Maximum Likelihood Algorithms for Generalized Linear Mixed Models

Journal of the American Statistical Association

Volumn 92, Issue 437, 1997, Pages 162-170

  McCulloch, Charles E ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Importance sampling; Metropolis Hastings algorithm; Monte Carlo EM; Newton Raphson algorithm; Penalized quasi likelihood; Simulated maximum likelihood

Indexed keywords

EID: 0031479575     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10473613     Document Type: Article

References (22)

1. Abramowitz, M., and Stegun, I. A. (1959). Handbook of Mathematical Functions, Washington. DC: National Bureau of Standards
2. Aptech Systems (1992), GAUSS Manual, Version 3.0, Kent, WA: Author.
3. Breslow, N. E., and Clayton, D. G. (1993). “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9-25.
4. Chan, K. S., and Ledholter, J. (1995). “Monte Carlo EM Estimation for Time Series Models Involving Counts:’ Journal of the American Statistical Association, 90, 242-252.
5. Diggle, P. J., Liang, K.-Y., and Zeger, S. L. (1994). Analysis of Longitudinal Data, Oxford, U.K.: Oxford University Press.
6. Fitzmaurice, G. M. (1995). “A Caveat Concerning Independence Estimating Equations With Multivariate Binary Data:’ Biometrics, 51, 309-317.
7. Gelfand, A. E., and Carlin, B. P. (1993) “Maximum Likelihood Estimation for Constrained-or Missing-Data Problems,” Canadian Journal of Statistics, 21, 303-311.
8. Geyer, C. J. (1994), “Estimating Normalizing Constants and Reweighting Mixtures in Markov Chain Monte Carlo:’ Technical Report 568, University of Minnesota, School of Statistics.
9. Geyer, C. J., and Thompson, E. A. (1992). “Constrained Monte Carlo Maximum Likelihood for Dependent Data,” Journal of the Royal Statistical Society, Ser. B, 54, 657-699.
10. Gilmour, A. R., Anderson, R. D., and Rae, A. L. (1985), “The Analysis of Binomial Data by a Generalized Linear Mixed Model,” Biometrika, 72, 593-599.
11. Harville, D. A., and Mee, R. W. (1984), “A Mixed-Model Procedure for Analyzing Ordered Categorical Data,” Biometrics, 40, 393-408.
12. Henderson, C. R., Kempthorne, O., Searle, S. R., and VonKrosigk, C. N. (I 959). “Estimation of Environmental and Genetic Trends From Records Subject to Culling,” Biometrics, 30, 5830-588.
13. Hobert, J., and Casella, G. (1991), “The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models,” Journal of the American Statistical Association, 91, 1461-1473.
14. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
15. McCulloch, C. E. (1994). “Maximum Likelihood Variance Components Estimation for Binary Data:’ Journal of the American Statistical Associaiion, 89, 330-335.
16. Natarajan, R., and McCulloch, C. E. (1995). “A Note on the Existence of the Posterior Distribution for a Class of Mixed Models for Binomial Responses:’ Biometrika, 82,639-643.
17. Schall, R. (1991). “Estimation in Generalized Linear Models With Random Effects,” Biometrika, 78, 719-727.
18. Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components, New York Wiley.
19. Tanner, M. A. (1993), Tools for Statistical Inference: Observed Data and Data Augmentation (2nd ed.), Berlin: Springer-Verlag.
20. Wolfinger, R. (1994). “Laplace’s Approximation for Nonlinear Mixed Models,” Biometrika, 80, 791-795.
21. Wu, C.-F. (1983). “On the Convergence Properties of the EM Algorithm:’ The Annals of Statistics, 11, 95-103.
22. Zeger, S. L., and Karim, M. R. (1991), “Generalized Linear Models With Random Effects: A Gibbs Sampling Approach,” Journal of the American Statistical Association, 86, 79-86.