Abstract
Studies have shown that it is possible to link serial crimes in an accurate fashion based on the statistical analysis of crime scene information. Logistic regression (LR) is one of the most common statistical methods in use and yields relatively accurate linking decisions. However, some research suggests there may be added value in using classification tree (CT) analysis to discriminate between offences committed by the same vs. different offenders. This study explored how three variations of CT analysis can be applied to the crime linkage task. Drawing on a sample of serial sexual assaults from Quebec, Canada, we examine the predictive accuracy of standard, iterative, and multiple CTs, and we contrast the results with LR analysis. Our results revealed that all statistical approaches achieved relatively high (and similar) levels of predictive accuracy, but CTs produce idiographic linking strategies that may be more appealing to practitioners. Future research will need to examine if and how these CTs can be useful as decision aides in operational settings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Other, nonbinary types of linkage decisions can be made (e.g. rank-ordering crime pairs based on probability values), but we will focus in this paper on binary, forced-choice linkage decisions.
A range of empirical methods are available to determine what threshold should be used for this purpose. See Swets et al. (2000) for a discussion of these methods.
Overfitting occurs when a statistical model applies well to the data used to construct the model; however, it is a poor fit for data that was not used to construct the model (Wang et al. 2010).
Note that Tonkin et al. (2012b) also attempted to examine ICTs, but their data did not allow such a model to be developed.
For each of the 10 models, a score of − 1 was provided to a participant if they were in the low-risk category for that model, a score of 0 was provided if they were unclassified, and a score of + 1 was provided if they were in the high-risk category. For each participant, these 10 model scores were then summed to provide the combined risk score.
In addition to these general procedures, a variety of user-specified decisions related to model parameters needed to be made when constructing CTs for the development and test samples. These included the selection of the particular chi-square test used for splitting the data according to the predictors, the level of significance set for these tests, the maximum number of intervals that the continuous predictors can be separated into, the minimum number of cases that must be present in each successive node, and the maximum tree depth allowed. First, in terms of the chi-square test used for determining node splitting, the likelihood ratio chi-square test was selected. Second, although the default significance level for partitioning nodes in SPSS is p < 0.05, it was decided to adjust this to p < 0.01 because the samples are relatively large, and a more conservative significance level makes it less likely that the resulting models capitalise on chance. Third, the default level of 10 was used as the maximum number of categories permitted to separate the continuous predictors. Fourth, we decided to maintain the default levels of 100 and 50 cases for parent and child nodes, respectively. Finally, although the SPSS default for tree depth is three, tree depth was set to the number of predictors involved in the analysis to ensure that each predictor had at least one chance to be included in the tree.
This was only done for this analysis. The full set of linked and unlinked crime pairs were used to develop and evaluate the LR, CT, ICT, and multiple CT/ICT models.
Readers may note that the rank-order of variables (based on their predictive power) changes depending on whether the results from the LR analysis or ROC analysis are relied on. Similar findings have been highlighted by others (e.g. Demler et al. 2011). We tend to rely on the results from ROC analysis in these cases, but future research should explore this issue in more depth.
The full CT graphic is too large to present in its entirety here.
There were an additional 6 pathways to making a linked decision using the ICT. Given that the CT and ICT resulted in similar levels of predictive accuracy, only the standard CT pathways will be discussed here for the sake of brevity.
We would like to thank one of the anonymous reviewers for bringing these issues to our attention.
References
Banks S, Robbins PC, Silver E, Vesselinov R, Steadman HJ, Monahan J, ... Roth LH (2004) A multiple-models approach to violence risk assessment among people with mental disorder. Crim Justice Behav 31(3):324–340
Beauregard E (2005) Hunting process of serial sex offenders: a rationale choice approach (Unpublished doctoral dissertation). University of Montreal, Canada
Beauregard E, Leclerc B, Lussier P (2012) Decision making in the crime commission process: comparing rapists, child molesters, and victim-crossover sex offenders. Crim Justice Behav 39:1275–1295
Bennell C (2002) Behavioural consistency and discrimination in serial burglary (Unpublished doctoral dissertation). University of Liverpool, UK
Bennell C, Canter DV (2002) Linking commercial burglaries by modus operandi: tests using regression and ROC analysis. Sci Justice 42(3):153–164
