tailieunhanh - Báo cáo sinh học: "Marginal maximum likelihood estimation of variance components in Poisson mixed models using Laplacian integration"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Marginal maximum likelihood estimation of variance components in Poisson mixed models using Laplacian integration | . . Dỗpartamint d QtnillOM Animei BIBUIOTHtOUE F 78351 40UY EN JOSAS Genet Sei Evol 1993 25 305-319 @ Elsevier INRA ill OCT. 1993 305 Original article Marginal maximum likelihood estimation of variance components in Poisson mixed models using Laplacian integration RJ Tempelman1 D Gianola2 1 Louisiana State University Department of Agricultural Statistics 53 Agricultural Administration Building Baton Rouge LA 70803-5606 2 University of Wisconsin Department of Dairy Science 266 Animal Sciences Building Madison WI 53706 USA Received 10 November 1992 accepted 18 May 1993 Summary - An algorithm for computing marginal maximum likelihood MML estimates of variance components in Poisson mixed models is presented. A Laplacian approximation is used to integrate fixed and random effects out of the joint posterior density of all parameters. This approximation is found to be identical to that invoked in the more commonly used expectation-maximization type algorithm for MML. Numerically however a different sequence of iterates is obtained although the same variance component estimates should result. The Laplacian algorithm is precisely DFREML derivative free REML optimization when applied to normally distributed data and could then be termed DFMML derivative-free marginal maximum likelihood . Because DFMML is based on an approximation to the marginal likelihood of the variance components it provides a mechanism for testing hypotheses about such components via posterior odds ratios or marginal likelihood ratio tests. Also asymptotic posterior standard errors of the variance components can be computed with DFMML. A Tierney-Kadane procedure for computing the posterior mean of a variance component is also developed however it requires 2 joint maximizations and consequently may not be expected to perform well in many linear and non-linear mixed models. An example of a Poisson model is presented in which the null estimate commonly found when jointly estimating variance .