A Comparative Study of Outlier Detection Methods in Poisson Regression

  • Faten Nabila Rustam AffandyEmail author
  • Sanizah Ahmad
Conference paper


Regression models using count data have a wide range of applications in engineering, econometrics, medicine and social sciences. Poisson regression models are widely used in the analysis and prediction of counts on potential independent variables. However, the presence of outliers can lead to inflated error rates and substantial distortions of parameter and statistic estimates. In this study, three methods of identification of outlier are used which are DFFITS, DFBETAS and Cook’s Square Distance (CD). The objective of the study is to investigate on the performance of the three detection methods (DFFITS, DFBETAS, and CD) in Poisson regression using simulation in R. A simulation study was performed with various regression conditions which include different number of predictors, sample sizes and percentage of outliers in the X-space, Y-pace and both X-and Y-space. The best outlier detection method is the one that can detect the most number of outliers. Results show that for outliers in X-space and Y-space, DFFITS performs better in detecting outliers for all sample sizes with low percentage of outliers while DFBETAS performs better for most of samples sizes with high percentage of outliers. In both X-and Y-space, the best method in detecting outliers for small sample size with low percentage of outliers is DFFITS. However, for large sample size, CD and DFBETAS perform better in detecting low and high percentage of outliers, respectively. Similar results were obtained when these methods were applied to a real data set.


Poisson Outlier DFFITS DFBETAS Cook’s square distance 



The authors wish to thank the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM) Shah Alam for the conference support fund.


  1. 1.
    Long, J.S.: Regression Models for Categorical and Limited Dependent Variables. SAGE Publication, New York (1997)zbMATHGoogle Scholar
  2. 2.
    Algamal, Z.Y.: Diagnostic in poisson regression models. Electron. J. Appl. Stat. Anal. 2, 178–186 (2012). Scholar
  3. 3.
    Jarrell, M.G.: A comparison of two procedures, the Mahalanobis distance and the Andrews-Pregibon statistic, for identifying multivariate outliers. Res. Sch. 1, 49–58 (1994)Google Scholar
  4. 4.
    Hawkins, D.M.: Identification of Outliers. Chapman and Hall, London (1980).
  5. 5.
    Belsley, D.A., Kuh, E., Welsch, R.E.: Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (1980).
  6. 6.
    Cook, R.D., Weisberg, S.: Residuals and Influence in Regression. Chapman & Hall, New York (1982).
  7. 7.
    Nor, A.: Investigating the performance of mallows-type estimator in logistic regression model with the presence of outliers. Dissertation Master Sci. (Appl. Sci.) (2010)Google Scholar
  8. 8.
    Oyeyemi, G.M., Bukoye, A., Akayede, I.: Comparison of outlier detection procedures in multiple linear Regression. Am. J. Math. Stat. 5(1), 37–41 (2015). Scholar
  9. 9.
    Brockmann, H.J.: Satellite male groups in horseshoe crabs. Limulus Polyphemus. Ethol. 102(1), 1–21 (1996). Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA Shah AlamShah AlamMalaysia

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