The “sickle‐hypothesis”: A time dependent Poisson model with applications to deviant behavior and occupational mobility

Abstract

Social scientists are frequently confronted with event history data which might be explained by a stochastic process. Examples are deviant behavior, occupational or geographic mobility, marriage dissolution, etc. Sometimes the assumption that the propensity to leave a position depends on the duration in that position seems to be realistic. In these examples one might expect that the rate of leaving a position initially increases, eventually reaches a maximum, and finally decreases again. The extended Poisson model studied in this paper exhibits such a pattern. If arrival time data are available, the parameters of the model can be estimated by maximum likelihood techniques. This model is applied to study deviant behavior and occupational mobility. The results are compared with those from alternative extensions of the Poisson process. Finally, further implications and extensions of this model are discussed.