New methodological approaches within criminology

A key aim of AQMeN was to develop new methodologies using quantitative data. Within the crime and victimisation strand, we have developed several projects using crime data that have made a significant contribution to methodological development within the field of criminology. Further details of these projects are given below.

(1) Modelling Escalation in Crime Seriousness (Francis and Liu)
Latent variable models are used to assess escalation in crime seriousness. The aim of this work was, firstly, to contrast a mixed-effects approach to modelling crime escalation with a latent variable approach (i.e. examine whether there are specific subgroups of offenders with distinct seriousness trajectory shapes); and secondly, to compare mixed-effects modelling used in previous work on escalation with group-based trajectory modelling and growth mixture modelling (mixture of mixed-effects models). We suggest that mixture models are necessary in modelling crime seriousness, that growth mixture models rather than group-based trajectory models provide the best fit to the data, and that R gives the best software environment for comparing models. Substantively, we identified three latent groups, with the largest group showing crime seriousness increases with criminal justice experience (measured through number of conviction occasions) and decreases with increasing age. The other two groups showed more dramatic non-linear effects with age, and non-significant effects of criminal justice experience.

Further information:
Francis, B. and Liu, J (2015) Modelling Escalation in Crime Seriousness: a Latent Variable Approach. Metron. 73(2): 277-297. DOI: 10.1007/s40300-015-0073-4

Francis, B. and Liu, J. (2016) Can we predict escalation in crime seriousness among offenders? AQMeN Research Briefing Paper 10

(2) Investigating the relationship between the diversity index and frequency of offending (Francis and Humphreys)
Recent work has suggested that specialization is correlated with frequency of offending, but this relationship may depend on the measurement used. The diversity index is a common method of measuring specialization, so we investigated whether the correlation between specialization and frequency of offending was due in part to the mathematical form of the diversity index itself. The criminological question as to whether specialization increases or decreases with offence frequency cannot be answered until the behaviour of the diversity index is better understood. We used simulations from known distributions of offending (from the UK Police National Computer) to investigate the behaviour of the diversity index where the number of crimes was small (the small sample problem). We found that the diversity index increased steeply with the frequency of offending at low frequencies, but this slowed around N=20 and became flat at N=500. This observed relationship can be used to correct the diversity index to allow the true relationship of specialization with offence frequency to be investigated. We recommend that the diversity index be used with caution when there are small numbers of crimes over fixed time periods. Any increase or decrease of the diversity index over the criminal career life course may reflect the behaviour of the measurement tool with the number of offences, rather than any change in specialization itself. Applying one of the suggested suitable correction methods to the diversity index will mitigate this problem.

Further information:
Francis, B. and Humphreys, L. (2016) Investigating the relationship between the diversity index and frequency of offending. Journal of Developmental and Life Course Criminology, 2(4): 397-416. DOI: 10.1007/s40865-016-0034-5

(3) Smoothing group-based trajectory models through B-splines (Francis, Elliot and Weldon)
Polynomials are commonly used to estimate trajectory shape in group-based trajectory models. However, they can cause undesirable curve shapes, such as uplifts at the end of the trajectory, which may not be present in the data. In addition, polynomial curves are global, meaning that a data point at one end of the trajectory can affect the shape of the curve at the other end. As an alternative to polynomials, we investigated the use of B-spline smoothers when estimating trajectory shape in group-based trajectory models. Using data from the UK Offenders Index 1963 birth cohort, we fitted models with Latent Gold to estimate the number of knots of the B-spline, as well as the number of groups. We found that B-splines provided a better fit to the observed data than cubic polynomials. The three offending trajectory groups we found corresponded to the classic groups of adolescent-limited, low-rate chronic and high-rate chronic which were proposed by Moffitt et al. The shapes of the two chronic trajectory curves from the B-spline fitting were more consistent with the life-course persistent nature of chronic offending than the traditional cubic polynomial curves. A simulation model also showed improved performance of the B-spline over cubic polynomials. We conclude that B-splines should be used when fitting group-based trajectory models.

Further information:
Francis, B., Elliott, A. and Weldon, M. (2016) Smoothing group-based trajectory models through B-splines. Journal of Developmental and Life Course Criminology, 2(1): 113-133. DOI: 10.1007/s40865-016-0025-6

Brian Francis
Susan McVie
Leslie Humphreys