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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: The authors discuss the value of confidence intervals, show how they could be used in addition to or instead of retrospective power analysis, and demonstrate that confidence intervals can convey information more effectively in some situations than power analyses alone.
Abstract: In this article, the authors outline methods for using fixed and random effects power analysis in the context of meta-analysis. Like statistical power analysis for primary studies, power analysis for meta-analysis can be done either prospectively or retrospectively and requires assumptions about parameters that are unknown. The authors provide some suggestions for thinking about these parameters, in particular for the random effects variance component. The authors also show how the typically uninformative retrospective power analysis can be made more informative. The authors then discuss the value of confidence intervals, show how they could be used in addition to or instead of retrospective power analysis, and also demonstrate that confidence intervals can convey information more effectively in some situations than power analyses alone. Finally, the authors take up the question “How many studies do you need to do a meta-analysis?” and show that, given the need for a conclusion, the answer is “two studies...

853 citations

Journal ArticleDOI
TL;DR: This article cast the generalized linear random effects model in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations, which is flexible to easily accommodate changes in the number of observations.
Abstract: Generalized linear models have unified the approach to regression for a wide variety of discrete, continuous, and censored response variables that can be assumed to be independent across experimental units. In applications such as longitudinal studies, genetic studies of families, and survey sampling, observations may be obtained in clusters. Responses from the same cluster cannot be assumed to be independent. With linear models, correlation has been effectively modeled by assuming there are cluster-specific random effects that derive from an underlying mixing distribution. Extensions of generalized linear models to include random effects has, thus far, been hampered by the need for numerical integration to evaluate likelihoods. In this article, we cast the generalized linear random effects model in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations. The resulting algorithm is flexible to easily accommodate changes in the number...

852 citations

Journal ArticleDOI
TL;DR: The authors suggest a measure of heterogeneity, the median odds ratio, that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios.
Abstract: The logistic regression model is frequently used in epidemiologic studies, yielding odds ratio or relative risk interpretations. Inspired by the theory of linear normal models, the logistic regression model has been extended to allow for correlated responses by introducing random effects. However, the model does not inherit the interpretational features of the normal model. In this paper, the authors argue that the existing measures are unsatisfactory (and some of them are even improper) when quantifying results from multilevel logistic regression analyses. The authors suggest a measure of heterogeneity, the median odds ratio, that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios. Quantifying cluster-level covariates in a meaningful way is a challenge in multilevel logistic regression. For this purpose, the authors propose an odds ratio measure, the interval odds ratio, that takes these difficulties into account. The authors demonstrate the two measures by investigating heterogeneity between neighborhoods and effects of neighborhood-level covariates in two examples--public physician visits and ischemic heart disease hospitalizations--using 1999 data on 11,312 men aged 45-85 years in Malmo, Sweden.

850 citations

Journal ArticleDOI
09 Oct 2014-PeerJ
TL;DR: Simulations show that in cases where overdispersion is caused by random extra-Poisson noise, or aggregation in the count data, observation-level random effects yield more accurate parameter estimates compared to when overdisPersion is simply ignored, and that their ability to minimise bias is not uniform across all types of over Dispersion and must be applied judiciously.
Abstract: Overdispersion is common in models of count data in ecology and evolutionary biology, and can occur due to missing covariates, non-independent (aggregated) data, or an excess frequency of zeroes (zero-inflation). Accounting for overdispersion in such models is vital, as failing to do so can lead to biased parameter estimates, and false conclusions regarding hypotheses of interest. Observation-level random effects (OLRE), where each data point receives a unique level of a random effect that models the extra-Poisson variation present in the data, are commonly employed to cope with overdispersion in count data. However studies investigating the efficacy of observation-level random effects as a means to deal with overdispersion are scarce. Here I use simulations to show that in cases where overdispersion is caused by random extra-Poisson noise, or aggregation in the count data, observation-level random effects yield more accurate parameter estimates compared to when overdispersion is simply ignored. Conversely, OLRE fail to reduce bias in zero-inflated data, and in some cases increase bias at high levels of overdispersion. There was a positive relationship between the magnitude of overdispersion and the degree of bias in parameter estimates. Critically, the simulations reveal that failing to account for overdispersion in mixed models can erroneously inflate measures of explained variance (r2), which may lead to researchers overestimating the predictive power of variables of interest. This work suggests use of observation-level random effects provides a simple and robust means to account for overdispersion in count data, but also that their ability to minimise bias is not uniform across all types of overdispersion and must be applied judiciously.

845 citations

Posted Content
TL;DR: In this paper, a true fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification, and the random effects model was reformulated as a special case of the random parameters model that retains the fundamental structure of the Stochastic Frontier model.
Abstract: Received analyses based on stochastic frontier modeling with panel data have relied primarily on results from traditional linear fixed and random effects models. This paper examines extensions of these models that circumvent two important shortcomings of the existing fixed and random effects approaches. The conventional panel data stochastic frontier estimators both assume that technical or cost inefficiency is time invariant. In a lengthy panel, this is likely to be a particularly strong assumption. Second, as conventionally formulated, the fixed and random effects estimators force any time invariant cross unit heterogeneity into the same term that is being used to capture the inefficiency. Thus, measures of inefficiency in these models may be picking up heterogeneity in addition to or even instead of technical or cost inefficiency. In this paper, a true fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. The random effects model is reformulated as a special case of the random parameters model that retains the fundamental structure of the stochastic frontier model. The techniques are illustrated through two applications, a large panel from the U.S. banking industry and a cross country comparison of the efficiency of health care delivery.

838 citations


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