Unidimensional Seriation: Implications for Evaluating Criminal Justice Data

The problem of validating a given unidimensional scale (that is, an ordering of a set of objects along a single dimension) is discussed in terms of a few simple properties of the data used to obtain the scale. Based on a set of asymmetric proximity values as raw data, a distinction between analyzing absolute-value information or sign information is presented that leads to a formal test of whether a given scale is being reliably represented. In short, a scale is generated from absolute-value information, but validated through sign information. A numerical example which deals with the perception of homicide rate over fifteen of the largest Standard Metropolitan Statistical Areas is included as an illustration of the general methodological discussion.