Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 32 No. 1 (2014): Revista Integración, temas de matemáticas
Research and Innovation Articles

Test for homogeneity of the dispersion for overdispersed proportions data through beta regression

PDF (Español (España)) HTML (Español (España))
  • Mario Morales,
  • Jose Lozano
Mario Morales
Universidad de Córdoba
Jose Lozano
Universidad de Antioquia

Published 2014-05-22

Keywords

  • Overdispersion,
  • proportion data,
  • beta regression,
  • likelihood ratio,
  • generalized linear models

How to Cite

Morales, M., & Lozano, J. (2014). Test for homogeneity of the dispersion for overdispersed proportions data through beta regression. Revista Integración, Temas De matemáticas, 32(1), 55–70. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4063

Abstract

In this paper we propose an approach to validate the hypothesis of homogeneity of the dispersion parameter using beta regression, when we have overdispersed proportions data. We corroborated that it is possible to analyze this type of data with an usual weighted generalized linear model, weighting the observations with weights obtained through beta regression. This procedure allows to correct the problem of overdispersion keeping the simplicity of the analysis. Furthermore, for several cases, we made a simulation study of the power of the test.

To cite this article: M. Morales, J. Lozano, Prueba de homogeneidad de la dispersión para datos de proporción sobredispersos mediante regresión beta, Rev. Integr. Temas Mat. 32 (2014), no. 1, 55–70.

PDF (Español (España)) HTML (Español (España))

Downloads

Download data is not yet available.

References

  1. Atkison A., Plots, Tranformations and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis, Oxford University Press, New York, 1985.
  2. Barrios D.E. y Peña E., “Obtención de un empaque antimicrobiano a partir de almidon de ñame con adición de sorbato de potasio para su aplicación en la conservación de ñame minimamente procesado”, Tesis, Programa de Ingeniería de Alimentos, Universidad de Córdoba, 2009.
  3. Brooks R.J., “Approximate Likelihood-Ratio Test in the Analysis of Beta-Binomial Data”, Stat. Appl. 12 (1978), 1589–1596.
  4. Cox D.R. and Hinkley D.V., Theoretical Statistics, Chapman & Hall, London, 1974.
  5. Cook R.D., “Detection of Influencial Observations in Linear Regression”, Technometrics 19 (1977), 15–18.
  6. Crowder M.J. “Beta-Binomial Anova for Proportions”, Appl. Stat. 27 (1978), no. 1, 34–37.
  7. Crowder M.J., “Inference About the Intraclass Correlation Coefficient in the Beta–binomial ANOVA for Proportions”, J. R. Stat. Soc. 41 (1979), no. 2, 230–234.
  8. Dobson A.J., An Introduction to Generalized Linear Models, Chapman & Hall/CRC, New York, 2 ed., 2002.
  9. Ferrari S.L.P. and Cribari-Neto F., “Beta Regression for Modelling Rates and Proportions”, J. Appl. Stat. 31 (2004), no. 7, 799–815.
  10. Gordon K.S., Optimization and Nonlinear Equations, Encyclopedia of Biostatistics, Chichester, 1998.
  11. Hinde J. and Demétrio C., Overdispersion: Models and Estimation, ABE, São Pablo, 1998.
  12. Nocedal J. and Wright S.J., Numerical Optimization, Springer–Verlag, New York, 1999.
  13. McCullagh P. and Nelder J., Generalized Linear Models, Chapmann & Hall/CRC, New York, 1989.
  14. Mood A., Graybill F., and Boes D., Introduction to the theory of statistics, McGraw–Hill, 3 ed., 1974.
  15. Moore D.F. and Tsiatis A., “Robust Estimation of the Variance in Moment Methods for Extra-binomial and Extra-Poisson Variation”, Biometrics 47 (1991), 383–401.
  16. Morales M.A. & López L.A., “Estudio de homogeneidad de la dispersión en diseño a una vía de clasificación para datos de proporciones y conteos”, Rev. Colombiana Estadíst. 32
  17. (2009), no. 1, 59–78.
  18. Nelder J.A. and Wedderburn D.W.M., “Generalized Linear Models”, J. R. Stat. Soc. Ser. A 135 (1972), no. 3, 370–384.
  19. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P., Numerical recipes in C: the art of scientific computing, Cambridge University Press, New York, 2 edition, 1992.
  20. R Development Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2012, URL
  21. http://www.r-project.org.
  22. Ravishanker N. and Dey D.K., A First Course in Linear Model Theory, Chapman & Hall/CRC, New York, 2001.
  23. Simas A., Barreto-Souza W., and Rocha A., “Improved Estimators for a General Class of Beta Regression Models”, Comput. Statist. Data Anal. 54 (2010), no. 2, 348–366.
  24. Smithson M. and Verkuilen J., “A Better Lemon Squeezer? Maximum–Likelihood Regression with Beta–Distributed Depedent Variables”, Psychological Methods 11 (2006), no. 1,
  25. –71.