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A survey of Monte Carlo algorithms for maximizing the likelihood of a twostage hierarchical model
, 2001
"... Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternati ..."
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Cited by 10 (4 self)
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Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternative approach is to approximate the intractable integrals using Monte Carlo averages. Several dierent algorithms based on this idea have been proposed. In this paper we discuss the relative merits of simulated maximum likelihood, Monte Carlo EM, Monte Carlo NewtonRaphson and stochastic approximation. Key words and phrases : Eciency, Monte Carlo EM, Monte Carlo NewtonRaphson, Rate of convergence, Simulated maximum likelihood, Stochastic approximation All three authors partially supported by NSF Grant DMS0072827. 1 1
Likelihood Inference for Small Variance Components
"... The authors explore likelihoodbased methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the bo ..."
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The authors explore likelihoodbased methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the restricted likelihood (REML). Also, they show that general REML estimates are less likely to fall on the boundary of the parameter space than maximum likelihood estimates and that the likelihood ratio test based on the local asymptotic approximation has higher power than the likelihood ratio test based on the usual chisquared approximation. They examine the finite sample properties of the proposed intervals by means of a simulation study. R ESUM E Les auteurs explorent l'emploi de methodes fondees sur la vraisemblance pour l'inference concernant les composantes de la variance dans le cadre d'u...
The Dynamics of Campaign Contributions in U.S. House Elections
, 1999
"... The Dynamics of Campaign Contributions in U.S. House Elections We use Federal Election Commission itemized contributions data from 1984 to estimate a model of campaign contributions in U.S. House elections. The model is a dynamic system of conditional compound Poisson processes in which there are ..."
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The Dynamics of Campaign Contributions in U.S. House Elections We use Federal Election Commission itemized contributions data from 1984 to estimate a model of campaign contributions in U.S. House elections. The model is a dynamic system of conditional compound Poisson processes in which there are contributions from both individuals and political action committees (PACs). The model includes random effects to allow for unobserved heterogeneity among districts and candidates. The dynamic effects measure how contributions to one candidate react to contributions to other candidates, as well as how contributions from individuals interact with contributions from PACs. We test the hypothesis that some candidates received higher contributions because of PAC endorsements. We also test whether national expectations about presidential election outcomes affect contributions to House candidates, as predicted by a policy moderating model. We use a Monte Carlo EM algorithm to optimize the li...
PoissonNormal Dynamic Generalized Linear Mixed Models of U.S. House Campaign Contributions
, 1999
"... PoissonNormal Dynamic Generalized Linear Mixed Models of U.S. House Campaign Contributions We develop generalized linear mixed models to analyze itemized contributions to U.S. House campaigns. Our basic model is a system of Poisson processes that have means that are loglinear functions of normal ..."
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PoissonNormal Dynamic Generalized Linear Mixed Models of U.S. House Campaign Contributions We develop generalized linear mixed models to analyze itemized contributions to U.S. House campaigns. Our basic model is a system of Poisson processes that have means that are loglinear functions of normally distributed random effects. Our model permits multiple random effects, including serially correlated effects. The mixed model specification involves an integration over the random effects that is analytically intractable. When there is only one, serially independent random effect, the model may be estimated using quadrature to evaluate the integral. With multiple random effects, quadrature is infeasible but the model may be estimated using the Monte Carlo EM (MCEM) algorithm proposed by McCulloch (1997). We illustrate these various estimation methods. The system we analyze includes contributions to Democratic and Republican candidates from different sources, including individuals and PACs...
Logistic Regression for Clustered/Correlated Data
, 1998
"... Introduction to clustered data analysis Overdispersion methods ?, ffi Robust variance estimation methods ? Analysis with xed eoeects ?, ffi Correction by intracluster correlation ffl Generalised estimating equations (GEE) ?, ffi ffl Generalised linear mixed models (GLMM) ffi ffl Repeated m ..."
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Introduction to clustered data analysis Overdispersion methods ?, ffi Robust variance estimation methods ? Analysis with xed eoeects ?, ffi Correction by intracluster correlation ffl Generalised estimating equations (GEE) ?, ffi ffl Generalised linear mixed models (GLMM) ffi ffl Repeated measures for binomial data (?, ffi) ? : analysis in Stata ; ffi : analysis in SAS : Overall (applied) references: ffl Collett, D., 1991. Modelling Binary Data. Chapman and Hall, London. ffl Diggle, P.J., Liang, K.Y. and Zeger, S.L., 1994. Analysis of Longitudinal Data. Clarendon Press, Oxford. 1 Clustered Data ffl some observations are more alike than others
Forthcoming Workshops
, 2003
"... introductory workshop to multilevel modelling using MLwiN will take place ..."
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introductory workshop to multilevel modelling using MLwiN will take place
Case Western Reserve University
"... We propose a method of inference for generalized linear mixed models ..."
48, Part 2, pp. 253^268 Multilevel modelling of the geographical distributions of diseases
, 1997
"... Summary. Multilevel modelling is used on problems arising from the analysis of spatially distributed health data. We use three applications to demonstrate the use of multilevel modelling in this area. The ®rst concerns small area allcause mortality rates from Glasgow where spatial autocorrelation b ..."
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Summary. Multilevel modelling is used on problems arising from the analysis of spatially distributed health data. We use three applications to demonstrate the use of multilevel modelling in this area. The ®rst concerns small area allcause mortality rates from Glasgow where spatial autocorrelation between residuals is examined. The second analysis is of prostate cancer cases in Scottish counties where we use a range of models to examine whether the incidence is higher in more rural areas. The third develops a multiplecause model in which deaths from cancer and cardiovascular disease in Glasgow are examined simultaneously in a spatial model. We discuss some of the issues surrounding the use of complex spatial models and the potential for future developments.