Unidimensional Seriation - Implications for Evaluating Criminal Justice Data (From Confirmatory and Exploratory Analysis of the Spatio and Temporal Properties of Crime Data, P 80-103, 1981, by Reginald G Golledge and Lawrence J Hubert - See NCJ-78709)

• NCJ Number: 78712
• Author(s): L J Hubert; R G Golledge; T Kenney; D Richardson
• Date Published: 1981
• Length: 24 pages
• Grant Number(s): 79-NI-AX-0057; NSF-GSOC-77-28227
• Sponsoring Agency: National Science Foundation; National Institute of Justice (NIJ); US Dept of Justice NIJ Pub
• Corporate Author: University of California, Santa Barbara
• Publication Format: Document
• Publication Type: Statistics
• Language: English
• Country: United States of America
• Note: Available on microfiche from NCJRS as NCJ-78709.

Annotation

Implications of unidimensional seriation for evaluating criminal justice data are discussed.

Abstract

The problem of validating a given unidimensional scale (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. A numerical example which deals with the perception of homicide rate over 15 of the largest Standard Metropolitan Statistical Areas is included as an illustration of the general methodological discussion. The type of inference strategy proposed for evaluating the pattern of signs can be extended to compare two arbitrary skew-symmetric matrices. Thus, it is possible to evaluate the consistency between two skew-symmetric interaction matrices where the latter may be based on migration data at two time points or from two different demographic subgroups. From a combinatorial optimization perspective, several theoretical paradigms recently introduced characterize a discrepancy between a given seriation and the original asymmetric data. Along these same combinatorial optimization lines, a general strategy has been suggested for locating and seriating only a part of a proximity matrix that appears to be most consistent with the basic underlying spatial model. This latter technique can assist in identifying subsets of an object set that can be seriated well and those subsets that are not represented satisfactorily along a continuum. Mathematical equations and 19 references are provided. (Author summary modified)