Advertisement

Model Diagnostics

  • Ronald ChristensenEmail author
Chapter
  • 77 Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

This chapter focuses on methods for evaluating the assumptions made in a standard linear model and on the use of transformations to correct such problems.

References

  1. Andrews, D. F. (1974). A robust method for multiple regression. Technometrics, 16, 523–531.CrossRefMathSciNetzbMATHGoogle Scholar
  2. Arnold, S. F. (1981). The theory of linear models and multivariate analysis. New York: Wiley.zbMATHGoogle Scholar
  3. Atkinson, A. C. (1981). Two graphical displays for outlying and influential observations in regression. Biometrika, 68, 13–20.CrossRefMathSciNetzbMATHGoogle Scholar
  4. Atkinson, A. C. (1982). Regression diagnostics, transformations and constructed variables (with discussion). Journal of the Royal Statistical Society, Series B, 44, 1–36.MathSciNetzbMATHGoogle Scholar
  5. Atkinson, A. C. (1985). Plots, transformations, and regression: An introduction to graphical methods of diagnostic regression analysis. Oxford: Oxford University Press.zbMATHGoogle Scholar
  6. Blom, G. (1958). Statistical estimates and transformed beta variates. New York: Wiley.zbMATHGoogle Scholar
  7. Box, G. E. P. (1953). Non-normality and tests on variances. Biometrika, 40, 318–335.CrossRefMathSciNetzbMATHGoogle Scholar
  8. Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, Series B, 26, 211–246.MathSciNetzbMATHGoogle Scholar
  9. Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering (2nd ed.). New York: Wiley.zbMATHGoogle Scholar
  10. Christensen, R. (1989). Lack of fit tests based on near or exact replicates. The Annals of Statistics, 17, 673–683.CrossRefMathSciNetzbMATHGoogle Scholar
  11. Christensen, R. (1996). Analysis of variance, design, and regression: Applied statistical methods. London: Chapman and Hall.zbMATHGoogle Scholar
  12. Christensen, R. (1997). Log-linear models and logistic regression (2nd ed.). New York: Springer.zbMATHGoogle Scholar
  13. Christensen, R. (2001). Advanced linear modeling: Multivariate, time series, and spatial data; nonparametric regression, and response surface maximization (2nd ed.). New York: Springer.CrossRefzbMATHGoogle Scholar
  14. Christensen, R. (2015). Analysis of variance, design, and regression: Linear modeling for unbalanced data (2nd ed.). Boca Raton: Chapman and Hall/CRC Press.Google Scholar
  15. Christensen, R., & Bedrick, E. J. (1997). Testing the independence assumption in linear models. Journal of the American Statistical Association, 92, 1006–1016.CrossRefMathSciNetzbMATHGoogle Scholar
  16. Christensen, R., Johnson, W., & Pearson, L. M. (1992). Prediction diagnostics for spatial linear models. Biometrika, 79, 583–591.CrossRefzbMATHGoogle Scholar
  17. Christensen, R., Johnson, W., & Pearson, L. M. (1993). Covariance function diagnostics for spatial linear models. Mathematical Geology, 25, 145–160.CrossRefGoogle Scholar
  18. Christensen, R., Johnson, W., Branscum, A., & Hanson, T. E. (2010). Bayesian ideas and data analysis: An introduction for scientists and statisticians. Boca Raton: Chapman and Hall/CRC Press.CrossRefzbMATHGoogle Scholar
  19. Christensen, R., Pearson, L. M., & Johnson, W. (1992). Case deletion diagnostics for mixed models. Technometrics, 34, 38–45.Google Scholar
  20. Cook, R. D. (1977). Detection of influential observations in linear regression. Technometrics, 19, 15–18.MathSciNetzbMATHGoogle Scholar
  21. Cook, R. D. (1998). Regression graphics: Ideas for studying regressions through graphics. New York: Wiley.CrossRefzbMATHGoogle Scholar
  22. Cook, R. D., & Weisberg, S. (1982). Residuals and influence in regression. New York: Chapman and Hall.zbMATHGoogle Scholar
  23. Cook, R. D., & Weisberg, S. (1994). An introduction to regression graphics. New York: Wiley.CrossRefzbMATHGoogle Scholar
