Outlier detection in social behaviour in latent class and group-based latent trajectory models

This application relates to an issue that is important for criminology and other social science
disciplines - that of detecting small outlier classes in large datasets. Latent Class Analysis(LCA)
(Lazarsfeld and Henry, 1968) and group-based trajectory models (GBTM) (Nagin, 2005) are now used
extensively in the social sciences to detect classes of individuals based on behaviour or survey
responses.
For example, in criminology, LCA has been used for detecting patterns in criminological offending
activity in the types of offending carried out (Francis, Soothill and Fligelstone, 2004). Such models
however fail to identify small latent classes. These unusual patterns of behaviour are probably the
most important to identify, but such individuals will instead be forced into other clusters,
contaminating these clusters and losing the important aberrant behaviour. Thus, there will be
individuals who focus their criminal activity on violent and sexual offending (Hodgins, 2004) but
these are rare in the population of offenders. LCA has failed to identify such individuals, instead
merging them into other latent classes. Extending into longitudinal data, GBTMs identify classes of
trajectory patterns over time in the frequency of offending. Again, there may be patterns of
behaviour in large datasets (such as very late starters) that are not detected through conventional
GBTM methods.