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Understanding How Offending Prevalence and Frequency Change with Age in the Cambridge Study in Delinquent Development Using Bayesian Statistical Models

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Abstract

Objectives

To provide a detailed understanding of how the prevalence and frequency of offending vary with age in the Cambridge Study in Delinquent Development (CSDD) and to quantify the influence of early childhood risk factors such as high troublesomeness on this variation.

Methods

We develop a statistical model for the prevalence and frequency of offending based on the hurdle model and curves called splines that allow smooth variation with age. We use the Bayesian framework to quantify estimation uncertainty. We also test a model that assumes that frequency is constant across all ages.

Results

For 346 males from the CSDD for whom the number of offenses at all ages from 10 to 61 are recorded, we found peaks in the prevalence of offending around ages 16 to 18. Whilst there were strong differences in prevalence between males of high troublesomeness and those of lower troublesomeness up to age 45, the level of troublesomeness had a weaker effect on the frequency of offenses, and this lasted only up to age 20. The risk factors of low nonverbal IQ, poor parental supervision and low family income affect how prevalence varies with age in a similar way, but their influence on the variation of frequency with age is considerably weaker. We also provide examples of quantifying the uncertainty associated with estimates of interesting quantities such as variations in offending prevalence across levels of troublesomeness.

Conclusions

Our methodology provides a quantified understanding of the effects of risk factors on age-crime curves. Our visualizations allow these to be easily presented and interpreted.

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Acknowledgements

For funding the CSDD, we are grateful to the Home Office, the Department of Health, the Department of Education, the Rayne Foundation, the Barrow Cadbury Trust, and the Smith-Richardson Foundation. For carrying out criminal record searches, we are grateful to Gwen Gundry in the 1960s and 1970s, Lynda Morley in the 1980s, Sandra Lambert in the 1990s, Debbie Wilson in the 2000s, Owen Thomas in 2011–2012 and Lisa Robinson in 2017. We also thank Tim Cole, UCL GOS Institute of Child Health, for introducing us to his work on SITAR models, and Mario Cortina-Borja, Hugh Davies, John Eales, and David Teague for interesting conversations about statistical inference and criminal behavior.

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Authors and Affiliations

  1. Centre for Mathematical Sciences, School of Engineering, Computing and Mathematics, University of Plymouth, Plymouth, PL8 2AP, UK

    Julian Stander

  2. Institute of Criminology, University of Cambridge, Sidgwick Avenue, Cambridge, CB3 9DA, UK

    David P. Farrington

  3. University of Plymouth, Plymouth, UK

    Caroline Lubert

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  1. Julian Stander
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Corresponding author

Correspondence to Julian Stander.

Appendix: Further Analysis of CSDD Risk Factors

Appendix: Further Analysis of CSDD Risk Factors

Results for Some Other Risk Factors

Figures 4, 5 and 6 show results similar to Fig. 3 for low nonverbal IQ, poor parental supervision and low family income.

Fig. 4
figure 4

Age-crime curves for low nonverbal IQ

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Fig. 5
figure 5

Age-crime curves for poor parental supervision

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Fig. 6
figure 6

Age-crime curves for low family income

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Stander, J., Farrington, D.P. & Lubert, C. Understanding How Offending Prevalence and Frequency Change with Age in the Cambridge Study in Delinquent Development Using Bayesian Statistical Models. J Quant Criminol 39, 583–601 (2023). https://doi.org/10.1007/s10940-022-09544-x

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