Journal of Quantitative Criminology

, Volume 34, Issue 2, pp 591–607 | Cite as

The Analysis of Bounded Count Data in Criminology

  • Chester L. Britt
  • Michael RocqueEmail author
  • Gregory M. Zimmerman
Original Paper



Criminological research utilizes several types of delinquency scales, including frequency counts and, increasingly, variety scores. The latter counts the number of distinct types of crimes an individual has committed. Often, variety scores are modeled via count regression techniques (e.g., Poisson, negative binomial), which are best suited to the analysis of unbounded count data. Variety scores, however, are inherently bounded.


We review common regression approaches for count data and then advocate for a different, more suitable approach for variety scores—binomial regression, and zero-inflated binomial regression, which allow one to consider variety scores as a series of binomial trials, thus accounting for bounding. We provide a demonstration with two simulations and data from the Fayetteville Youth Study.


Binomial regression generally performs better than traditional regression models when modeling variety scores. Importantly, the interpretation of binomial regression models is straightforward and related to the more familiar logistic regression. We recommend researchers use binomial regression models when faced with variety delinquency scores.


Binomial regression Variety scores Count data Poisson regression Negative binomial regression 


  1. Bendixen M, Endresen IM, Olweus D (2003) Variety and frequency scales of antisocial involvement: which one is better? Legal Criminol Psychol 8:135–150CrossRefGoogle Scholar
  2. Berk R, MacDonald JM (2008) Overdispersion and Poisson regression. J Quant Criminol 24:269–284CrossRefGoogle Scholar
  3. Burt CH, Simons RL (2013) Self-control, thrill seeking, and crime motivation matters. Crim Justice Behav 40:1326–1348CrossRefGoogle Scholar
  4. Cameron C, Trivedi P (1998) Models for count data. Cambridge University Press, New YorkGoogle Scholar
  5. Cheng SL, Micheals R, Lu ZQJ (2010) Comparison of confidence intervals for large operational biometric data by parametric and non-parametric methods. NISTIR 7740. U. S. Department of Commerce, National Institute of Standards and Technology.
  6. Decker S, Katz C, Webb VJ (2008) Understanding the black box of gang organization. Crime Delinq 54:153–172CrossRefGoogle Scholar
  7. Elliott DS, Ageton SS (1980) Reconciling race and class differences in self-reported and official estimates of delinquency. Am Sociol Rev 45:95–110CrossRefGoogle Scholar
  8. Esbensen FA, Osgood DW, Peterson D, Taylor TJ, Carson DC (2013) Short-and long-term outcome results from a multisite evaluation of the GREAT program. Criminol Public Policy 12:375–411CrossRefGoogle Scholar
  9. Hilbe JM (2011) Negative binomial regression. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  10. Hindelang MJ, Hirschi T, Weis JG (1979) Correlates of delinquency: the illusion of discrepancy between self-report and official measures. Am Sociol Rev 44:995–1014CrossRefGoogle Scholar
  11. Hindelang MJ, Hirschi T, Weis JG (1981) Measuring delinquency. Sage Publications, Beverly HillsGoogle Scholar
  12. Hirschi T (1969) Causes of delinquency. University of California Press, BerkeleyGoogle Scholar
  13. Long JS (1997) Regression models for categorical and limited dependent variables. Advanced quantitative techniques in the social sciences. Sage, Thousand OaksGoogle Scholar
  14. Lussier P, LeBlanc M, Proulx J (2005) The generality of criminal behavior: a confirmatory factor analysis of the criminal activity of sex offenders in adulthood. J Crim Justice 33:177–189CrossRefGoogle Scholar
  15. MacDonald JM, Lattimore PK (2010) Count models in criminology. In: Piquero AR, Weisburd D (eds) Handbook of quantitative criminology. Springer, New York, pp 683–698CrossRefGoogle Scholar
  16. McCullagh P, Nelder JA (1989) Generalized linear models. Chapman & Hall, New YorkCrossRefGoogle Scholar
  17. Osgood DW (2000) Poisson-based regression analysis of aggregate crime rates. J Quant Criminol 16:21–43CrossRefGoogle Scholar
  18. Osgood DW, McMorris BJ, Potenza MT (2002) Analyzing multiple-item measures of crime and deviance I: item response theory scaling. J Quant Criminol 18:267–296CrossRefGoogle Scholar
  19. Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling: multilevel, longitudinal, and structural equation models. CRC Press, Boca RatonCrossRefGoogle Scholar
  20. Sweeten G (2012) Scaling criminal offending. J Quant Criminol 28:533–557CrossRefGoogle Scholar
  21. Sweeten G, Piquero AR, Steinberg L (2013) Age and the explanation of crime, revisited. J Youth Adolesc 42:921–938CrossRefGoogle Scholar
  22. Tittle CR, Villemez WJ, Smith DA (1978) The myth of social class and criminality: an empirical assessment of the empirical evidence. Am Sociol Rev 43:643–656CrossRefGoogle Scholar
  23. Welch MR, Tittle CR, Yonkoski J, Meidinger N, Grasmick HG (2008) Social integration, self-control, and conformity. J Quant Criminol 24:73–92CrossRefGoogle Scholar
  24. Winkelmann R (2008) Econometric analysis of count data. Springer, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Chester L. Britt
    • 1
  • Michael Rocque
    • 2
    Email author
  • Gregory M. Zimmerman
    • 3
  1. 1.Department of SociologyIowa State UniversityAmesUSA
  2. 2.Department of SociologyBates CollegeLewistonUSA
  3. 3.School of Criminology and Criminal JusticeNortheastern UniversityBostonUSA

Personalised recommendations