On Theory, Models, Model-Testing, and Estimation

I reply to comments and criticisms of my article raised in this Special Issue by Cantor and Land, Britt, O'Brien, Levitt, and Paternoster and Bushway.     

The historical variability of the age-crime relationship

Methodological problems arising in fitting nonlinear regressions to a dataset are identified in context of research on the age-crime relationship. A modified chisquare distribution is fit to the age distribution of the seven Index crimes for the years 1952, 1957, 1962, 1967, 1972, 1977, 1982, and 1988 to assess the historical invariance of the distribution. Problematic features of Britt's (J. Quant. Criminol. 8, 175–187, 1992) analysis of the same data are highlighted.Britt states no rationale for the choice of these two functions, but his statement that his findings provide support for Greenberg's (1991) use of the Poisson gamma density to model individual offending patterns and questions Rowe and co-workers' (1990) use of the lognormal density as an appropriate model of individual violent offending suggests that this earlier work motivated his choice. Actually, this earlier work is not relevant to Britt's project. Greenberg (1991) and Roweet al. (1990) were concerned with the distribution of criminal propensities across individuals of a given age, not with the distribution of prevalence or participation rates across the ages, and changes therein over time.     

Age-cohort analysis of arrest rates

Logistic regressions of age-period-cohort models for city arrest rates are estimated with data from seven U.S. cities for the years 1970–1980 to study the dependence of officially designated criminality in select offense categories on age. A sensitivity analysis is carried out to determine how dependent the findings are on details of model specification.