Asymptotic likelihood approximations using a partial Laplace approximation

Australian and New Zealand Journal of Statistics

Volumn 48, Issue 4, 2006, Pages 465-476

  Taylor, Julian D ^a   Verbyla, Arunas P ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Laplace approximation; Mixed models; Restricted maximum likelihood; t distribution

Indexed keywords

EID: 33845618608     PISSN: 13691473     EISSN: 1467842X     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2006.00451.x     Document Type: Article

References (17)

1. BARNDORFF-NIELSEN, O.E. & COX, D.R. (1989). Asymptotic Techniques for Use in Statistics. London: Chapman and Hall.
2. BRESLOW, N.E. & CLAYTON, D.G. (1993). Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88, 9-25.
3. BROOKS, S.P. (1998). Markov chain Monte Carlo method and its application. The Statistician 47, 69-100.
4. DE BRUIJN, N.G. (1961). Asymptotic Methods in Analysis. Amsterdam: North-Holland.
5. LIN, X. & BRESLOW, N. (1996). Bias correction in generalized linear models with multiple components of dispersion. J. Amer. Statist. Assoc. 91, 1007-1016.
6. LINDLEY, D.V. (1980). Approximate Bayesian methods. In Bayesian Statistics, eds J.M. Bernardo, M.H. De Groot, D.V. Lindley & A.F.M. Smith, pp. 223-245. Valencia, Spain: University Press.
7. LIU, Q. & PIERCE, D.A. (1993). Heterogeniety in Mantel-Haenszel type models. Biometrika 80, 543-556.
8. PATTERSON, H.D. & THOMPSON, R. (1971). Recovery of interblock information when block sizes are unequal. Biometrika 58, 545-554.
9. RAUDENBUSH, S.W., YANG, M. & YOSEF, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. J. Comput. Graph. Statist. 9, 141-157.
10. SHUN, Z. & MCCALLAUGH, P. (1995). Laplace approximation of high dimensional integrals. J. Roy. Statist. Soc. Ser. B 57, 749-760.
11. SMYTH, G.K. & VERBYLA, A.P. (1996). A conditional likelihood approach to REML in generalized linear models. J. Roy. Statist. Soc. Ser. B 58, 565-572.
12. SOLOMON, P.J. & COX, D.R. (1992). Non-linear component of variance models. Biometrika 79, 1-11.
13. TAYLOR, J.D. (2005). Scale Parameter Modelling of the T-distribution. PhD thesis, Adelaide University.
14. TIERNEY, L. & KADANE, J. (1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81, 82-86.
15. TIERNEY, L., KASS, R. & KADANE, J. (1989). Fully exponential Laplace approximations to expectations and variances of non-positive functions. J. Amer. Statist. Assoc. 84, 710-716.
16. VERBYLA, A.P. (1990). A conditional derivation of residual maximum likelihood. Aust. N. Z. J. Stat. 32, 227-230.
17. WOLFINGER, R. (1993). Laplace's approximation for non-linear mixed models. Biometrika 80, 791-795.