Linear Mixed Effects Models with Flexible Generalized Skew-Elliptical Random Effects

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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Selection Strategy for Covariance Structure of Random Effects in Linear Mixed-effects Models

Scandinavian Journal of Statistics ◽

10.1111/sjos.12179 ◽

2015 ◽

Vol 43 (1) ◽

pp. 275-291 ◽

Cited By ~ 2

Author(s):

Xinyu Zhang ◽

Hua Liang ◽

Anna Liu ◽

David Ruppert ◽

Guohua Zou

Keyword(s):

Random Effects ◽

Covariance Structure ◽

Mixed Effects ◽

Mixed Effects Models ◽

Selection Strategy ◽

Linear Mixed Effects Models ◽

Linear Mixed Effects

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Simultaneous fixed and random effects selection in finite mixture of linear mixed-effects models

Canadian Journal of Statistics ◽

10.1002/cjs.11192 ◽

2013 ◽

Vol 41 (4) ◽

pp. 596-616 ◽

Cited By ~ 4

Author(s):

Yeting Du ◽

Abbas Khalili ◽

Johanna G. Nešlehová ◽

Russell J. Steele

Keyword(s):

Random Effects ◽

Mixed Effects ◽

Finite Mixture ◽

Mixed Effects Models ◽

Linear Mixed Effects Models ◽

Linear Mixed Effects ◽

Fixed And Random Effects

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Random effects structure for confirmatory hypothesis testing: Keep it maximal

10.31234/osf.io/39mhs ◽

2018 ◽

Author(s):

Dale Barr ◽

Roger Philip Levy ◽

Christoph Scheepers ◽

Harry Tily

Keyword(s):

Hypothesis Testing ◽

Random Effects ◽

Gold Standard ◽

Mixed Effects ◽

Mixed Effects Models ◽

Data Driven ◽

Linear Mixed Effects Models ◽

Linear Mixed Effects ◽

Within Subjects ◽

Maximal Models

Linear mixed-effects models (LMEMs) have become increasingly prominent in psycholinguistics and related areas. However, many researchers do not seem to appreciate how random effects structures affect the generalizability of an analysis. Here, we argue that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades. Through theoretical arguments and Monte Carlo simulation, we show that LMEMs generalize best when they include the maximal random effects structure justified by the design. The generalization performance of LMEMs including data-driven random effects structures strongly depends upon modeling criteria and sample size, yielding reasonable results on moderately-sized samples when conservative criteria are used, but with little or no power advantage over maximal models. Finally, random-intercepts-only LMEMs used on within-subjects and/or within-items data from populations where subjects and/or items vary in their sensitivity to experimental manipulations always generalize worse than separate F1 and F2 tests, and in many cases, even worse than F1 alone. Maximal LMEMs should be the ‘gold standard’ for confirmatory hypothesis testing in psycholinguistics and beyond.

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