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Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model

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  • Peter G.M. Van Der Heijden
  • Maarten Cruyff
  • Hans C. Van Houwelingen

Abstract

The truncated Poisson regression model is used to arrive at point and interval estimates of the size of two offender populations, i.e. drunk drivers and persons who illegally possess firearms. The dependent capture–recapture variables are constructed from Dutch police records and are counts of individual arrests for both violations. The population size estimates are derived assuming that each count is a realization of a Poisson distribution, and that the Poisson parameters are related to covariates through the truncated Poisson regression model. These assumptions are discussed in detail, and the tenability of the second assumption is assessed by evaluating the marginal residuals and performing tests on overdispersion. For the firearms example, the second assumption seems to hold well, but for the drunk drivers example there is some overdispersion. It is concluded that the method is useful, provided it is used with care.

Suggested Citation

  • Peter G.M. Van Der Heijden & Maarten Cruyff & Hans C. Van Houwelingen, 2003. "Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 289-304, August.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:3:p:289-304
    DOI: 10.1111/1467-9574.00232
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    Cited by:

    1. Spencer P. Chainey & Dennis L. Lazarus, 2021. "More Offenders, More Crime: Estimating the Size of the Offender Population in a Latin American Setting," Social Sciences, MDPI, vol. 10(9), pages 1-19, September.
    2. Azam, Anahita & Hendrickx, Jef & Adriaenssens, Stef, 2021. "Estimating the Prostitution Population in the Netherlands and Belgium: A Capture-Recapture Application to Online Data," MPRA Paper 110505, University Library of Munich, Germany.
    3. Yulu Ji & Yang Liu, 2024. "A Penalized Empirical Likelihood Approach for Estimating Population Sizes under the Negative Binomial Regression Model," Mathematics, MDPI, vol. 12(17), pages 1-23, August.
    4. Mark E. Piatek & Dankmar Böhning, 2024. "Deriving a zero-truncated modelling methodology to analyse capture–recapture data from self-reported social networks," METRON, Springer;Sapienza Università di Roma, vol. 82(2), pages 135-160, August.
    5. Wen-Han Hwang & Jakub Stoklosa & Ching-Yun Wang, 2022. "Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 303-320, June.
    6. Baksh, M. Fazil & Böhning, Dankmar & Lerdsuwansri, Rattana, 2011. "An extension of an over-dispersion test for count data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 466-474, January.
    7. Marco Alfò & Dankmar Böhning & Irene Rocchetti, 2021. "Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments," Biometrics, The International Biometric Society, vol. 77(1), pages 237-248, March.
    8. Dankmar Böhning & Ekkehart Dietz & Ronny Kuhnert & Dieter Schön, 2005. "Mixture models for capture-recapture count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(1), pages 29-43, February.
    9. Lanumteang, K. & Böhning, D., 2011. "An extension of Chao's estimator of population size based on the first three capture frequency counts," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2302-2311, July.
    10. Sa-aat Niwitpong & Dankmar Böhning & Peter Heijden & Heinz Holling, 2013. "Capture–recapture estimation based upon the geometric distribution allowing for heterogeneity," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 495-519, May.
    11. Thandrayen, Joanne & Wang, Yan, 2009. "A latent variable regression model for capture-recapture data," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2740-2746, May.

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