scholarly journals Understanding Mixed-Effects Models Through Data Simulation

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592096511
Author(s):  
Lisa M. DeBruine ◽  
Dale J. Barr
Keyword(s):  
Random Effects ◽  
Analysis Of Variance ◽  
R Package ◽  
Mixed Effects ◽  
Experimental Designs ◽  
Mixed Effects Models ◽  
Data Simulation ◽  
Linear Mixed Effects ◽  
Power Calculations

Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed-effects models. However, much of this research is analyzed using analysis of variance on aggregated responses because researchers are not confident specifying and interpreting mixed-effects models. This Tutorial explains how to simulate data with random-effects structure and analyze the data using linear mixed-effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters. Data simulation not only can enhance understanding of how these models work, but also enables researchers to perform power calculations for complex designs. All materials associated with this article can be accessed at https://osf.io/3cz2e/ .

scholarly journals Understanding mixed effects models through data simulation

2019 ◽  
Author(s):  
Lisa Marie DeBruine ◽  
Dale J. Barr
Keyword(s):  
Random Effects ◽  
R Package ◽  
Mixed Effects ◽  
Experimental Designs ◽  
Mixed Effects Models ◽  
Data Simulation ◽  
Linear Mixed Effects ◽  
Power Calculations

Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed effects models. However, much of this research is analyzed using ANOVA on aggregated responses because researchers are not confident specifying and interpreting mixed effects models. The tutorial will explain how to simulate data with random effects structure and analyse the data using linear mixed effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters. Data simulation can not only enhance understanding of how these models work, but also enables researchers to perform power calculations for complex designs. All materials associated with this article can be accessed at https://osf.io/3cz2e/.

scholarly journals Computationally Stable Estimation Procedure for the Multivariate Linear Mixed-Effect Model and Application to Malaria Public Health Problem

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Eric Houngla Adjakossa ◽  
Norbert Mahouton Hounkonnou ◽  
Grégory Nuel
Keyword(s):  
Em Algorithm ◽  
Covariance Matrix ◽  
Random Effects ◽  
Estimation Procedure ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Consistent Estimate ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
The Em Algorithm

Abstract In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. This strategy can be viewed as the generalization of the estimation procedure used by Douglas Bates and his co-authors in the context of the fitting of one-dimensional linear mixed-effects models. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non-consistent. In a simulation study, we compare the estimates obtained from the present method with the EM algorithm-based estimates. We finally apply the method to a study of an immune response to Malaria in Benin.

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