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.

Hartung-Knapp-Sidik-Jonkman approach and its modification for random-effects meta-analysis with few studies

Abstract: Random-effects meta-analysis is commonly performed by first deriving an estimate of the between-study variation, the heterogeneity, and subsequently using this as the basis for combining results, i.e., for estimating the effect, the figure of primary interest. The heterogeneity variance estimate however is commonly associated with substantial uncertainty, especially in contexts where there are only few studies available, such as in small populations and rare diseases. Confidence intervals and tests for the effect may be constructed via a simple normal approximation, or via a Student-t distribution, using the Hartung-Knapp-Sidik-Jonkman (HKSJ) approach, which additionally uses a refined estimator of variance of the effect estimator. The modified Knapp-Hartung method (mKH) applies an ad hoc correction and has been proposed to prevent counterintuitive effects and to yield more conservative inference. We performed a simulation study to investigate the behaviour of the standard HKSJ and modified mKH procedures in a range of circumstances, with a focus on the common case of meta-analysis based on only a few studies. The standard HKSJ procedure works well when the treatment effect estimates to be combined are of comparable precision, but nominal error levels are exceeded when standard errors vary considerably between studies (e.g. due to variations in study size). Application of the modification on the other hand yields more conservative results with error rates closer to the nominal level. Differences are most pronounced in the common case of few studies of varying size or precision. Use of the modified mKH procedure is recommended, especially when only a few studies contribute to the meta-analysis and the involved studies’ precisions (standard errors) vary.

A random effects model for binary data

Abstract: SUMMARY This paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects. With the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects, the marginal likelihood can be computed without numerical integrations. The method uses local independence models as well as those that incorporate additional dependence among the responses. Two examples, a panel study with binary responses and an analysis of item-response data, will be used to illustrate the method.

Bayesian methods of analysis for cluster randomized trials with binary outcome data.

Abstract: We explore the potential of Bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data, and apply the methods to a trial randomized by general practice. An approximate relationship is derived between the intracluster correlation coefficient (ICC) and the between-cluster variance used in a hierarchical logistic regression model. By constructing an informative prior for the ICC on the basis of available information, we are thus able implicitly to specify an informative prior for the between-cluster variance. The approach also provides us with a credible interval for the ICC for binary outcome data. Several approaches to constructing informative priors from empirical ICC values are described. We investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set, while its interval estimate is more sensitive. The Bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering. This enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption. In a model with a more complex variance structure, Bayesian methods can provide credible intervals for a difference between two variance components, in order for example to investigate whether the effect of intervention varies across clusters. We compare our results with those obtained from classical estimation, discuss the relative merits of the Bayesian framework, and conclude that the flexibility of the Bayesian approach offers some substantial advantages, although selection of prior distributions is not straightforward.

The Hausman test in a Cliff and Ord panel model

Abstract: Summary This paper studies the random effects model and the fixed effects model for spatial panel data. The model includes a Cliff and Ord type spatial lag of the dependent variable as well as a spatially lagged one-way error component structure, accounting for both heterogeneity and spatial correlation across units. We discuss instrumental variable estimation under both the fixed and the random effects specifications and propose a spatial Hausman test which compares these two models accounting for spatial autocorrelation in the disturbances. We derive the large sample properties of our estimation procedures and show that the test statistic is asymptotically chi-square distributed. A small Monte Carlo study demonstrates that this test works well even in small panels.