Improved methods for surveying and monitoring crimes through likelihood based cluster analysis

Abstract

This paper focuses on a development of a classification model that gives an accurate placement of regions into classes of the relative risk of crimes over time. The analysis was based on statistics on the cases of burglary and murder from 13 regions of Namibia for the period 2002 - 2006. Since crime statistics are counts, they are often contaminated by heterogeneity. The effect of population heterogeneity in the crime counts in particular makes comparison of crime risk across regions using traditional methods of classification impossible. As such a method for standardizing crime counts was introduced and models for modeling population heterogeneity proposed. In particular a mixture likelihood approach to clustering by McLachlan and Basford (1988) which was further extended for covariate effects was used. This is due to its ability in identifying important clusters and in mapping the relative risk of crime onto the study regions via the maximum a posteriori (MAP) method while inference was done via the EM algorithm of Dempster et al (1997). The result shows that the space - time mixture model conducted under non - parametric form gives a good account of the relative risk of the two crimes over time, while both space - time mixture and covariate adjusted space - time mixture models points to a 3 risk classification of the regional relative risk of the two crimes namely high, medium and low risk class respectively.