A Comparison of Logistic Regression and Classification Tree Analysis for Behavioural Case Linkage

Abstract

Much previous research on behavioural case linkage has used binary logistic regression to build predictive models that can discriminate between linked and unlinked offences. However, classification tree analysis has recently been proposed as a potential alternative owing to its ability to build user‐friendly and transparent predictive models. Building on previous research, the current study compares the relative ability of logistic regression analysis and classification tree analysis to construct predictive models for the purposes of case linkage. Two samples are utilised in this study: a sample of 376 serial car thefts committed in the UK and a sample of 160 serial residential burglaries committed in Finland. In both datasets, logistic regression and classification tree models achieve comparable levels of discrimination accuracy, but the classification tree models demonstrate problems in terms of reliability or usability that the logistic regression models do not. These findings suggest that future research is needed before classification tree analysis can be considered a viable alternative to logistic regression in behavioural case linkage. Copyright © 2012 John Wiley & Sons, Ltd.

Linking Crimes Using Behavioural Clues: Current Levels of Linking Accuracy and Strategies for Moving Forward

“…(), and Tonkin, Santtila, and Bull () (interestingly, levels of linking accuracy in Finnish burglaries appear to be substantially higher; Tonkin, Santtila et al ., ). The AUC ranges in studies of car theft are also very wide (0.54–0.93 in Davies et al ., ; 0.56–0.81 in Tonkin et al ., ; and 0.50–0.82 in Tonkin, Woodhams, Bull, Bond, & Santtila, ), as is the range in the lone study of personal robbery (0.45–0.92; Burrell et al ., ).…”

“…Upon examination of the studies in the , there seems to be relatively consistent variation from one behavioural domain to the next in terms of the AUC. The most consistent finding is that inter‐crime distance and temporal proximity are associated with some of the largest AUC values, and these values often exceed the AUCs associated with more common MO behaviours (such as the type of home that was targeted in a burglary or what property was stolen; Bennell & Canter, ; Bennell & Jones, ; Markson et al ., ; Tonkin, Santtila et al ., ; Tonkin, Woodhams, Bull, Bond, & Santtila, ). As Tonkin (forthcoming) has noted, similar findings have also been observed with car theft (Davies et al ., ; Tonkin et al ., ) and personal robbery (Burrell et al ., ), but research examining the potential value of spatial and temporal variables in cases of sexual assault/rape and homicide is lacking.…”

“…The majority of linking studies that report AUCs (approximately 68%) have relied on logistic regression analysis to develop linking models. One study used both logistic regression and classification tree analysis (Tonkin, Woodhams, Bull, Bond, & Santtila, ), and one study used discriminant function analysis and naïve Bayesian classifiers (Winter et al ., ). The remaining studies used only ROC analysis without an accompanying prediction tool (e.g.…”

“…That being said, it does appear that logistic regression can sometimes produce slightly higher AUCs than other statistical techniques. For example, Tonkin, Woodhams, Bull, Bond, & Santtila () used a sample of residential burglaries to compare the performance of iterative classification trees (ICT) to stepwise logistic regression modelling and found that, although both procedures selected the same predictors (i.e. inter‐crime distance, internal behaviours, and entry behaviours), the logistic regression model (AUC = 0.87) outperformed the ICT model (AUC = 0.80), but not significantly.…”

“…Instead, linking accuracy will likely be maximised by carefully considering multiple factors, including the behaviours focused on in the analysis, the way these behaviours are operationalised, the method used to assess across‐crime similarity, and the statistical technique used to analyse similarity scores (e.g. refer to Davies, Tonkin, Bull, & Bond, ; Ellingwood, Mugford, Melnyk, Bennell, & Fritzon, ; Tonkin, Woodhams, Bull, Bond, & Santtila, for explorations of these various issues). To achieve this goal, we must first understand how good we are currently at detecting crime linkages.…”