Efficient laplacian and adaptive Gaussian quadrature algorithms for multilevel generalized linear mixed models

Journal of Computational and Graphical Statistics

Volumn 15, Issue 1, 2006, Pages 58-81

  Pinheiro, José C ^a   Chao, Edward C ^b  

^a NOVARTIS PHARMA AG   (Switzerland)

^b Insightful Corporation   (United States)

Author keywords

Binomial; Grouped data; Penalized quasi likelihood; Poisson

Indexed keywords

EID: 33645565987     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186006X96962     Document Type: Article

References (23)

1. Abramowitz, M., and Stegun, I. A. (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover.
2. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
3. Clarkson, D. B., and Zhan, Y. (2002), "Using Spherical-Radial Quadrature to Fit Generalized Linear Mixed Effects Models," Journal of Computational and Graphical Statistics, 11, 639-659.
4. Davis, P. J., and Rabinowitz, P. (1984), Methods of Numerical Integration, New York: Academic Press.
5. Geweke, J. (1989), "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, 57, 1317-1339.
6. Golub, G. H. (1973), "Some Modified Matrix Eigenvalue Problems," SIAM Review, 15, 318-334.
7. Gloub, G. H., and Welsch, J. H. (1969), "Calculation of Gaussian Quadrature Rules," Mathematical Computing, 23, 221-230.
8. Hox, J. (2002), Multilevel Analysis, Mahwah, NJ: Lawrence Erlbaum Associates.
9. Laird, N. M., and Ware, J. H. (1982), "Random-Effects Models for Longitudinal Data," Biometrics, 38, 963-974.
10. Leonard, T., Hsu, J. S. J., and Tsui, K. W. (1989), "Bayesian Marginal Inference," Journal of the American Statistical Association, 84, 1051-1058.
11. Leyland, A. H., and Goldstein, H. (eds.) (2001), Multilevel Modelling of Health Statistics, New York: Wiley.
12. Lindstrom, M. J., and Bates, D. M. (1988), "Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measurements Data," Journal of the American Statistical Association, 83, 1014-1022.
13. Lindstrom, M. J., and Bates, D. M. (1990), "Nonlinear Mixed-Effects Models for Repeated-Measures Data," Biometrics, 46, 673-687.
14. Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, Cary, NC: SAS Institute, Inc.
15. McCulloch and Searle (2001), Generalized, Linear, and Mixed Models, New York: Wiley.
16. Pinheiro, J. C., and Bates, D. M. (1995), "Approximations to the Log-likelihood Function in the Nonlinear Mixed Effects Model," Journal of Computational and Graphical Statistics, 4, 12-35.
17. _ (2000), Mixed-Effects Models in S and S-Plus, New York: Springer-Verlag.
18. Raudenbush, S. W., and Bryk, A. S. (2002), Hierarchical Linear Models (2nd ed.), Thousand Oaks, CA: Sage Publications.
19. Raudenbush, S.W., Yang, M. Y., and Yosef, M. (2000), "Maximum Likelihood for Generalized Linear Models with Nested Random Effects via High-order, Multivariate Laplace Approximations," Journal of Computational and Graphical Statistics, 9, 141-157.
20. Rodriguez, G., and Goldman, N. (1995), "An Assessment of Estimation Procedures for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society, Series A, 158, 73-90.
21. Soo, Y.-W., and Bates, D. M. (1992), "Loosely Coupled Nonlinear Least Squares," Computational Statistics and Data Analysis, 14, 249-259.
22. Tierney, L., and Kadane, J. B. (1986), "Accurate Approximation for Posterior Moments and Marginal Densities," Journal of the American Statistical Association, 81, 82-86.
23. Thisted, R. A. (1988), Elements of Statistical Computing, London: Chapman & Hall.