Normal distribution

Statistics

Algorithm

Mathematical optimization

Internal medicine

Statistical inference

Generalized linear mixed model

Artificial intelligence

Composite material

Mixed model

Random effects model

Expectation–maximization algorithm

Materials science

Range (aeronautics)

Normality

Inference

Maximization

Flexibility (engineering)

Mathematics

Computer science

Skew

Maximum likelihood

Medicine

Telecommunications

Meta-analysis

Marginal likelihood

Journal of Data Science

Normality (symmetric) of the random effects and the withinsubject errors is a routine assumptions for the linear mixed model, but it may be unrealistic, obscuring important features of among-and within-subjects variation.We relax this assumption by considering that the random effects and model errors follow a skew-normal distributions, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior.The marginal distribution for the observed quantity is derived which is expressed in closed form, so inference may be carried out using existing statistical software and standard optimization techniques.We also implement an EM type algorithm which seem to provide some advantages over a direct maximization of the likelihood.Results of simulation studies and applications to real data sets are reported.

Skew-normal Linear Mixed Models