Partial order scalogram analysis with base coordinates (POSAC): Its application to crime patterns in all the states in the United States

In this paper, a new nonmetric method called POSAC is presented and illustrated through an analysis of the crime patterns of all the states in the United States. POSAC is a graphical technique for the display of multivariate data in a two-dimensional space. It maps the rows (e.g., states) of a matrix in a way that maximizes the preservation of theirpartial order, with similar states located in close proximity on the map. POSAC is based on the partial order among observations rather than their actual magnitude. POSAC seems to bear the same relationship to the principal-component analysis (PCA) as that borne by the median to the arithmetic mean. As a matter of fact, POSAC is a form of ordinal factor analysis. Its advantage over PCA is its robustness to the data. The technique enables observations and variables to be studied simultaneously. Seven index crime categories are analyzed. In order to demonstrate the utility of POSAC in detecting changes in crime patterns over time, we included in our analysis three selected years: 1944, 1965, and 1987. The results for the year 1987 are compared to those obtained by PCA.