In defence of multidimensional scaling for the analysis of sexual offence behaviour: cautionary notes regarding analysis and interpretation

Abstract

Multidimensional scaling (MDS) has become a popular form of statistical analysis in the field of psychology and law. A recent paper in this journal by Sturidsson and colleagues (12, 221–230, 2006) used MDS to replicate an earlier study of sexual offence behaviour by Canter and Heritage (Journal of Forensic Psychiatry, 1, 185–212, 1990). They concluded that the model was not replicable and cast grave doubts on the applicability of MDS for the analysis of sexual offences. In this paper I argue that neither conclusion is correct. Initial difficulties in interpretation of the MDS results were clearly due to errors in calculation that should have been recognised. Indeed, a frequency analysis of Sturidsson and colleagues’ variables indicated that their results were in fact remarkably congruent with those of Canter and Heritage. It is concluded that statistical software should not obviate the need for a working knowledge of the statistics being computed.

Keywords:

• sexual offending
• rape
• multidimensional scaling
• profiling
• statistical analysis

Acknowledgements

The author is grateful to Professor David Canter for his helpful comments on a draft of this manuscript.

Notes

1. Swartzwelder, J. (Writer), & Moore, R. (Director). (1994). Homer the Vigilante [Television series episode]. In D. Mirkin (Executive Producer), The Simpsons. Beverly Hills, CA: Twentieth Century Fox Film Corporation.

2. Practically all studies of offending behaviour have utilised a non-metric form of MDS that represents the rank order of the associations between behaviours. This is often described as smallest space analysis (SSA). For the purposes of this paper, the term MDS will refer to this non-metric form.

3. This may explain, at least partially, why the MDS plot was a less than stellar representation of the ‘reversed similarity matrix’ (as evidenced by the high Kruskal's stress I value of 0.37).

4. From a fourfold table where a=cases of co-occurrence, b and c=cases of differences, and d=joint non-occurrence, the Jaccard coefficient is calculated as: a/(a+b+c). The Lance and Williams measure (also known as the Bray–Curtis nonmetric coefficient) is calculated as: (b+c)/(2a+b+c). Thus, both coefficients range from zero to one and are conceptually similar as neither takes into account joint non-occurrence of a variable. This coefficient has been successfully used in several MDS analyses of offence behaviour (e.g. Bennett, 2005; Bennett et al., in prep.; Häkkänen, Lindlof et al., 2004; Häkkänen, Puolakka et al., 2004).