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The Log-Logistic Rate Model

The log-logistic distribution is a widely used model in event history analysis. It is well-known that the log-logistic model is able to model social processes with monotonically decreasing, as well as nonmonotonic, reversed U-type hazard rates. In this article two three-parameter generalizations of the log-logistic model are introduced. These generalizations are very flexible in describing a great variety of processes with reversed U-type hazard rates. In addition, the first generalized model allows for separating upward rate shifts (intensity effects) from horizontal rate shifts (timing effects). With the second model it is possible to model immunity, that is, allow for the fact that some persons might not have an event at all. The usefulness of these models will be illustrated by an application to demographic data from the United States and Germany: The effects of education on marriage rates are analyzed. Finally, the relationship between the proposed hazard rate models and certain social diffusion processes is investigated.