Jaccard’s heel : are radex models of criminal behaviour falsifiable when derived using Jaccard coefficient?

Purpose. This article considers whether the modular facet of popular ‘radex’ models of offender behaviour is falsifiable or a statistical inevitability when using Jaccard coefficient, as evidence from other domains suggests. Method. Data equivalent to that examined in previous papers, and artificial data varying on four parameters, were examined using the conventional procedure of deriving Jaccard coefficients and submitting these to a smallest space analyses (SSA-I). The parameters were number of variables, number of cases, highest frequency of variable occurrence, and distribution of occurrences. Evidence of a modular pattern in each SSA-I solution was assessed using one qualitative and two quantitative measures. Results. When variables were free to occur in more than 50% of cases, none of the Jaccard-based SSA-I solutions supported the null hypothesis of no modular facet. This contrasts equivalent analyses using Yules Q, where 95.7% of the solutions supported the null hypothesis. When variables were restricted to occur in less than 50% of cases, the number of solutions supporting the null hypothesis changes to .003 and 78%, respectively. Analyses of the artificial data found that reducing the number of variables in a Jaccard-based solution increased the likelihood of supporting the null hypothesis, which suggests that these solutions are structured by variable occurrence (i.e., frequency) rather than variable co-occurrence. Implications. Research using Jaccard coefficient to measure co-occurrences among behaviours should not claim that the modular facet of their radex model is an empirical finding. Unfortunately, this is many of the existing publications.