A Fortran IV Program Generalizing the Schönemann-Carroll Matrix Fitting Algorithm To Monotone and Linear Fitting of Configurations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66700/2/10.1177_001316447403400117.pd

Some boundary conditions for a monotone analysis of symmetric matrices

This paper gives a rigorous and greatly simplified proof of Guttman's theorem for the least upper-bound dimensionality of arbitrary real symmetric matrices S , where the points embedded in a real Euclidean space subtend distances which are strictly monotone with the off-diagonal elements of S . A comparable and more easily proven theorem for the vector model is also introduced. At most n -2 dimensions are required to reproduce the order information for both the distance and vector models and this is true for any choice of real indices, whether they define a metric space or not. If ties exist in the matrices to be analyzed, then greatest lower bounds are specifiable when degenerate solutions are to be avoided. These theorems have relevance to current developments in nonmetric techniques for the monotone analysis of data matrices.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45729/1/11336_2005_Article_BF02291398.pd

Book review

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45718/1/11336_2005_Article_BF02289749.pd

Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm

In connection with a least-squares solution for fitting one matrix, A , to another, B , under optimal choice of a rigid motion and a dilation, Schönemann and Carroll suggested two measures of fit: a raw measure, e , and a refined similarity measure, e s , which is symmetric. Both measures share the weakness of depending upon the norm of the target matrix, B , e.g. , e ( A , kB ) ≠ e ( A , B ) for k ≠ 1. Therefore, both measures are useless for answering questions of the type: “Does A fit B better than A fits C ?”. In this note two new measures of fit are suggested which do not depend upon the norms of A and B , which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45731/1/11336_2005_Article_BF02291666.pd

On evaluating the equivalency of alternative MDS representations

A typical question in MDS is whether two alternative configurations that are both acceptable in terms of data fit may be considered “practically the same”. To answer such questions on the equivalency of MDS solutions. Lingoes & Borg (1983) have recently proposed a quasistatistical decision strategy that allows one to take various features of the situation into account. This paper adds another important piece of information to this approach: for the Lingoes-Borg decision criterion R , we compute what proportion of R -values is greater/less than the observed coefficient if one were to consider all possible alternative distance sets within certain bounds defined by the observed fit coefficients for two alternative MDS solutions, what are the limits of acceptability for such fit coefficients, and how are the observed MDS configurations interrelated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43557/1/11135_2004_Article_BF00227428.pd

What weight should weights have in individual differences scaling?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43554/1/11135_2004_Article_BF00144137.pd

An alternative approach to confirmatory inference and geometric models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43556/1/11135_2004_Article_BF00221555.pd

How similar are the different results?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43555/1/11135_2004_Article_BF00145805.pd

Louis E. Guttman (1916–1987)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45742/1/11336_2005_Article_BF02294129.pd

Body Part Removal: A Thematic Exploration of U.K. Homicide Offenses

Body part removal (BPR) is a rare homicide phenomena, which emerges as a result of a variety of motives. Fifty-eight BPR U.K. homicide cases were analyzed. Findings indicated key characteristics within BPR murder offenses, with most offenders males; aged around 31 years; knew their victims; with presence of alcohol, drugs, and mental health issues; and more than two thirds of the sample had previous convictions, more than 50% for theft. Offense behaviors showed “multiple wounds” and “victim naked” as highest frequency, with the head as the most frequently removed body part. Smallest space analysis (SSA) identified two behavioral themes (expressive and instrumental) with 62.1% of cases classified as one of these. The study has provided the largest U.K. sample of BPR homicide, furthering understanding this type of offense and the offenders who commit it