  24. Cook, R. D., & Weisberg, S. (1999). Applied regression including computing and graphics. New York: Wiley.CrossRefzbMATHGoogle Scholar
  25. Daniel, C. (1959). Use of half-normal plots in interpreting factorial two-level experiments. Technometrics, 1, 311–341.CrossRefMathSciNetGoogle Scholar
  26. Daniel, C. (1976). Applications of statistics to industrial experimentation. New York: Wiley.CrossRefzbMATHGoogle Scholar
  27. Daniel, C., & Wood, F. S. (1980). Fitting equations to data (2nd ed.). New York: Wiley.zbMATHGoogle Scholar
  28. Draper, N., & Smith, H. (1998). Applied regression analysis (3rd ed.). New York: Wiley.CrossRefzbMATHGoogle Scholar
  29. Duan, N. (1981). Consistency of residual distribution functions. Working Draft No. 801-1-HHS (106B-80010), Rand Corporation, Santa Monica, CA.Google Scholar
  30. Durbin, J., & Watson, G. S. (1951). Testing for serial correlation in least squares regression II. Biometrika, 38, 159–179.CrossRefMathSciNetzbMATHGoogle Scholar
  31. Freedman, D. A. (2006). On the so-called “Huber sandwich estimator” and “robust standard errors”. The American Statistician, 60, 299–302.CrossRefMathSciNetGoogle Scholar
  32. Grizzle, J. E., Starmer, C. F., & Koch, G. G. (1969). Analysis of categorical data by linear models. Biometrics, 25, 489–504.CrossRefMathSciNetzbMATHGoogle Scholar
  33. Haslett, J. (1999). A simple derivation of deletion diagnostic results for the general linear model with correlated errors. Journal of the Royal Statistical Society, Series B, 61, 603–609.CrossRefMathSciNetzbMATHGoogle Scholar
  34. Haslett, J., & Hayes, K. (1998). Residuals for the linear model with general covariance structure. Journal of the Royal Statistical Society, Series B, 60, 201–215.CrossRefMathSciNetzbMATHGoogle Scholar
  35. Lenth, R. V. (2015). The case against normal plots of effects (with discussion). Journal of Quality Technology, 47, 91–97.CrossRefGoogle Scholar
  36. Mandansky, A. (1988). Prescriptions for working statisticians. New York: Springer.CrossRefzbMATHGoogle Scholar
  37. Martin, R. J. (1992). Leverage, influence and residuals in regression models when observations are correlated. Communications in Statistics - Theory and Methods, 21, 1183–1212.CrossRefMathSciNetzbMATHGoogle Scholar
  38. Picard, R. R., & Berk, K. N. (1990). Data splitting. The American Statistician, 44, 140–147.Google Scholar
  39. Picard, R. R., & Cook, R. D. (1984). Cross-validation of regression models. Journal of the American Statistical Association, 79, 575–583.CrossRefMathSciNetzbMATHGoogle Scholar
  40. Rao, C. R. (1973). Linear statistical inference and its applications (2nd ed.). New York: Wiley.CrossRefzbMATHGoogle Scholar
  41. Searle, S. R. (1988). Parallel lines in residual plots. The American Statistician, 42, 211.Google Scholar
  42. Shapiro, S. S., & Francia, R. S. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67, 215–216.CrossRefGoogle Scholar
  43. Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.CrossRefMathSciNetzbMATHGoogle Scholar
  44. Shewhart, W. A. (1931). Economic control of quality. New York: Van Nostrand.Google Scholar
  45. Shewhart, W. A. (1939). Statistical method from the viewpoint of quality control. Graduate School of the Department of Agriculture, Washington. Reprint (1986), Dover, New York.Google Scholar
  46. Shi, L., & Chen, G. (2009). Influence measures for general linear models with correlated errors. The American Statistician, 63, 40–42.CrossRefMathSciNetzbMATHGoogle Scholar
  47. Stefanski, L. A. (2007). Residual (sur)realism. The American Statistician, 61, 163–177.CrossRefMathSciNetGoogle Scholar
  48. Tukey, J. W. (1949). One degree of freedom for nonadditivity. Biometrics, 5, 232–242.CrossRefGoogle Scholar
  49. Weisberg, S. (2014). Applied linear regression (4th ed.). New York: Wiley.zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations