The Analysis of Bounded Count Data in Criminology
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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.
KeywordsBinomial regression Variety scores Count data Poisson regression Negative binomial regression
- Cameron C, Trivedi P (1998) Models for count data. Cambridge University Press, New YorkGoogle Scholar
- 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. http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=906844
- Hindelang MJ, Hirschi T, Weis JG (1981) Measuring delinquency. Sage Publications, Beverly HillsGoogle Scholar
- Hirschi T (1969) Causes of delinquency. University of California Press, BerkeleyGoogle Scholar
- Long JS (1997) Regression models for categorical and limited dependent variables. Advanced quantitative techniques in the social sciences. Sage, Thousand OaksGoogle Scholar
- Winkelmann R (2008) Econometric analysis of count data. Springer, New YorkGoogle Scholar