robust Statistics and Diagnostics, Part I, W. S. . S. Weisberg, Ed. Berlin: Springer, 1991, pp. 141–157.
[8] E. B. Andersen, “Diagnostics in Categorical Data Analysis,” Journal of the Royal Statistical Society, Series B, vol. 54, no. 3, pp. 784–791, 1992. [Online]. Available: http://www.jstor.org/stable/2345858
[9] F. Critchley, R. A. Atkinson, G. Lu, and E. Biazi, “Influence Analysis Based on the Case Sensitivity Function,” Journal of the Royal Statistical Society, Series B, vol. 63, no. 2, pp. 307–323, 2001. [Online]. Available: http://dx.doi.org/10.1111/1467-9868.00287
[10] H. T. Zhu and S. Y. Lee, “Local Influence for Incomplete Data Models,” Journal of the Royal Statistical Society, Series B, vol. 63, no. 1, pp. 111–126, 2001. [Online]. Available: http://www.jstor.org/stable/2680637
[11] R. Tsai and U. Böckenholt, “Two-Level Linear Paired Comparison Models: Estimation and Identifiable Issues,” Mathematical Social Science, vol. 43, no. 3, pp. 429–449, 2002. [Online]. Available: http://dx.doi.org/10.1016/S0165-4896(02)00019-7
[12] S. Y. Lee and N. S. Tang, “Local Influence Analysis of Nonlinear Structural Equation Models,” Psychometrica, vol. 69, no. 4, pp. 573–592, 2004. [Online]. Available: http://dx.doi.org/10.1007/BF02289856
[13] L. Xu, W. Y. Poon, and S. Y. Lee, “Influence Analysis for the Factor Analysis Model with Ranking Data,” British Journal of Mathematical and Statistical Psychology, vol. 61, no. 1, pp. 133–161, 2008. [Online]. Available: http://dx.doi.org/10.1348/000711006X169991
[14] D. C. Montgomery, Design and Analysis of Experiments, 8th ed. New York: John Wiley & Sons, 2012.
[15] D. A. Belsley, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons, 1980.
[16] D. C. Hoaglin and R. E. Welsch, “The Hat Matrix in Regression and ANOVA,” The American Statistician, vol. 32, no. 1, pp. 17–22, 1978.
[17] D. Peña-Sánchez, Estadística Modelos y Métodos. Madrid: Alianza Editorial, 1995.
[18] N. R. Draper and H. Smith, Applied Regresión Analysis, 3rd ed. New York: John Wiley & Sons, 1998.
[19] N. Draper and J. A. John, “Influential Observations and Outliers in Regression,” Technometrics, vol. 23, no. 1, pp. 21–26, 1981.
[20] M. S. Bartlett, “Some Examples of Statistical Methods of Research in Agriculture y Applied Botany,” Journal Royal of the Statistical Society B, vol. 4, pp. 137–170, 1937.
[21] J. A. Jiménez, “Propuesta metodológica para imputar valores no influyentes en modelos de regresión lineal múltiple con información incompleta,” Master’s thesis, Universidad Nacional de Colombia, Bogotá, 1999.
[22] ——, “Un criterio para identificar datos atípicos,” Revista Colombiana de Estadística, vol. 27, no. 2, pp. 109–121, 2011. [Online]. Available: http://www.revistas.unal.edu.co/index.php/estad/article/view/28709
[23] D. C. Montgomery, Introduction to Linear Regression Analysis. New York: John Wiley & Sons, 1992.
[24] O. O. Melo, L. A. López, and S. E. Melo, Diseño de Experimentos: Métodos y Aplicaciones, 1st ed. Bogotá: Facultad de Ciencias, Universidad Nacional de Colombia, 2007.
[25] I. Méndez, “Diseño de Experimentos,” in Memorias del X Coloquio Distrital de Matemáticas y Estadística, Bogotá, 1993.
[2] C. R., “Assessment of Local Influence (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 48, pp. 133–169, 1986.
[3] ——, “Robust Test for the Equality of Variantes,” Technometrics, vol. 19, pp. 15–18, 1977.
[4] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data Via the EM Algorithm (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 39, no. 1, pp. 1–38, 1977.
