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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: This paper describes the inversion scheme using a worked example based upon simulated electrophysiological responses, and uses empirical priors from the second level to iteratively optimize posterior densities over parameters at the first level.
Abstract: This technical note considers a simple but important methodological issue in estimating effective connectivity; namely, how do we integrate measurements from multiple subjects to infer functional brain architectures that are conserved over subjects. We offer a solution to this problem that rests on a generalization of random effects analyses to Bayesian inference about nonlinear models of electrophysiological time-series data. Specifically, we present an empirical Bayesian scheme for group or hierarchical models, in the setting of dynamic causal modeling (DCM). Recent developments in approximate Bayesian inference for hierarchical models enable the efficient estimation of group effects in DCM studies of multiple trials, sessions, or subjects. This approach estimates second (e.g., between-subject) level parameters based on posterior estimates from the first (e.g., within-subject) level. Here, we use empirical priors from the second level to iteratively optimize posterior densities over parameters at the first level. The motivation for this iterative application is to finesse the local minima problem inherent in the (first level) inversion of nonlinear and ill-posed models. Effectively, the empirical priors shrink the first level parameter estimates toward the global maximum, to provide more robust and efficient estimates of within (and between-subject) effects. This paper describes the inversion scheme using a worked example based upon simulated electrophysiological responses. In a subsequent paper, we will assess its robustness and reproducibility using an empirical example.

98 citations

Book ChapterDOI
01 Jan 2004

98 citations

Journal ArticleDOI
TL;DR: It is shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach, which enables analyses of animal models with large numbers of observations.
Abstract: Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

97 citations

Journal ArticleDOI
TL;DR: In this article, a direct method for computing the coefficient of a variance or covariance component in the expectation of a mean square or mean product when the inverse of the coefficient matrix is available is presented for use with models containing only noninteracting sets of random effects in addition to error.
Abstract: A direct method of computing the coefficient of a variance or covariance component in the expectation of a mean square or mean product when the inverse of the coefficient matrix is available is presented for use with models containing only non-interacting sets of random effects in addition to error. These models may contain any number of sets of fixed effects including interactions and partial regressions for continuous variables. Shortcut computational procedures are presented for the estimation of components of variance and covariance when one set of random effects interacts with one or two sets of fixed main effects and subclass frequencies are unequal. A computational example is given for the two-way classification without interaction and one is available in mimeograph form from the author for the three-way classification with interactions.

97 citations

Journal ArticleDOI
TL;DR: In this paper, a bridge distribution function for the random effect in the random intercept logistic regression model is proposed, where the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation.
Abstract: SUMMARY Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration.

97 citations


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