Abstract
An influential observation and influential sets would cause noticeable differentiations on the fitted values in regression. Since these differentiations decrease explicable of model, detecting the influential observation or the influential sets in data is important for efficiency of regression analysis. In this study DFFITS, DFBETAS, COVRATIO, Cook Distance, S statistics and graphical technique used for detecting an influential observation are examined. These methods are compared with regard to ratios of detecting influential observation in data which includes an influential observation.
References
- Altunkaynak, B. (2003). “Doğrusal Sınırlamalar ve İzdüşüm Teorisi Yardımıyla Çoklu Doğrusal Reg-resyonda Etkili Gözlemlerin Tespiti”, Gazi Üniversitesi Fen Bilimleri Dergisi 16(3), 457- 466.
- Andrews, D.F. ve Pregibon, D. (1976). “Finding Outliers That Matter”, J. Roy. Statist. Soc., Ser. B. 40, 85-93.
- Belsley, D.A., Kuh, E. ve Welsch, R.E. (1980). “Regression Diagnostics: Identifying Influential Data and Sources of Collinearity”, Willey Series in Probability and Mathematical Statistics, New York 6-84.
- Chatterjee, S. ve Hadi, A.S. (1986). “Influential Observations, High Leverage Points and Outliers in Linear Regression”, Statistical Science 1(3), 379-416.
- Cook, R.D. (1977a). “Detection of Influential Observations in Linear Regression”, Technometrics 19 (1), 15-18.
- Cook, R.D. ve Weisberg, S. (1982). “Residuals and Influence in Regression”, Chapman and Hall, New York 10-20, 101-156.
- David, H.A. (1981). “Order Statistics, 2nd Edn.”, Willey, New York, 110-150.
- Hadi, A.S. ve Simonoff, J.S. (1993). “Procedures for the Identification of Multiple Outliers in Linear Models”, Journal of the American Statistical Association 88(424), 1264-1272.
- Hoaglin, D.C. ve Welsch, R.E. (1978). “The Hat Matrix in Regression and ANOVA”, The American Statistician 32(1), 17-22.
- Li, B., Martin, E.B. ve Morris, A.J. (2001). “A Graphical Technique for Detecting Influential Cases in Regression Analysis”, Communications in Statistics – Theory and Methods 30(3), 463-483.
- Margolin, B.H. (1977). “The Distribution of Internally Studentized Statistics via Laplace Transform Inversion”, Biometrica 64, 573-582.
- Montgomery, D.C., Peck, E.A.. ve Vining, G.G. (2001). “Introduction to Linear Regression Analysis”, Willey Series in Probability and Mathematical Statistics New York, 207-219.
- Pena, D. (2005). “A New Statistics for Influence in Linear Regression”, American Statistical Associa- tion and the American Society for Quality 47(1), 1-12.
- Vupa, Ö. (2009). “Investigation of Influence Observation and Outliers in Logistic Regression Model”, VI. İstatistik Günleri Sempozyumu Bildiriler Kitabı 453-457.
Abstract
Regresyonda etkili gözlem ve gözlem grupları, tahmin değerlerinde önemli derecede farklılaşmalara neden olabilir. Bu farklılaşmalar modelin açıklanabilirliğini azalttığı için verideki etkili gözlem veya gözlem gruplarının saptanması regresyon analizinin verimliliği açısından önemlidir. Bu çalışmada etkili gözlem ve gözlem gruplarının saptanması için kullanılan DFFITS, DFBETAS, COVRATIO, Cook Uzaklığı, S tanı istatistikleri ve grafik yöntemi incelenmiştir. Bu yöntemler etkili bir gözlem içeren veride bu gözlemi etkili gözlem olarak saptama oranı bakımından karşılaştırılmıştır.
References
- Altunkaynak, B. (2003). “Doğrusal Sınırlamalar ve İzdüşüm Teorisi Yardımıyla Çoklu Doğrusal Reg-resyonda Etkili Gözlemlerin Tespiti”, Gazi Üniversitesi Fen Bilimleri Dergisi 16(3), 457- 466.
- Andrews, D.F. ve Pregibon, D. (1976). “Finding Outliers That Matter”, J. Roy. Statist. Soc., Ser. B. 40, 85-93.
- Belsley, D.A., Kuh, E. ve Welsch, R.E. (1980). “Regression Diagnostics: Identifying Influential Data and Sources of Collinearity”, Willey Series in Probability and Mathematical Statistics, New York 6-84.
- Chatterjee, S. ve Hadi, A.S. (1986). “Influential Observations, High Leverage Points and Outliers in Linear Regression”, Statistical Science 1(3), 379-416.
- Cook, R.D. (1977a). “Detection of Influential Observations in Linear Regression”, Technometrics 19 (1), 15-18.
- Cook, R.D. ve Weisberg, S. (1982). “Residuals and Influence in Regression”, Chapman and Hall, New York 10-20, 101-156.
- David, H.A. (1981). “Order Statistics, 2nd Edn.”, Willey, New York, 110-150.
- Hadi, A.S. ve Simonoff, J.S. (1993). “Procedures for the Identification of Multiple Outliers in Linear Models”, Journal of the American Statistical Association 88(424), 1264-1272.
- Hoaglin, D.C. ve Welsch, R.E. (1978). “The Hat Matrix in Regression and ANOVA”, The American Statistician 32(1), 17-22.
- Li, B., Martin, E.B. ve Morris, A.J. (2001). “A Graphical Technique for Detecting Influential Cases in Regression Analysis”, Communications in Statistics – Theory and Methods 30(3), 463-483.
- Margolin, B.H. (1977). “The Distribution of Internally Studentized Statistics via Laplace Transform Inversion”, Biometrica 64, 573-582.
- Montgomery, D.C., Peck, E.A.. ve Vining, G.G. (2001). “Introduction to Linear Regression Analysis”, Willey Series in Probability and Mathematical Statistics New York, 207-219.
- Pena, D. (2005). “A New Statistics for Influence in Linear Regression”, American Statistical Associa- tion and the American Society for Quality 47(1), 1-12.
- Vupa, Ö. (2009). “Investigation of Influence Observation and Outliers in Logistic Regression Model”, VI. İstatistik Günleri Sempozyumu Bildiriler Kitabı 453-457.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | July 4, 2011 |
| Published in Issue | Year 2011 Volume: 1 Issue: 2 |