[5] Thomas W. and R. D. Cook, “Assessing Influence on Regression Coefficients in Generalized Linear Models,” Biometrika, vol. 76, no. 4, pp. 741–749, 1989. [Online]. Available: http://www.jstor.org/stable/2336634
[6] ——, “Assessing Influence on Predictions from Generalized Linear Models,” Technometrics, vol. 32, no. 1, pp. 59–65, 1990. [Online]. Available:http://dx.doi.org/10.2307/1269845
[7] A. J. Lawrence, “Local and Deletion Influence,” in Directions in Robust Statistics and Diagnostics, Part I, W. S. . S. Weisberg, Ed. Berlin: Springer, 1991, pp. 141–157.
[8] E. B. Andersen, “Diagnostics in Categorical Data Analysis,” Journal of the Royal Statistical Society, Series B, vol. 54, no. 3, pp. 784–791, 1992. [Online]. Available: http://www.jstor.org/stable/2345858
[9] F. Critchley, R. A. Atkinson, G. Lu, and E. Biazi, “Influence Analysis Based on the Case Sensitivity Function,” Journal of the Royal Statistical Society, Series B, vol. 63, no. 2, pp. 307–323, 2001. [Online]. Available: http://dx.doi.org/10.1111/1467-9868.00287
[10] H. T. Zhu and S. Y. Lee, “Local Influence for Incomplete Data Models,” Journal of the Royal Statistical Society, Series B, vol. 63, no. 1, pp. 111–126, 2001. [Online]. Available: http://www.jstor.org/stable/2680637
[11] R. Tsai and U. Böckenholt, “Two-Level Linear Paired Comparison Models: Estimation and Identifiable Issues,” Mathematical Social Science, vol. 43, no. 3, pp. 429–449, 2002. [Online]. Available: http://dx.doi.org/10.1016/S0165-4896(02)00019-7
[12] S. Y. Lee and N. S. Tang, “Local Influence Analysis of Nonlinear Structural Equation Models,” Psychometrica, vol. 69, no. 4, pp. 573–592, 2004. [Online]. Available: http://dx.doi.org/10.1007/BF02289856
[13] L. Xu, W. Y. Poon, and S. Y. Lee, “Influence Analysis for the Factor Analysis Model with Ranking Data,” British Journal of Mathematical and Statistical Psychology, vol. 61, no. 1, pp. 133–161, 2008. [Online]. Available: http://dx.doi.org/10.1348/000711006X169991
[14] D. C. Montgomery, Design and Analysis of Experiments, 8th ed. New York: John Wiley & Sons, 2012.
[15] D. A. Belsley, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons, 1980.
[16] D. C. Hoaglin and R. E. Welsch, “The Hat Matrix in Regression and ANOVA,” The American Statistician, vol. 32, no. 1, pp. 17–22, 1978.
[17] D. Peña-Sánchez, Estadística Modelos y Métodos. Madrid: Alianza Editorial, 1995.
[18] N. R. Draper and H. Smith, Applied Regresión Analysis, 3rd ed. New York: John Wiley & Sons, 1998.
[19] N. Draper and J. A. John, “Influential Observations and Outliers in Regression,” Technometrics, vol. 23, no. 1, pp. 21–26, 1981.
[20] M. S. Bartlett, “Some Examples of Statistical Methods of Research in Agriculture y Applied Botany,” Journal Royal of the Statistical Society B, vol. 4, pp. 137–170, 1937.
[21] J. A. Jiménez, “Propuesta metodológica para imputar valores no influyentes en modelos de regresión lineal múltiple con información incompleta,” Master’s thesis, Universidad Nacional de Colombia, Bogotá, 1999.
[22] ——, “Un criterio para identificar datos atípicos,” Revista Colombiana de Estadística, vol. 27, no. 2, pp. 109–121, 2011. [Online]. Available: http://www.revistas.unal.edu.co/index.php/estad/article/view/28709
[23] D. C. Montgomery, Introduction to Linear Regression Analysis. New York: John Wiley & Sons, 1992.
[24] O. O. Melo, L. A. López, and S. E. Melo, Diseño de Experimentos: Métodos y Aplicaciones, 1st ed. Bogotá: Facultad de Ciencias, Universidad Nacional de Colombia, 2007.
[25] I. Méndez, “Diseño de Experimentos,” in Memorias del X Coloquio Distrital de Matemáticas y Estadística, Bogotá, 1993.