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Composite Link Functions in Generalized Linear Models

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  • R. Thompson
  • R. J. Baker

Abstract

In generalized linear models each observation is linked with a predicted value based on a linear function of some systematic effects. We sometimes require to link each observation with a linear function of more than one predicted value. We embed such models into the generalized linear model framework using composite link functions. The computer program GLIM‐3 can be used to fit these models. Illustrative examples are given including a mixed‐up contingency table and grouped normal data.

Suggested Citation

  • R. Thompson & R. J. Baker, 1981. "Composite Link Functions in Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 125-131, June.
    • Handle: RePEc:bla:jorssc:v:30:y:1981:i:2:p:125-131
    DOI: 10.2307/2346381
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    1. Adrien Remund & Carlo G. Camarda & Tim Riffe, 2018. "A Cause-of-Death Decomposition of Young Adult Excess Mortality," Demography, Springer;Population Association of America (PAA), vol. 55(3), pages 957-978, June.
    2. Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
    3. Adrien Remund & Carlo G. Camarda & Timothy Riffe, 2017. "A cause-of-death decomposition of the young adult mortality hump," MPIDR Working Papers WP-2017-007, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. David Rindskopf, 1992. "A general approach to categorical data analysis with missing data, using generalized linear models with composite links," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 29-42, March.
    5. Lambert, Philippe, 2011. "Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 429-445, January.
    6. Amelia Simó & M. Victoria Ibáñez & Irene Epifanio & Vicent Gimeno, 2020. "Generalized partially linear models on Riemannian manifolds," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 641-661, June.
    7. Carlo G. Camarda & Ugofilippo Basellini, 2021. "Smoothing, Decomposing and Forecasting Mortality Rates," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 569-602, July.
    8. V. F. Miranda-Soberanis & Thomas W. Yee, 2023. "Two-parameter link functions, with applications to negative binomial, Weibull and quantile regression," Computational Statistics, Springer, vol. 38(3), pages 1463-1485, September.
    9. Sophia Rabe-Hesketh & Anders Skrondal, 2007. "Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 123-140, June.
    10. Ayma Anza, Diego Armando & Durbán, María & Lee, Dae-Jin & Van de Kassteele, Jan, 2016. "Modelling latent trends from spatio-temporally grouped data using composite link mixed models," DES - Working Papers. Statistics and Econometrics. WS 23448, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Fischer, M.M. & Nijkamp, P., 1985. "Explanatory discrete spatial data and choice analysis : a state-of-the-art review," Serie Research Memoranda 0006, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    12. Lambert, Philippe, 2023. "Nonparametric density estimation and risk quantification from tabulated sample moments," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 177-189.
    13. L. Fahrmeir & H. Kaufmann, 1991. "On kalman filtering, posterior mode estimation and fisher scoring in dynamic exponential family regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 37-60, December.
    14. Galecki, Andrzej T. & Have, Thomas R. Ten & Molenberghs, Geert, 2001. "A simple and fast alternative to the EM algorithm for incomplete categorical data and latent class models," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 265-281, January.
    15. Hae-Won Uh & Paul H C Eilers, 2011. "Haplotype Estimation from Fuzzy Genotypes Using Penalized Likelihood," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-9, September.

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