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.

Multivariate Random-effects Meta-regression: Updates to Mvmeta:

Abstract: An extension of mvmeta, my program for multivariate random-effects meta-analysis, is described The extension handles meta-regression Estima- tion methods available are restricted maximum likelihood, maximum likelihood, method of moments, and fixed effects The program also allows a wider range of models (Riley’s overall correlation model and structured between-studies covari- ance); better estimation (using Mata for speed and correctly allowing for missing data); and new postestimation facilities (I-squared, standard errors and confidence intervals for between-studies standard deviations and correlations, and identifi- cation of the best intervention) The program is illustrated using a multiple- treatments meta-analysis Copyright 2011 by StataCorp LP

Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions

Abstract: SUMMARY Hierarchical generalised linear models are developed as a synthesis of generalised linear models, mixed linear models and structured dispersions. We generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models. The method allows models with (i) any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects, (ii) structured dispersion components, (iii) different link and variance functions for the fixed and random effects, and (iv) the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models. Inferences can be made by applying standard procedures, in particular those for model checking, to components of either generalised linear model. We also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance. Likelihood-type inference is extended to this wide class of models in a unified way.

Double hierarchical generalized linear models (with discussion)

Abstract: Summary. We propose a class of double hierarchical generalized linear models in which random effects can be specified for both the mean and dispersion. Heteroscedasticity between clusters can be modelled by introducing random effects in the dispersion model, as is heterogeneity between clusters in the mean model. This class will, among other things, enable models with heavy-tailed distributions to be explored, providing robust estimation against outliers. The h-likelihood provides a unified framework for this new class of models and gives a single algorithm for fitting all members of the class. This algorithm does not require quadrature or prior probabilities.

Efficient parametrisations for normal linear mixed models

Abstract: SUMMARY The generality and easy programmability of modern sampling-based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice. However, these methods can often be extremely slow to converge, due to high correlations between, or weak identifiability of, certain model parameters. We present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models. In particular, we study the two-stage hierarchical normal linear model, the Laird-Ware model for longitudinal data, and a general structure for hierarchically nested linear models. Using analytical arguments, simulation studies, and an example involving clinical markers of acquired immune deficiency syndrome (AIDS), we indicate when reparametrisation is likely to provide substantial gains in efficiency.

Estimating Genotypic Correlations and Their Standard Errors Using Multivariate Restricted Maximum Likelihood Estimation with SAS Proc MIXED

Abstract: Plant breeders traditionally have estimated genotypic and phenotypic correlations between traits using the method of moments on the basis of a multivariate analysis of variance (MANOVA). Drawbacks of using the method of moments to estimate variance and covariance components include the possibility of obtaining estimates outside of parameter bounds, reduced estimation efficiency, and ignorance of the estimators' distributional properties when data are missing. An alternative approach that does not suffer these problems, but depends on the assumption of normally distributed random effects and large sample sizes, is restricted maximum likelihood (REML). This paper illustrates the use of Proc MIXED of the SAS system to implement REML estimation of genotypic and phenotypic correlations. Additionally, a method to obtain approximate parametric estimates of the sampling variances of the correlation estimates is presented. MANOVA and REML methods were compared with a real data set and with simulated data. The simulation study examined the effects of different correlation parameter values, genotypic and environmental sample sizes, and proportion of missing data on Type I and Type II error rates and on accuracy of confidence intervals. The two methods provided similar results when data were balanced or only 5% of data were missing. However, when 15 or 25% data were missing, the REML method generally performed better, resulting in higher power of detection of correlations and more accurate 95% confidence intervals. Samples of at least 75 genotypes and two environments are recommended to obtain accurate confidence intervals using the proposed method.