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The Log-Logistic Rate Model

Author

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  • JOSEF BRÃœEDERL

    (University of Munich)

  • ANDREAS DIEKMANN

    (University of Bern)

Abstract

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.

Suggested Citation

  • Josef Brãœederl & Andreas Diekmann, 1995. "The Log-Logistic Rate Model," Sociological Methods & Research, , vol. 24(2), pages 158-186, November.
    • Handle: RePEc:sae:somere:v:24:y:1995:i:2:p:158-186
    DOI: 10.1177/0049124195024002002
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    References listed on IDEAS

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    3. Keeley, Michael C, 1979. "An Analysis of the Age Pattern of First Marriage," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 527-544, June.
    4. Tim Heaton, 1990. "Marital stability throughout the child-rearing years," Demography, Springer;Population Association of America (PAA), vol. 27(1), pages 55-63, February.
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    2. Milan Bouchet-Valat, 2014. "La fin de l'hypergamie féminine? L’inversion du sens de l'écart entre diplômes des conjoints au fil des cohortes en France," Working Papers 2014-50, Center for Research in Economics and Statistics.
    3. Congdon, Peter, 2008. "A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4346-4356, May.
    4. Francesco C. Billari, 2001. "A sickle transition-rate model with starting threshold," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 139-155, January.
    5. Norman Braun & Henriette Engelhardt, 2002. "Diffusion processes and event history analysis," MPIDR Working Papers WP-2002-007, Max Planck Institute for Demographic Research, Rostock, Germany.
    6. Sabine Zinn, 2014. "The MicSim Package of R: An Entry-Level Toolkit for Continuous-Time Microsimulation," International Journal of Microsimulation, International Microsimulation Association, vol. 7(3), pages 3-32.
    7. Peter Todd & Francesco Billari & Jorge Simão, 2005. "Aggregate age-at-marriage patterns from individual mate-search heuristics," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 559-574, August.
    8. Fabrizio Bernardi, 2001. "Is it a Timing or a Probability Effect? Four Simulations and an Application of Transition Rate Models to the Analysis of Unemployment Exit," Quality & Quantity: International Journal of Methodology, Springer, vol. 35(3), pages 231-252, August.
    9. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.
    10. Norman Braun & Henriette Engelhardt, 2004. "Diffusion Processes and Event History Analysis," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 2(1), pages 111-132.

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