Bennell C, Jones NJ (2005) Between a ROC and a hard place: a method for linking serial burglaries by modus operandi. J Investig Psychol Offender Profiling 2(1):23–41
Bennell C, Jones NJ, Melnyk T (2009) Addressing problems with traditional crime linkage methods using receiver operating characteristic analysis. Leg Criminol Psychol 14(2):293–310
Bennell C, Mugford R, Ellingwood H, Woodhams J (2014) Linking crimes using behavioural clues: current levels of linking accuracy and strategies for moving forward. J Investig Psychol Offender Profiling 11:29–56
Brookman F (2010) Beyond the interview: complementing and validating accounts of incarcerated violent offenders. In Bernasco W (ed), Offenders on offending: Learning about crime from criminals (pp 84–105). Portland, OR: Willan
Demler OV, Pencina MJ, D’Agostino RB Sr (2011) Equivalence of improvement in area under ROC curve and linear discriminant analysis coefficient under assumption of normality. Stat Med 30(12):1410–1418
Deslauriers-Varin N, Beauregard E (2013) Investigating offending consistency of geographic and environmental factors among serial sex offenders a comparison of multiple analytical strategies. Crim Justice Behav 40(2):156–179
Everitt BS (2002) The Cambridge dictionary of statistics, 2nd edn. Cambridge University Press, Cambridge, UK
Field A (2013) Discovering statistics using SPSS (and sex, drugs, and rock ‘n’ roll), 4th edn. Sage Publications Inc., Thousand Oaks, CA
Gee D, Belofastov A (2014) Sex crime linkage: sexual fantasy and offense plasticity. In: Woodhams J, Bennell C (eds) Crime linkage: Theory, research, and practice. CRC Press, Boca Raton, FL, pp 33–53
Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29–36
Hart SD, Douglas KS, Guy LS (2017) The structured professional judgement approach to violence risk assessment: origins, nature, and advances. In: Boer DP, Beech AR, Ward T, Craig LA, Rettenberger M, Marshall LE, Marshall WL (eds) The Wiley handbook on the theories, assessment, and treatment of sexual offending. Wiley Blackwell, pp 643–666
Hewitt A, Beauregard E, Davies G (2012) “Catch and release”: predicting encounter and victim release location choice in serial rape events. Policing 35:835–856
Jaccard P (1908) Nouvelle recherches sur la distribution florale. Bulletin De La Soc Vaud Des Sci Nat 44:223–270
Lundrigan S, Czarnomski S, Wilson M (2010) Spatial and environmental consistency in serial sexual assault. J Investig Psychol Offender Profiling 7:15–30
Monahan J, Steadman HJ, Silver E, Appelbaum PS, Robbins PC, ... Banks S (2001) Rethinking risk assessment: the MacArthur study of mental disorder and violence. Oxford University Press, New York, NY
Reid JA, Beauregard E, Fedina KM, Frith EN (2014) Employing mixed methods to explore motivational patterns of repeat sex offenders. J Crim Just 42:203–212
Rosenthal R (1991) Effect sizes: Pearson's correlation, its display via the BESD, and alternative indices. Am Psychol 46(10):1086–1087
Swets JA (1988) Measuring the accuracy of diagnostic systems. Science 240(4857):1285–1293
Swets JA, Dawes RM, Monahan J (2000) Psychological science can improve diagnostic decisions. Psychol Sci Public Interest 1(1):1–26
Thongkam J, Xu G, Zhang Y 2008) AdaBoost algorithm with random forests for predicting breast cancer survivability. In 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence) (pp 3062–3069). IEEE
Tonkin M, Pakkanen T, Siren J, Bennell C, Woodhams J, Burrell A, ... Santtila P (2017) Using offender crime scene behavior to link stranger sexual assaults: a comparison of three statistical approaches. J Crim Just 50:19–28
Tonkin M, Woodhams J (2015) The feasibility of using crime scene behaviour to detect versatile serial offenders: an empirical test of behavioural consistency, distinctiveness, and discrimination. Leg Criminol Psychol 22(1):99–115
Tonkin M, Woodhams J, Bull R, Bond JW (2012a) Behavioural case linkage with solved and unsolved crimes. Forensic Sci Int 222(1–3):146–153
Tonkin M, Woodhams J, Bull R, Bond JW, Santtila P (2012b) A comparison of logistic regression and classification tree analysis for behavioural case linkage. J Investig Psychol Offender Profiling 9:235–258
Wang T, Qin Z, Jin Z, Zhang S (2010) Handling over-fitting in test cost-sensitive decision tree learning by feature selection, smoothing and pruning. J Syst Softw 83(7):1137–1147
Winter JM, Lemeire J, Meganck S, Geboers J, Rossi G, Mokros A (2013) Comparing the predictive accuracy of case linkage methods in serious sexual assaults. J Investig Psychol Offender Profiling 10:28–56
Woodhams J, Komarzynska K (2014) The effect of mental disorder on crime scene behaviour, its consistency, and variability. In: Woodhams J, Bennell C (eds) Crime linkage: Theory, research, and practice. CRC Press, Boca Raton, FL, pp 55–82
Woodhams J, Tonkin M, Burrell A, Imre H, Winter JM, Lam EK, Santtila P (2019) Linking serial sexual offences: moving towards an ecologically valid test of the principles of crime linkage. Leg Criminol Psychol 24(1):123–140
Funding
This research was supported by an award from the British Academy, which was provided to JW.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethics Approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bennell, C., Mugford, R., Woodhams, J. et al. Linking Serial Sex Offences Using Standard, Iterative, and Multiple Classification Trees. J Police Crim Psych 36, 691–705 (2021). https://doi.org/10.1007/s11896-021-09483-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11896-021-09483-6