Dimension Reduction in Criminology - A Comparison Between Ridge Regression and Principal Components Analysis (From Measurement Issue in Criminal Justice, P 121-134, 1983, Gordon P Waldo, ed. - See NCJ-92338)

• NCJ Number: 92345
• Author(s): Y Liu; R H Bee
• Date Published: 1983
• Length: 14 pages
• Sale Source: Sage Publications, Inc
• Language: English
• Country: United States of America

Annotation

Ridge regression and principal component procedures are statistical procedures which are useful both for reducing the problem of multicollinearity among explanatory variables and for reducing the number of dimensions with as little loss of information as possible.

Abstract

These techniques are needed to overcome the confusion created in multiple linear regression modeling when some of the information obtained is overlapping in nature. This confusion, which results from the linear relationships among some explanatory variables, makes it difficult to investigate the influence of an individual explanatory variable on the dependent variable. Hoerl and Kennard developed the ridge regression procedure as an improvement over the least-squares procedure when data were found to be ill-conditioned or nonorthogonal. The procedure is still new in many disciplines, although interest in it has increased since the early 1970's. The principal components procedure transforms the original data matrix into a new matrix which contains a smaller number of new variables, which are called the principal components. The new variables are linear combinations of the previous variables. Application of these procedures to crime for the 45 quarters from 1969 through 1980 and for economic variables revealed that unemployment has a significant positive relationship to property crimes, while manhours worked is significantly related in a negative way to property crimes. Figures, data tables, and nine references are provided. (Author summary modified)