Approximate inference in generalized linear mixed models
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...Wood (2004), using Breslow and Clayton (1993), or Fahrmeir et al. (2004), using Harville (1977)), and in practice convergence problems are not unusual: examples are provided in Wood (2004, 2008), and in Appendix A. Early prediction-error-based methods were also based on single iteration (e.g. Gu (1992) and Wood (2004)), and suffered similar convergence problems, but these were overcome by Wood’s (2008) nested iteration method for GCV, generalized approximate cross-validation, and AIC smoothness selection. Wood (2008) cannot be extended to REML or ML while maintaining good numerical stability, so the purpose of this paper is to provide an efficient and stable nested iteration method for REML or ML smoothness selection, thereby removing the major practical obstacle to use of these criteria....
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...Wood (2004), using Breslow and Clayton (1993), or Fahrmeir et al. (2004), using Harville (1977)), and in practice convergence problems are not unusual: examples are provided in Wood (2004, 2008), and in Appendix A. Early prediction-error-based methods were also based on single iteration (e.g. Gu (1992) and Wood (2004)), and suffered similar convergence problems, but these were overcome by Wood’s (2008) nested iteration method for GCV, generalized approximate cross-validation, and AIC smoothness selection....
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...Note that the Laplace approximation that is employed here does not suffer from the difficulties that are common to most penalized quasi-likelihood (PQL) (Breslow and Clayton, 1993) implementations when used with binary data....
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...Note that the Laplace approximation that is employed here does not suffer from the difficulties that are common to most penalized quasi-likelihood (PQL) (Breslow and Clayton, 1993)...
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...Wood (2004), using Breslow and Clayton (1993), or Fahrmeir et al....
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"Approximate inference in generalize..." refers background in this paper
...The most rigorous demonstrations to date of these properties are those of Liang and Zeger (1986) and Prentice (1988) for the case of block diagonal V....
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