Clustering of legal problems
It was shown in Figure 3.3 that 25.6 per cent of the Australian respondents experienced legal problems from two or more problem groups. As noted earlier, the co-occurrence of problems may reflect connections or relationships between those problems, such as:
- direct causation between the problems (e.g. one problem may trigger another)
- the problems arising from identical or similar defining circumstances (e.g. two types of problems may both require money transactions)
- people having coinciding vulnerabilities to the problems (e.g. certain demographic groups may be exceptionally vulnerable to particular types of problems).
However, it is also possible that problems sometimes coincide by chance, without there being any inherent connection or meaningful relationship between them (e.g. two problems may co-occur simply because both occur frequently in the population).
To examine whether certain types of legal problems tended to co-occur (i.e. tended to be experienced by the same respondents), a hierarchical cluster analysis was conducted on the legal problem groups using all Australian respondents. The cluster analysis placed problem groups that tended to be experienced together in the same cluster, and problem groups that tended not to be experienced together in different clusters.(13)
Figure 4.3 summarises the results of the cluster analysis for Australia in the form of a dendrogram (or tree diagram). The branches of the dendrogram join together legal problem groups that tended to co-occur, with shorter branches representing greater co-occurrence between problem groups than longer branches. The dendrogram reveals three main clusters:(14)
Figure 4.3: Dendrogram — clustering of problem groups, Australia
Note: N=20 716 respondents. The cluster analysis used complete linkage with Jaccard scores.
- The first cluster was dominated by the four most frequent problem groups — namely, the consumer, crime, government and housing problem groups. However, it also included the money problem group.
- The second cluster included ‘economic and family’ issues, consisting of the credit/debt and family problem groups.
- The third cluster included ‘rights and injury/health’ issues, comprising the employment, health, personal injury and rights problem groups. The health problem group was the weakest component of this cluster. Note that many of the problems within the employment problem group involved work-related rights issues, while the rights problem group comprised rights issues unrelated to work.(15)
The finding that some problem groups clustered together suggests the possibility that these problem groups may be causally related in some way, although it is difficult to completely rule out the possibility that problems may sometimes coincide by chance rather than because of intrinsic connections. In particular, it is noteworthy that the first cluster comprised the four problem groups with the highest prevalence (see first two data columns in Table 3.2). The high volume of these types of problems increases the likelihood that they may sometimes coincide simply because they occur so frequently, rather than because of some real connection or relationship between them. The second and third clusters, however, comprised problem groups with more moderate or lower prevalence (see Table 3.2). Thus, it is less probable that these problems coincided purely by chance.
The co-occurrence of problem groups is further explored in Table 4.9, which examines the overlap between each pair of problem groups. For example, 1605 respondents experienced accidents problems, 4269 experienced consumer problems, and 540 experienced both of these types of problems. Those who experienced both types of problems represent 33.7 per cent of the 1605 respondents with accidents problems and 12.7 per cent of the 4269 respondents with consumer problems.
Table 4.9: Co-occurrence of problem groups, Australia
Note: N=20 716 respondents.
The most striking pattern in Table 4.9 is for the four problem groups with the highest prevalence, which dominated the first cluster — namely, the consumer, crime, government and housing problem groups. Generally, these four problem groups had a high degree of overlap with all problem groups and often had the greatest degree of overlap. As argued above, while this overlap may reflect that these four problem groups are intrinsically connected to a wide range of problem types, the possibility that this overlap may sometimes occur by chance cannot be ruled out.
The table also reveals sizeable overlap between some other problem groups that clustered together. The percentage overlap between the employment, personal injury and rights problem groups was generally around 20. For example, of the respondents who experienced employment problems, 22.0 per cent also experienced personal injury problems and 21.1 per cent also experienced rights problems.
13. Cluster analysis can determine whether certain types of problems tend to be experienced close in time by the same people, but cannot determine whether any relationships between problems are causal. The cluster analysis was conducted on unweighted data, because such analyses cannot be conducted on weighted data. See Appendix A2, ‘Data analysis: Cluster analysis’ section for further details.
14. The number of clusters was decided by subjective inspection of the dendrogram in conjunction with consideration of large jumps in the fusion coefficient at each stage of the analysis. Clusters evident at a rescaled distance of 20 are discussed. See Appendix A2, ‘Data analysis: Cluster analysis’ section for further details and Appendix Figure A4.1 for the fusion coefficient at each stage of the analysis.
15. The accidents problem group did not cohere strongly with any cluster or subcluster.