  Linear Mixed Effects (LME) models have been widely applied in clustered data
analysis in many areas including marketing research, clinical trials, and
biomedical studies. Inference can be conducted using maximum likelihood
approach if assuming Normal distributions on the random effects. However, in
many applications of economy, business and medicine, it is often essential to
impose constraints on the regression parameters after taking their real-world
interpretations into account. Therefore, in this paper we extend the classical
(unconstrained) LME models to allow for sign constraints on its overall
coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN)
distribution on the random effects instead of the unconstrained Normal
distribution which is often found in classical literature. With the
aforementioned change, difficulty has dramatically increased as the exact
distribution of the dependent variable becomes analytically intractable. We
then develop likelihood-based approaches to estimate the unknown model
parameters utilizing the approximation of its exact distribution. Simulation
studies have shown that the proposed constrained model not only improves
real-world interpretations of results, but also achieves satisfactory
performance on model fits as compared to the existing model.
