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Part of the book series: Lecture Notes in Statistics ((LNS,volume 14))

Summary

Loglinear models with linear composite link functions constitute a very flexible class of models which can accommodate a wide range of estimation problems for probability models in genetics. It is shown how GLIM-3 may be used to obtain estimates of gene frequencies, inbreeding coefficients and other parameters and their asymptotic covari-ances and standard errors. Examples are taken from medical genetics and evolutionary biology.

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References

  • ARNOLD, J. (1981). Statistics of natural populations. I: Estimating an allele probability in cryptic fathers with a fixed number of offspring. Biometrics, 37, 495–504.

    Article  MathSciNet  MATH  Google Scholar 

  • BISHOP, Y.M.M., FIENBERG, S.E. and HOLLAND, P.W. (1975). Discrete Multivariate Analysis. M.I.T. Press.

    MATH  Google Scholar 

  • BURN, R. and THOMSON, R. (1981). A macro for calculating the covariance matrix of functions of parameter estimates. The GLIM Newsletter, no. 5. Oxford: Numerical Algorithms Group.

    Google Scholar 

  • CEPELLINI, R., SINISCALCO, M. and SMITH, C.A.B. (1955). The estimation of gene frequencies in a random mating population. Ann. Hum. Genet., 20, 97–115.

    Article  Google Scholar 

  • DEMPSTER, A.P., LAIRD, N.M. and RUBIN, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm, J.R. Statist, Soc. b., 39, 1–38.

    MathSciNet  MATH  Google Scholar 

  • ELANDT-JOHNSON, R.G. (1971). Probability Models and Statistical Methods in Genetics. New York: Wiley.

    MATH  Google Scholar 

  • HABERMAN, S.J. (1974). Loglinear models for frequency tables derived by indirect observation: maximum likelihood equations. Ann. Statist., 2, 911–924.

    Article  MathSciNet  MATH  Google Scholar 

  • HABERMAN, S.J. (1977). Product models for frequency tables involving indirect observation. Ann. Statist., 5, 1124–1147.

    Article  MathSciNet  MATH  Google Scholar 

  • KEMPTHORNE, O. (1969). An Introduction to Genetic Statistics. Ames, Iowa: Iowa State University Press.

    MATH  Google Scholar 

  • NELDER, J.A. and WEDDERBURN, R.W.M. (1972) Generalised linear models, J.R. Statist. Soc. A, 135, 370–383.

    Article  Google Scholar 

  • THOMSON, R. and BAKER, R.J. (1981). Composite link functions in generalised linear models. Appi. Statist., 30, 125–131.

    Article  Google Scholar 

  • THOMSON, R. (1981). Estimating the origins of human trisomies and triploids. Ann. Hum. Genet., 45, 65–78.

    Article  MATH  Google Scholar 

  • THOMSON, R. (1982). PhD Thesis (to appear). University College, London.

    Google Scholar 

  • YASUDA, N. (1968). Estimation of the inbreeding coefficient from phenotype frequencies by a method of maximum likelihood scoring. Biometrics, 24, 915–934.

    Article  MathSciNet  Google Scholar 

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© 1982 Springer-Verlag New York Inc.

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Burn, R. (1982). Loglinear Models with Composite Link Functions in Genetics. In: Gilchrist, R. (eds) GLIM 82: Proceedings of the International Conference on Generalised Linear Models. Lecture Notes in Statistics, vol 14. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5771-4_14

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  • DOI: https://doi.org/10.1007/978-1-4612-5771-4_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90777-2

  • Online ISBN: 978-1-4612-5771-4

  • eBook Packages: Springer Book Archive

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