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COMPSTAT pp 97–107Cite as

HGLMs for analysis of correlated non-normal data

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Abstract

Hierarchical generalized linear models (HGLMs) are developed as a synthesis of (i) generalized linear models (GLMs) (ii) mixed linear models, (iii) joint modelling of mean and dispersion and (iv) modelling of spatial and temporal correlations. Statistical inferences for complicated phenomena can be made from such a HGLM, which is capable of being decomposed into diverse component GLMs, allowing the application of standard GLM procedures to those components, in particular those for model checking.

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References

  • Baltagi, B.H. (1995). Economic Analysis of Panel Data. New York: Wiley.

    Google Scholar 

  • Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian com-putation and stochastic systems (with discussion). Statistical Science, 10, pp. 3–66.

    Article  MathSciNet  MATH  Google Scholar 

  • Besag, J. and Higdon, P. (1999). Bayesian analysis of agriculture field exper-iments (with discussion). J. R. Statist. Soc. B, 61, pp. 691–746.

    Article  MathSciNet  MATH  Google Scholar 

  • Breslow, N.E. (1984). Extra-Poisson variation in log-linear models. J. Roy. Statist. Soc.Ser.C, 33, pp. 38–44.

    Google Scholar 

  • Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. J. Am. Statist. Ass., 88, pp. 9–25.

    MATH  Google Scholar 

  • Cressie, N. (1991). Statistics for Spatial Data. Wiley: New York.

    MATH  Google Scholar 

  • Diggle, P.J., Liang, K. and Zeger, S.L. (1994). Analysis of Longitudinal Data. Oxford: Clarendon Press.

    Google Scholar 

  • Durbin, J. and Koopman, S.J. (2000). Time series analysis of non-Gaussian observations, based on state space models from both classical and Bayesian perspectives, (with discussion). J. R. Statist. Soc. B., 62, pp. 3–56.

    Article  MathSciNet  MATH  Google Scholar 

  • Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.

    Google Scholar 

  • Kenward, M.G. and Smith, D.M. (1995). Computing the generalized estimating equations with quadratic covariance estimation for repeated measurements. Genstat Newsletter, 32, pp. 50–62.

    Google Scholar 

  • Laird, N. and Ware, J.H. (1982). Random-effects models for longitudinal data. Biometrics, 38, pp. 963–974.

    Article  MATH  Google Scholar 

  • Lee, Y. (2000). Discussion of Durbin and Koopman’s paper, J. R. Statist. Soc, B.

    Google Scholar 

  • Lee, Y. and Neider, J.A. (1996). Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B, 58, pp. 619–678.

    MATH  Google Scholar 

  • Lee, Y. and Neider, J.A. (1998). Generalized linear models for the analysis of quality-improvement experiments. The Canadian Journal of Statistics, 26, pp. 95–105.

    Article  MATH  Google Scholar 

  • Lee, Y. and Neider, J.A. (2000a). HGLMs: a synthesis of GLMs, random effect models and structured dispersions. Unpublished manuscript.

    Google Scholar 

  • Lee, Y. and Neider, J.A. (2000b). Modelling and analysing correlated non-normal data. Unpublished manuscript.

    Google Scholar 

  • Lee, Y. and Neider, J.A. (2000c). The relationship between double exponential families and extended quasi-likelihood families, with application to modelling Geissler’s human sex ratio data. To appear in Applied Statistics, No.4.

    Google Scholar 

  • Lee, Y. and Neider, J.A. (in press). Two ways of modelling overdispersion. To appear in Applied Statistics.

    Google Scholar 

  • Longford, N. (1993). Random Coefficient Models. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • McColloch, C. E. (1997). Maximum Likelihood Algorithms for Generalized Linear Mixed Models, J. Am. Statist. Ass, 92, pp. 162–170.

    Article  Google Scholar 

  • McCullagh P. and Neider, J.A. (1989). Generalized Linear Models, 2nd edn. London: Chapman and Hall.

    MATH  Google Scholar 

  • Neider, J.A. (1993). The K system for GLMs in Genstat. Technical report TRI/93. Oxford: NAG.

    Google Scholar 

  • Neider, J.A. and Lee, Y. (1991). Generalized linear models for the analysis of Taguchi-type experiments. Applied Stochastic Models and Data Analysis, 7, pp. 107–120.

    Article  Google Scholar 

  • Neider, J.A. and Lee, Y. (1992). Likelihood, quasi-likelihood and pseudo-likelihood: Some comparisons. J. R. Statist. Soc. B, 54, pp. 273–284.

    Google Scholar 

  • Neider, J.A. and Lee, Y. (1998). Letters to the editor. Technometrics, 40, pp. 168–175.

    Article  Google Scholar 

  • Neider, J.A. and Pregibon, D. (1987). An extended quasi-likelihood function. Biometrika, 74, pp. 221–231.

    Article  MathSciNet  Google Scholar 

  • Neider, J.A. and Wedderburn, R.W.M. (1972). Generalized linear models. J.R. Statist. Soc. A, 135, pp. 370–384.

    Article  Google Scholar 

  • Patterson, H.D. and Thompson, R. (1971). Recovery of interblock informa-tion when block sizes are unequal. Biometrika, 58, pp. 545–554.

    Article  MathSciNet  MATH  Google Scholar 

  • Schall, R. (1991). Estimation in generalized linear models with random ef-fects. Biometrika,78, pp. 719–727.

    Article  MATH  Google Scholar 

  • Pierce, D.A. and Sands, B.R. (1975). Extra-Bernoulli Variation in binary data. Department of Statistics, Oregon State University, bfTR46.

    Google Scholar 

  • Pierce, D.A. and Schafer, D.W. (1986). Residuals in generalized linear models. J. Am. Statist. Ass., 81, pp. 977–986.

    Article  MathSciNet  MATH  Google Scholar 

  • Reid, N. (1991). itApproximations and asymptotics. Statistical Theory and Modelling, edn. by D. V. Hinkely, N. Reid and E. J. Snell. London: Chapman and Hall.

    Google Scholar 

  • Robinson, G.K. (1991). That BLUP is a good thing: the estimation of random effects. Statist. Sci,6, pp. 15–51.

    Article  MathSciNet  MATH  Google Scholar 

  • Wedderburn, R.W.M. (1974). Quasi-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61, pp. 439–447.

    MathSciNet  MATH  Google Scholar 

  • Zeger, S.L., Liang, K.Y. and Albert, P.S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics, 44, pp. 1049–1060.

    Article  MathSciNet  MATH  Google Scholar 

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Lee, Y., Nelder, J.A. (2000). HGLMs for analysis of correlated non-normal data. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57678-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-57678-2_9

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1326-5

  • Online ISBN: 978-3-642-57678-2

  • eBook Packages: Springer Book Archive

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