Models for Bivariate Count Data with an Application to Teenage Delinquency and Paternity

In this article, a new model, the bivariate lognormal Poisson, is developed to examine the relationships between two count processes. This model is an extension of Schoenberg's (1985) univariate lognormal Poisson model. Although computationally more cumbersome, it is substantially more flexible than previous bivariate count data models because it allows heterogeneity and correlation to be parameterized independently. As an application, the processes underlying out-of-wedlock teenage paternities and juvenile arrests are assessed for the extent to which they are manifestations of the same underlying factors. Using three birth cohorts of data, the processes generating these paternities and crimes are found to be related although not identical. Moreover, the strength of the correlations of the processes that generate paternities and crimes is much stronger in the population of white teenagers when compared to that of blacks.