Models for Underreporting: A Bernoulli Sampling Approach for Reported Counts

Authors

  • Gerhard Neubauer Joanneum Research, Graz Austria
  • Gordana Djuraš Joanneum Research, Graz Austria
  • Herwig Friedl Graz University of Technology, Austria

DOI:

https://doi.org/10.17713/ajs.v40i1&2.200

Abstract

Underreporting in register systems can be analyzed using a binomial approach, where both the size and the probability parameter have to be estimated. Parameter estimation fails when overdispersion is present. Extensions of the binomial model are derived by randomizing the parameters, i.e. considering mixed models. Among these models are the beta-binomial, which results from allowing for a random reporting probability; the negativebinomial, that is the marginal when the size parameter is randomized; and the
beta-Poisson model, where both binomial parameters are considered random. Likelihood based estimation is developed and inference issues are discussed. Finally the method is applied to data from the Austrian crime register.

References

Allcroft, D. J., and Glasbey, C. A. (2003). A simulation-based method for model evaluation. Statistical Modelling, 3, 1-14.

Burnham, K. P., and Anderson, D. R. (1998). Model Selection and Inference: A Practical Information-Theoretic Approach. New York: Springer.

Consul, P. C. (1989). Generalized Poisson Distributions. Properties and Applications. New York: Marcel Dekker.

Johnson, N. L., Kemp, A. W., and Kotz, S. (2005). Univariate Discrete Distributions. Hoboken: Wiley.

Neubauer, G., and Djuraš, G. (2008). A generalized Poisson model for underreporting. In P. Eilers (Ed.), Proceedings of the 23rd International Workshop on Statistical Modelling. Utrecht, 7-11 July 2008 (p. 368-373).

Neubauer, G., and Djuraš, G. (2009). A beta-Poisson model for underreporting. In J. Booth (Ed.), Proceedings of the 24th International Workshop on Statistical Modelling. Ithaca, NY, 20-24 July 2009 (p. 255-260).

Neubauer, G., Djuraš, G., and Friedl, H. (2009). Maximum Likelihood for Size-Estimation: Some Results on Properties and Limitations. (Tech. Rep. No. 4). Graz: Joanneum Research.

Neubauer, G., and Friedl, H. (2006). Modelling sample sizes of frequencies. In J. Hinde, J. Einbeck, and J. Newell (Eds.), Proceedings of the 21st International Workshop on Statistical Modelling. Galway, Ireland, 3-7 July 2006 (p. 401-408).

Winkelmann, R. (2000). Econometric Analysis of Count Data. Berlin: Springer.

Downloads

Published

2016-02-24

How to Cite

Neubauer, G., Djuraš, G., & Friedl, H. (2016). Models for Underreporting: A Bernoulli Sampling Approach for Reported Counts. Austrian Journal of Statistics, 40(1&2), 85–92. https://doi.org/10.17713/ajs.v40i1&2.200

Issue

Vol. 40 No. 1&2 (2011)

Section

Articles

License

The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. 

The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.

Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.

 

Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.