Skip to main content
Log in

Multiple deletion diagnostics in beta regression models

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

We consider the problem of identifying multiple outliers in a general class of beta regression models proposed by Ferrari and Cribari-Neto (J Appl Stat 31:799–815, 2004). The currently available single-case deletion diagnostic measures, e.g., the standardized weighted residual (SWR), the Cook-like distance (LD), etc., often fail to identify multiple outlying observations, because they suffer from the well-known problems of masking and swamping effects. In this article, we develop group deletion diagnostic measures, such as generalized SWR, generalized LD, generalized DFFITS and generalized DFBETAS, and suggest a simple procedure for identifying multiple outliers using these. The performance of the proposed methods is investigated through simulation studies and two practical examples.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Atkinson AC (1994) Fast very robust methods for the detection of multiple outliers. J Am Stat Assoc 89:1329–1339

    Article  MATH  Google Scholar 

  • Atkinson AC, Riani M (2000) Robust diagnostic regression analysis. Springer, New York

    Book  MATH  Google Scholar 

  • Atkinson AC, Riani M, Cerioli A (2010) The forward search: theory and data analysis (with discussion). J Korean Stat Soc 39:117–134

    Article  MathSciNet  Google Scholar 

  • Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York

    Book  MATH  Google Scholar 

  • Cribari-Neto F, Zeileis A (2010) Beta regression in R. J Stat Softw 34:1–24

    Google Scholar 

  • Espinheira PL, Ferrari SLP, Cribari-Neto F (2008a) On beta regression residuals. J Appl Stat 35:407–419

    Article  MathSciNet  MATH  Google Scholar 

  • Espinheira PL, Ferrari SLP, Cribari-Neto F (2008b) Influence diagnostics in beta regression. Comput Stat Data Anal 52:4417–4431

    Article  MathSciNet  MATH  Google Scholar 

  • Ferrari SLP, Cribari-Neto F (2004) Beta regression for modeling rates and proportions. J Appl Stat 31: 799–815

    Article  MathSciNet  MATH  Google Scholar 

  • Hadi AS, Simonoff JS (1993) Procedures for the identification of multiple outliers in linear models. J Am Stat Assoc 88:1264–1272

    Article  MathSciNet  Google Scholar 

  • Imon AHMR (2005) Identifying multiple influential observations in linear regression. J Appl Stat 32: 929–946

    Article  MathSciNet  MATH  Google Scholar 

  • Imon AHMR, Hadi AS (2008) Identification of multiple outliers in logistic regression. Commun Stat Theory Methods 37:1697–1709

    Article  MathSciNet  MATH  Google Scholar 

  • Kieschnick R, McCullough BD (2003) Regression analysis of variates observed on (0, 1): percentage, proportions, fractions. Stat Model 3:193–213

    Article  MathSciNet  Google Scholar 

  • Nurunnabi AAM, Imon AHMR, Nasser M (2010) Identification of multiple influential observations in logistic regression. J Appl Stat 37:1605–1624

    Article  MathSciNet  Google Scholar 

  • Simas AB, Barreto-Souza W, Rocha AV (2010) Improved estimators for a general class of beta regression models. Comput Stat Data Anal 54:348–366

    Article  MathSciNet  MATH  Google Scholar 

  • Smithson M, Verkuilen J (2006) A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychol Methods 11:54–71

    Article  Google Scholar 

Download references

Acknowledgments

The author is deeply indebted to the associate editor and two referees for their helpful comments and suggestions that substantially improve this present version of the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li-Chu Chien.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chien, LC. Multiple deletion diagnostics in beta regression models. Comput Stat 28, 1639–1661 (2013). https://doi.org/10.1007/s00180-012-0370-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-012-0370-9

Keywords

Navigation