Random effects model

About: Random effects model is a research topic. Over the lifetime, 8388 publications have been published within this topic receiving 438823 citations. The topic is also known as: random effects & random effect.

Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data.

Abstract: We consider random effects meta-analysis where the outcome variable is the occurrence of some event of interest. The data structures handled are where one has one or more groups in each study, and in each group either the number of subjects with and without the event, or the number of events and the total duration of follow-up is available. Traditionally, the meta-analysis follows the summary measures approach based on the estimates of the outcome measure(s) and the corresponding standard error(s). This approach assumes an approximate normal within-study likelihood and treats the standard errors as known. This approach has several potential disadvantages, such as not accounting for the standard errors being estimated, not accounting for correlation between the estimate and the standard error, the use of an (arbitrary) continuity correction in case of zero events, and the normal approximation being bad in studies with few events. We show that these problems can be overcome in most cases occurring in practice by replacing the approximate normal within-study likelihood by the appropriate exact likelihood. This leads to a generalized linear mixed model that can be fitted in standard statistical software. For instance, in the case of odds ratio meta-analysis, one can use the non-central hypergeometric distribution likelihood leading to mixed-effects conditional logistic regression. For incidence rate ratio meta-analysis, it leads to random effects logistic regression with an offset variable. We also present bivariate and multivariate extensions. We present a number of examples, especially with rare events, among which an example of network meta-analysis.

Fixed- Versus Random-Effects Models in Meta-Analysis: Model Properties and an Empirical Comparison of Differences in Results

Abstract: Today most conclusions about cumulative knowledge in psychology are based on meta-analysis. We first present an examination of the important statistical differences between fixed-effects (FE) and random-effects (RE) models in meta-analysis and between two different RE procedures, due to Hedges and Vevea, and to Hunter and Schmidt. The implications of these differences for the appropriate interpretation of published meta-analyses are explored by applying the two RE procedures to 68 meta-analyses from five large meta-analytic studies previously published in Psychological Bulletin. Under the assumption that the goal of research is generalizable knowledge, results indicated that the published FE confidence intervals (CIs) around mean effect sizes were on average 52% narrower than their actual width, with similar results being produced by the two RE procedures. These nominal 95% FE CIs were found to be on average 56% CIs. Because most meta-analyses in the literature use FE models, these findings suggest that the precision of meta-analysis findings in the literature has often been substantially overstated, with important consequences for research and practice.

Bayesian inference for generalized additive mixed models based on Markov random field priors

Abstract: Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo (MCMC) simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as usual covariates with fixed effects, metrical covariates with nonlinear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. The approach is particularly appropriate for discrete and other fundamentally non-Gaussian responses, where Gibbs sampling techniques developed for Gaussian models cannot be applied, but it also works well for Gaussian responses. We use the close relation between nonparametric regression and dynamic or state space models to develop posterior sampling procedures, based on Markov random field priors. They include recent Metropolis-Hastings block move algorithms for dynamic generalized linear models and extensions for spatial covariates as building blocks. We illustrate the approach with a number of applications that arose out of consulting cases, showing that the methods are computionally feasible also in problems with many covariates and large data sets.

Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models

Abstract: Best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known. If the true values are replaced by estimated values, the mean squared errors of the estimators of the fixed and random effects increase in size. The magnitude of this increase is investigated, and a general approximation is proposed. The performance of this approximation is investigated in the context of (a) the estimation of the effects of the balanced one-way random model and (b) the estimation of treatment contrasts for balanced incomplete block designs.

Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology

Abstract: BACKGROUND Introduction Data Sets Bayesian Inference and Modeling Likelihood Models Prior Distributions Posterior Distributions Predictive Distributions Bayesian Hierarchical Modeling Hierarchical Models Posterior Inference Exercises Computational Issues Posterior Sampling Markov Chain Monte Carlo Methods Metropolis and Metropolis-Hastings Algorithms Gibbs Sampling Perfect Sampling Posterior and Likelihood Approximations Exercises Residuals and Goodness-of-Fit Model Goodness-of-Fit Measures General Residuals Bayesian Residuals Predictive Residuals and the Bootstrap Interpretation of Residuals in a Bayesian Setting Exceedence Probabilities Exercises THEMES Disease Map Reconstruction and Relative Risk Estimation An Introduction to Case Event and Count Likelihoods Specification of the Predictor in Case Event and Count Models Simple Case and Count Data Models with Uncorrelated Random Effects Correlated Heterogeneity Models Convolution Models Model Comparison and Goodness-of-Fit Diagnostics Alternative Risk Models Edge Effects Exercises Disease Cluster Detection Cluster Definitions Cluster Detection using Residuals Cluster Detection using Posterior Measures Cluster Models Edge Detection and Wombling Ecological Analysis General Case of Regression Biases and Misclassification Error Putative Hazard Models Multiple Scale Analysis Modifiable Areal Unit Problem (MAUP) Misaligned Data Problem (MIDP) Multivariate Disease Analysis Notation for Multivariate Analysis Two Diseases Multiple Diseases Spatial Survival and Longitudinal Analyses General Issues Spatial Survival Analysis Spatial Longitudinal Analysis Extensions to Repeated Events Spatiotemporal Disease Mapping Case Event Data Count Data Alternative Models Infectious Diseases Appendix A: Basic R and WinBUGS Appendix B: Selected WinBUGS Code Appendix C: R Code for Thematic Mapping References Index