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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.


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Journal ArticleDOI
TL;DR: Overall, in between-study comparisons, panels of children with diagnosed asthma or pre-existing respiratory symptoms appeared less affected by PM10 levels than those without, and effect estimates were larger where studies were conducted in higher ozone conditions, so limited confidence may be placed on summary estimates of effect.
Abstract: Background: Panel studies have been used to investigate the short term effects of outdoor particulate air pollution across a wide range of environmental settings. Aims: To systematically review the results of such studies in children, estimate summary measures of effect, and investigate potential sources of heterogeneity. Methods: Studies were identified by searching electronic databases to June 2002, including those where outcomes and particulate level measurements were made at least daily for ⩾8 weeks, and analysed using an appropriate regression model. Study results were compared using forest plots, and fixed and random effects summary effect estimates obtained. Publication bias was considered using a funnel plot. Results: Twenty two studies were identified, all except two reporting PM 10 (24 hour mean) >50 μg.m −3 . Reported effects of PM 10 on PEF were widely spread and smaller than those for PM 2.5 (fixed effects summary: −0.012 v −0.063 l.min −1 per μg.m −3 rise). A similar pattern was evident for symptoms. Random effects models produced larger estimates. Overall, in between-study comparisons, panels of children with diagnosed asthma or pre-existing respiratory symptoms appeared less affected by PM 10 levels than those without, and effect estimates were larger where studies were conducted in higher ozone conditions. Larger PM 10 effect estimates were obtained from studies using generalised estimating equations to model autocorrelation and where results were derived by pooling subject specific regression coefficients. A funnel plot of PM 10 results for PEF was markedly asymmetrical. Conclusions: The majority of identified studies indicate an adverse effect of particulate air pollution that is greater for PM 2.5 than PM 10 . However, results show considerable heterogeneity and there is evidence consistent with publication bias, so limited confidence may be placed on summary estimates of effect. The possibility of interaction between particle and ozone effects merits further investigation, as does variability due to analytical differences that alter the interpretation of final estimates.

194 citations

Journal ArticleDOI
TL;DR: The authors showed that conditional maximum likelihood can eliminate this bias by partitioning the covariate into between-and within-cluster components and models that include separate terms for these components also eliminate the source of the bias.
Abstract: Summary. We consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors, which leads to inconsistent estimators. We show that conditional maximum likelihood can eliminate this bias. Conditional likelihood leads naturally to the partitioning of the covariate into between- and within-cluster components and models that include separate terms for these components also eliminate the source of the bias. Another viewpoint that we develop is the idea that many violations of the assumptions (including correlation between the random effects and a covariate) in a generalized linear mixed model may be cast as misspecified mixing distributions. We illustrate the results with two examples and simulations.

193 citations

Journal ArticleDOI
TL;DR: In this article, the authors relax the assumption that the random effects and model errors follow a skew-normal distribution, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior.
Abstract: Normality (symmetric) of the random effects and the within-subject errors is a routine assumptions for the linear mixed model, but it may be unrealistic, obscuring important features of among- and within-subjects variation. We relax this assumption by considering that the random effects and model errors follow a skew-normal distributions, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior. The marginal distribution for the observed quantity is derived which is expressed in closed form, so inference may be carried out using existing statistical software and standard optimization techniques. We also implement an EM type algorithm which seem to provide some advantages over a direct maximization of the likelihood. Results of simulation studies and applications to real data sets are reported.

193 citations

Journal ArticleDOI
TL;DR: Inference for the fixed effects under the assumption of independent normally distributed errors with constant variance is shown to be robust when the errors are either non-gaussian or heteroscedastic, except when the error variance depends on a covariate included in the model with interaction with time.

191 citations

Journal ArticleDOI
TL;DR: The performances of 3 alternatives to the standard CI procedure are examined under a random-effects model and 8 different tau2 estimators to estimate the weights: the t distribution CI, the weighted variance CI (with an improved variance), and the quantile approximation method (recently proposed).
Abstract: One of the main objectives in meta-analysis is to estimate the overall effect size by calculating a confidence interval (CI). The usual procedure consists of assuming a standard normal distribution and a sampling variance defined as the inverse of the sum of the estimated weights of the effect sizes. But this procedure does not take into account the uncertainty due to the fact that the heterogeneity variance (tau2) and the within-study variances have to be estimated, leading to CIs that are too narrow with the consequence that the actual coverage probability is smaller than the nominal confidence level. In this article, the performances of 3 alternatives to the standard CI procedure are examined under a random-effects model and 8 different tau2 estimators to estimate the weights: the t distribution CI, the weighted variance CI (with an improved variance), and the quantile approximation method (recently proposed). The results of a Monte Carlo simulation showed that the weighted variance CI outperformed the other methods regardless of the tau2 estimator, the value of tau2, the number of studies, and the sample size.

190 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023198
2022433
2021409
2020380
2019404