英国诺丁大学讲义：如何估计随机效应模型stata.ppt

MCMC Estimation for Random Effect Modelling – The MLwiN experience Dr William J. Browne School of Mathematical Sciences University of Nottingham Contents Random effect modelling, MCMC and MLwiN. Methods comparison – Guatemalan child health example. Extendibility of MCMC algorithms: Cross classified and multiple membership models. Artificial insemination and Danish chicken examples. Further Extensions. Random effect models Models that account for the underlying structure in the dataset. Originally developed for nested structures (multilevel models), for example in education, pupils nested within schools. An extension of linear modelling with the inclusion of random effects. A typical 2-level model is Here i indexes pupils and j indexes schools. MLwiN Software package designed specifically for fitting multilevel models. Developed by a team led by Harvey Goldstein and Jon Rasbash at the Institute of Education in London over past 15 years or so. Earlier incarnations ML2, ML3, MLN. Originally contained ‘classical’ IGLS estimation methods for fitting models. MLwiN launched in 1998 also included MCMC estimation. My role in team was as developer of MCMC functionality in MLwiN during 4.5 years at the IOE. Estimation Methods for Multilevel Models Due to additional random effects no simple matrix formulae exist for finding estimates in multilevel models. Two alternative approaches exist: Iterative algorithms e.g. IGLS, RIGLS, EM in HLM that alternate between estimating fixed and random effects until convergence. Can produce ML and REML estimates. Simulation-based Bayesian methods e.g. MCMC that attempt to draw samples from the posterior distribution of the model. MCMC Algorithm Consider the 2-level model MCMC algorithms work in a Bayesian framework and so we need to add prior distributions for the unknown parameters. Here there are 4 sets of unknown parameters: We will add prior distributions MCMC Algorithm (2) The algorithm for this model then involves simulating i