Empirical Bayes Analysis for Systems of Mixed Models with Linked Autocorrelated Random Effects

1991 ◽  
Vol 86 (416) ◽  
pp. 1007-1012
Author(s):  
John Bryant ◽  
Roger Day
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Empirical Bayes ◽  
Bayes Analysis

Using empirical Bayes predictors from generalized linear mixed models to test and visualize associations among longitudinal outcomes

2018 ◽  
Vol 28 (5) ◽  
pp. 1399-1411 ◽  
Author(s):  
Susan K Mikulich-Gilbertson ◽  
Brandie D Wagner ◽  
Gary K Grunwald ◽  
Paula D Riggs ◽  
Gary O Zerbe
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Empirical Bayes ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
P Values ◽  
Association Analyses ◽  
Second Stage

Medical research is often designed to investigate changes in a collection of response variables that are measured repeatedly on the same subjects. The multivariate generalized linear mixed model (MGLMM) can be used to evaluate random coefficient associations (e.g. simple correlations, partial regression coefficients) among outcomes that may be non-normal and differently distributed by specifying a multivariate normal distribution for their random effects and then evaluating the latent relationship between them. Empirical Bayes predictors are readily available for each subject from any mixed model and are observable and hence, plotable. Here, we evaluate whether second-stage association analyses of empirical Bayes predictors from a MGLMM, provide a good approximation and visual representation of these latent association analyses using medical examples and simulations. Additionally, we compare these results with association analyses of empirical Bayes predictors generated from separate mixed models for each outcome, a procedure that could circumvent computational problems that arise when the dimension of the joint covariance matrix of random effects is large and prohibits estimation of latent associations. As has been shown in other analytic contexts, the p-values for all second-stage coefficients that were determined by naively assuming normality of empirical Bayes predictors provide a good approximation to p-values determined via permutation analysis. Analyzing outcomes that are interrelated with separate models in the first stage and then associating the resulting empirical Bayes predictors in a second stage results in different mean and covariance parameter estimates from the maximum likelihood estimates generated by a MGLMM. The potential for erroneous inference from using results from these separate models increases as the magnitude of the association among the outcomes increases. Thus if computable, scatterplots of the conditionally independent empirical Bayes predictors from a MGLMM are always preferable to scatterplots of empirical Bayes predictors generated by separate models, unless the true association between outcomes is zero.

scholarly journals Gradient boosting for linear mixed models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Colin Griesbach ◽  
Benjamin Säfken ◽  
Elisabeth Waldmann
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Selection Procedure ◽  
Classification Theory ◽  
Gradient Boosting ◽  
Random Structure ◽  
Boosting Algorithm ◽  
The One ◽  
Biased Estimates ◽  
Selection Of

Abstract Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

scholarly journals Mixed Models as a Tool for Comparing Groups of Time Series in Plant Sciences

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 362
Author(s):  
Ioannis Spyroglou ◽  
Jan Skalák ◽  
Veronika Balakhonova ◽  
Zuzana Benedikty ◽  
Alexandros G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Repeated Measurements ◽  
Time Series Models ◽  
Additional Time ◽  
Biotic Stresses ◽  
Viable Solution ◽  
Long Time

Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

scholarly journals A novel sandwich algorithm for empirical Bayes analysis of rank data

2017 ◽  
Vol 10 (4) ◽  
pp. 543-556 ◽  
Author(s):  
Arnab Kumar Laha ◽  
Somak Dutta ◽  
Vivekananda Roy
Keyword(s):  
Empirical Bayes ◽  
Bayes Analysis

scholarly journals Estimating Bayes Factors for Linear Models with Random Slopes on Continuous Predictors

2017 ◽  
Author(s):  
Mirko Thalmann ◽  
Marcel Niklaus ◽  
Klaus Oberauer
Keyword(s):  
Bayesian Statistics ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Effects ◽  
Bayes Factors ◽  
Mixed Effects Models ◽  
Type I ◽  
Frequentist Statistics ◽  
Random Slopes ◽  
Continuous Predictors

Using mixed-effects models and Bayesian statistics has been advocated by statisticians in recent years. Mixed-effects models allow researchers to adequately account for the structure in the data. Bayesian statistics – in contrast to frequentist statistics – can state the evidence in favor of or against an effect of interest. For frequentist statistical methods, it is known that mixed models can lead to serious over-estimation of evidence in favor of an effect (i.e., inflated Type-I error rate) when models fail to include individual differences in the effect sizes of predictors ("random slopes") that are actually present in the data. Here, we show through simulation that the same problem exists for Bayesian mixed models. Yet, at present there is no easy-to-use application that allows for the estimation of Bayes Factors for mixed models with random slopes on continuous predictors. Here, we close this gap by introducing a new R package called BayesRS. We tested its functionality in four simulation studies. They show that BayesRS offers a reliable and valid tool to compute Bayes Factors. BayesRS also allows users to account for correlations between random effects. In a fifth simulation study we show, however, that doing so leads to slight underestimation of the evidence in favor of an actually present effect. We only recommend modeling correlations between random effects when they are of primary interest and when sample size is large enough. BayesRS is available under https://cran.r-project.org/web/packages/BayesRS/, R code for all simulations is available under https://osf.io/nse5x/?view_only=b9a7caccd26a4764a084de3b8d459388

scholarly journals P075 Travel or cheers? Examining the drivers and mechanisms of home court advantage in the 2020/2021 NBA regular season

2021 ◽  
Vol 2 (Supplement_1) ◽  
pp. A45-A45
Author(s):  
J Leota ◽  
D Hoffman ◽  
L Mascaro ◽  
M Czeisler ◽  
K Nash ◽  
...  
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Natural Experiment ◽  
National Basketball Association ◽  
Home Team ◽  
The Road ◽  
On The Road ◽  
The Impact ◽  
The Relationship

Abstract Introduction Home court advantage (HCA) in the National Basketball Association (NBA) is well-documented, yet the co-occurring drivers responsible for this advantage have proven difficult to examine in isolation. The Coronavirus disease (COVID-19) pandemic resulted in the elimination of crowds in ~50% of games during the 2020/2021 NBA season, whereas travel remained unchanged. Using this ‘natural experiment’, we investigated the impact of crowds and travel-related sleep and circadian disruption on NBA HCA. Methods 1080 games from the 2020/2021 NBA regular season were analyzed using mixed models (fixed effects: crowds, travel; random effects: team, opponent). Results In games with crowds, home teams won 58.65% of the time and outrebounded (M=2.28) and outscored (M=2.18) their opponents. In games without crowds, home teams won significantly less (50.60%, p = .01) and were outrebounded (M=-0.41, p < .001) and outscored (M=-0.13, p < .05) by their opponents. Further, the increase in home rebound margin fully mediated the relationship between crowds and home points margin (p < .001). No significant sleep or circadian effects were observed. Discussion Taken together, these results suggest that HCA in the 2020/2021 NBA season was predominately driven by the presence of crowds and their influence on the effort exerted by the home team to rebound the ball. Moreover, we speculate that the strict NBA COVID-19 policies may have mitigated the travel-related sleep and circadian effects on the road team. These findings are of considerable significance to a domain wherein marginal gains can have immense competitive, financial, and even historical consequences.

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