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Statistical diagnostics of models for binomial response

Author Affiliations

  • 1School of Science, Department of Probability and mathematical Statistics Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, P.R., China
  • 2School of Science, Department of Probability and mathematical Statistics Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, P.R., China
  • 3School of Science, Department of Probability and mathematical Statistics Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, P.R., China
  • 4School of Science, Department of Probability and mathematical Statistics Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, P.R., China

Res. J. Mathematical & Statistical Sci., Volume 7, Issue (1), Pages 1-6, January,12 (2019)

Abstract

In regression analysis, outliers are frequently encountered. Diagnostics of outliers is an essential tool of the model building process. Most of the time analysts depend on ordinary least square (OLS) method without identifying outliers. It is evident that OLS utterly fails in the identification of outliers. In this paper, we use diagnostics techniques to detect residuals and influential points in statistical models for binomial the response. Gauss-Newton and likelihood distance methods were considered to identify the outliers in parameter estimation in non-linear regression analysis. The results illustrated single and multiple outliers in dataset.

References

  1. Vonesh E. (1992)., Nonlinear models for the analysis of longitudinal data., Statistics in medicine, 11(11), 1929-1954.
  2. McKenzie E., Gettinby G., Lloyd J. and Caddy B. (1995)., A statistical model for the response patterns to chemical tests for the absence or presence of trace materials., Science & Justice, 35(1), 31-36.
  3. Pregibon D. (1981)., Logistic regression diagnostics., The Annals of Statistics, 9(4), 705-724.
  4. Bedrick E.J. and Tsai C.L. (1993)., Diagnostics for binomial response models using power divergence statistics., Computational statistics & data analysis, 15(4), 381-392.
  5. Altman N. and Krzywinski M. (2016)., Erratum: Analyzing outliers: Influential or nuisance (Nature Methods)., Nature Methods, 13(6), 281-282.
  6. Gökpınar E. (2018)., Standardized Log-Likelihood Ratio Test for the Equality of Inverse Gaussian Scale Parameters., Iranian Journal of Science and Technology, Transactions A: Science, 2(10), 1-7.
  7. Vanegas L.H., Rondón L.M. and Cysneiros F.J.A. (2012)., Diagnostic procedures in Birnbaum-Saunders nonlinear regression models., Computational Statistics & Data Analysis, 56(6), 1662-1680.
  8. Cook R.D. (1979)., Influential observations in linear regression., Journal of the American Statistical Association, 74(365), 169-174.
  9. Ellenberg J.H. (1976)., Testing for a single outlier from a general linear regression., Biometrics, 32(3), 637-645.
  10. Kalivas J.H. (1999)., Cyclic subspace regression with analysis of the hat matrix., Chemometrics and intelligent laboratory systems, 45(1-2), 215-224.
  11. Chambers R.L. (1986)., Outlier robust finite population estimation., Journal of the American Statistical Association, 81(396), 1063-1069.
  12. Presscot C.R.D. (1981)., Approximation significance levels for detecting outlier in linear regression., Technimetrics, 23, 59-64.
  13. Noy D. and Menezes R. (2018)., Parameter estimation of the Linear Phase Correction model by hierarchical linear models., Journal of Mathematical Psychology, 84, 1-12.
  14. Ali M., Ali Z. and Choo A. (2018)., Diagnostics of single and multiple outliers on likelihood distance., AJER, 07(7), 352-357.
  15. Law M. and Jackson D. (2017)., Residual plots for linear regression models with censored outcome data: A refined method for visualizing residual uncertainty., Communications in Statistics-Simulation and Computation, 46(4), 3159-3171.
  16. Ong V.M.H., Nott D.J., Tran M.N., Sisson S.A. and Drovandi C.C. (2018)., Likelihood-free inference in high dimensions with synthetic likelihood., Computational Statistics & Data Analysis, 128, 271-291.
  17. Deunis Cook R. (1947)., Sanford Veisberg "Residuals and influence in regression., ISBN 0-412-24280-X.
  18. Schader M. and Schmid F. (1985)., Computation of ML estimates for the parameters of a negative binomial distribution from grouped data. A comparison of the scoring, Newton-Raphson and E‐M algorithms., Applied Stochastic Models and Data Analysis, 1(1), 11-23.
  19. Inahama Y. (2010)., A stochastic Taylor-like expansion in the rough path theory., Journal of Theoretical Probability, 23(3), 671-714.
  20. Landwehr J.M., Pregibon D. and Shoemaker A.C. (1984)., Graphical methods for assessing logistic regression models., Journal of the American Statistical Association, 79(385), 61-71.