Effect of Influential Data in 3 ω Fixed Factorial Designs
Main Article Content
Keywords
factorial design, influential data, variance analysis, outliers data, sums of squares
Abstract
This paper provides a methodology alternative for the detection of in- fluential observations in factorial design of fixed effects 3 ω . Our proposal is developed through the approach of the test statistic (Fq), and the characterization of the impact of such observations on the analysis, the sums of squares and the estimators of the model that describes the experimental design.
MSC: 62K15, 62E15, 62-07, 62J20
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References
[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
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[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.