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Extra‐Poisson Variation in Log‐Linear Models

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  • N. E. Breslow

Abstract

A modification of the iterated reweighted least squares scheme of Williams (1982) conveniently accommodates extra‐Poisson variation when fitting log‐linear models to tables of frequencies or rates. The method is applied to the analysis of cancer death rates by age and birth cohort and to testing for mutagenic effects in a standard bioassay.

Suggested Citation

  • N. E. Breslow, 1984. "Extra‐Poisson Variation in Log‐Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 38-44, March.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:1:p:38-44
    DOI: 10.2307/2347661
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    1. Nasim Vahabi & Anoshirvan Kazemnejad & Somnath Datta, 2018. "A Marginalized Overdispersed Location Scale Model for Clustered Ordinal Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 103-134, December.
    2. Garrett M. Fitzmaurice & John H. Goldthorpe, 1997. "Adjusting for Overdispersion in an Analysis of Comparative Social Mobility," Sociological Methods & Research, , vol. 25(3), pages 267-283, February.
    3. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.
    4. Peter Congdon, 1990. "Issues in the Analysis of Small Area Mortality," Urban Studies, Urban Studies Journal Limited, vol. 27(4), pages 519-536, August.
    5. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    6. Jeonghwan Kim & Woojoo Lee, 2019. "On testing the hidden heterogeneity in negative binomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 457-470, May.
    7. Oludare Ariyo & Emmanuel Lesaffre & Geert Verbeke & Adrian Quintero, 2022. "Bayesian Model Selection for Longitudinal Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 516-547, November.
    8. Richard B. Davies & Robert Crouchley, 1986. "The Mover-Stayer Model," Sociological Methods & Research, , vol. 14(4), pages 356-380, May.
    9. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    10. Hanan Elsaied & Roland Fried, 2021. "On robust estimation of negative binomial INARCH models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 137-158, August.
    11. Lee, Keunbaik & Joo, Yongsung, 2019. "Marginalized models for longitudinal count data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 47-58.
    12. Mengya Liu & Qi Li & Fukang Zhu, 2020. "Self-excited hysteretic negative binomial autoregression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 385-415, September.
    13. Erni Tri Astuti & Takashi Yanagawa, 2002. "Testing Trend for Count Data with Extra-Poisson Variability," Biometrics, The International Biometric Society, vol. 58(2), pages 398-402, June.
    14. Peter Congdon, 2000. "Monitoring Suicide Mortality: A Bayesian Approach," European Journal of Population, Springer;European Association for Population Studies, vol. 16(3), pages 251-284, September.
    15. Gene A. Pennello & Susan S. Devesa & Mitchell H. Gail, 1999. "Using a Mixed Effects Model to Estimate Geographic Variation in Cancer Rates," Biometrics, The International Biometric Society, vol. 55(3), pages 774-781, September.
    16. Mabel Morales-Otero & Vicente Núñez-Antón, 2021. "Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates," Mathematics, MDPI, vol. 9(3), pages 1-33, January.
    17. Andrew D. Martin, 2003. "Bayesian Inference for Heterogeneous Event Counts," Sociological Methods & Research, , vol. 32(1), pages 30-63, August.

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