"Parametric" invariance requires the characteristics of each distribution to be identical over time and across different offense types. "Mathematical-form" invariance requires that a single class of mathematical functions, differing only in the parameter values, closely approximates each age-crime curve. To test for both types of invariance, this study fit two common probability density functions -- gamma and lognormal -- to the age distribution of index offenses in the United States from 1952 to 1987. Consistent with prior research, the results do not support parametric invariance. There is considerable support, however, for mathematical-form invariance. This support holds whether the gamma or lognormal results are considered. The model fits for both density functions are uniformly high, especially for property offenses and rape. 3 tables and 30 references
Constancy and Change in the U.S. Age Distribution of Crime: A Test of the "Invariance Hypothesis"
NCJ Number
137283
Journal
Journal of Quantitative Criminology Volume: 8 Issue: 2 Dated: (June 1992) Pages: 175-187
Date Published
1992
Length
13 pages
Annotation
The recent controversy over the age relationship with criminal behavior can be traced to Hirschi and Gottfredson's failure to define "invariance." This paper distinguishes two types of invariance -- "parametric" and "mathematical form" -- that explain both the pattern of stability claimed by Hirschi and Gottfredson and the pattern of variability observed in more recent research; each type of invariance is tested.
Abstract
Date Published: January 1, 1992