Skip to main content

Model Diagnostics

  • Chapter
  • First Online:
  • 3248 Accesses

Part of the book series: Springer Texts in Statistics ((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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Andrews, D. F. (1974). A robust method for multiple regression. Technometrics, 16, 523–531.

    Article  MathSciNet  MATH  Google Scholar 

  • Arnold, S. F. (1981). The theory of linear models and multivariate analysis. New York: Wiley.

    MATH  Google Scholar 

  • Atkinson, A. C. (1981). Two graphical displays for outlying and influential observations in regression. Biometrika, 68, 13–20.

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson, A. C. (1982). Regression diagnostics, transformations and constructed variables (with discussion). Journal of the Royal Statistical Society, Series B, 44, 1–36.

    MathSciNet  MATH  Google Scholar 

  • Atkinson, A. C. (1985). Plots, transformations, and regression: An introduction to graphical methods of diagnostic regression analysis. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Blom, G. (1958). Statistical estimates and transformed beta variates. New York: Wiley.

    MATH  Google Scholar 

  • Box, G. E. P. (1953). Non-normality and tests on variances. Biometrika, 40, 318–335.

    Article  MathSciNet  MATH  Google Scholar 

  • Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, Series B, 26, 211–246.

    MathSciNet  MATH  Google Scholar 

  • Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Christensen, R. (1989). Lack of fit tests based on near or exact replicates. The Annals of Statistics, 17, 673–683.

    Article  MathSciNet  MATH  Google Scholar 

  • Christensen, R. (1996). Analysis of variance, design, and regression: Applied statistical methods. London: Chapman and Hall.

    MATH  Google Scholar 

  • Christensen, R. (1997). Log-linear models and logistic regression (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Christensen, R. (2001). Advanced linear modeling: Multivariate, time series, and spatial data; nonparametric regression, and response surface maximization (2nd ed.). New York: Springer.

    Book  MATH  Google Scholar 

  • 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 

  • Christensen, R., & Bedrick, E. J. (1997). Testing the independence assumption in linear models. Journal of the American Statistical Association, 92, 1006–1016.

    Article  MathSciNet  MATH  Google Scholar 

  • Christensen, R., Johnson, W., & Pearson, L. M. (1992). Prediction diagnostics for spatial linear models. Biometrika, 79, 583–591.

    Article  MATH  Google Scholar 

  • Christensen, R., Johnson, W., & Pearson, L. M. (1993). Covariance function diagnostics for spatial linear models. Mathematical Geology, 25, 145–160.

    Article  Google Scholar 

  • 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.

    Book  MATH  Google Scholar 

  • Christensen, R., Pearson, L. M., & Johnson, W. (1992). Case deletion diagnostics for mixed models. Technometrics, 34, 38–45.

    Google Scholar 

  • Cook, R. D. (1977). Detection of influential observations in linear regression. Technometrics, 19, 15–18.

    MathSciNet  MATH  Google Scholar 

  • Cook, R. D. (1998). Regression graphics: Ideas for studying regressions through graphics. New York: Wiley.

    Book  MATH  Google Scholar 

  • Cook, R. D., & Weisberg, S. (1982). Residuals and influence in regression. New York: Chapman and Hall.

    MATH  Google Scholar 

  • Cook, R. D., & Weisberg, S. (1994). An introduction to regression graphics. New York: Wiley.

    Book  MATH  Google Scholar 

  • Cook, R. D., & Weisberg, S. (1999). Applied regression including computing and graphics. New York: Wiley.

    Book  MATH  Google Scholar 

  • Daniel, C. (1959). Use of half-normal plots in interpreting factorial two-level experiments. Technometrics, 1, 311–341.

    Article  MathSciNet  Google Scholar 

  • Daniel, C. (1976). Applications of statistics to industrial experimentation. New York: Wiley.

    Book  MATH  Google Scholar 

  • Daniel, C., & Wood, F. S. (1980). Fitting equations to data (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Draper, N., & Smith, H. (1998). Applied regression analysis (3rd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Duan, N. (1981). Consistency of residual distribution functions. Working Draft No. 801-1-HHS (106B-80010), Rand Corporation, Santa Monica, CA.

    Google Scholar 

  • Durbin, J., & Watson, G. S. (1951). Testing for serial correlation in least squares regression II. Biometrika, 38, 159–179.

    Article  MathSciNet  MATH  Google Scholar 

  • Freedman, D. A. (2006). On the so-called “Huber sandwich estimator” and “robust standard errors”. The American Statistician, 60, 299–302.

    Article  MathSciNet  Google Scholar 

  • Grizzle, J. E., Starmer, C. F., & Koch, G. G. (1969). Analysis of categorical data by linear models. Biometrics, 25, 489–504.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Lenth, R. V. (2015). The case against normal plots of effects (with discussion). Journal of Quality Technology, 47, 91–97.

    Article  Google Scholar 

  • Mandansky, A. (1988). Prescriptions for working statisticians. New York: Springer.

    Book  MATH  Google Scholar 

  • Martin, R. J. (1992). Leverage, influence and residuals in regression models when observations are correlated. Communications in Statistics - Theory and Methods, 21, 1183–1212.

    Article  MathSciNet  MATH  Google Scholar 

  • Picard, R. R., & Berk, K. N. (1990). Data splitting. The American Statistician, 44, 140–147.

    Google Scholar 

  • Picard, R. R., & Cook, R. D. (1984). Cross-validation of regression models. Journal of the American Statistical Association, 79, 575–583.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao, C. R. (1973). Linear statistical inference and its applications (2nd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Searle, S. R. (1988). Parallel lines in residual plots. The American Statistician, 42, 211.

    Google Scholar 

  • Shapiro, S. S., & Francia, R. S. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67, 215–216.

    Article  Google Scholar 

  • Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.

    Article  MathSciNet  MATH  Google Scholar 

  • Shewhart, W. A. (1931). Economic control of quality. New York: Van Nostrand.

    Google Scholar 

  • 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 

  • Shi, L., & Chen, G. (2009). Influence measures for general linear models with correlated errors. The American Statistician, 63, 40–42.

    Article  MathSciNet  MATH  Google Scholar 

  • Stefanski, L. A. (2007). Residual (sur)realism. The American Statistician, 61, 163–177.

    Article  MathSciNet  Google Scholar 

  • Tukey, J. W. (1949). One degree of freedom for nonadditivity. Biometrics, 5, 232–242.

    Article  Google Scholar 

  • Weisberg, S. (2014). Applied linear regression (4th ed.). New York: Wiley.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ronald Christensen .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Christensen, R. (2020). Model Diagnostics. In: Plane Answers to Complex Questions. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-32097-3_12

Download citation

Publish with us

Policies and ethics