We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm.
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