Estimating linear mixed effect models with non-normal random effects through saddlepoint approximation and its...

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Linear Mixed Effects (LME) models are widely used in retail, marketing, and medical research.
• Standard LME inference relies on normality assumptions for random effects.
• Retail applications often require non-Normal random effects for accurate parameter interpretation.

Purpose of the Study:

• To develop a flexible LME framework accommodating non-Normal random effects.
• To improve the business interpretability of parameter estimates in LME models.
• To provide a general estimating framework applicable to various LME scenarios.

Main Methods:

• A novel estimating framework based on saddlepoint approximation (SA) of the probability density function.
• Constrained nonlinear optimization problems are formulated.
• The classical LME model is shown to be a special case within the SA framework.

Main Results:

• The proposed SA-based method allows for non-Normal random effects distributions.
• Enhanced real-world interpretability of model estimates is achieved.
• Satisfactory model fits are demonstrated compared to existing approaches.

Conclusions:

• The SA framework offers a generalized approach to LME modeling.
• This method is particularly beneficial for retail analytics requiring nuanced parameter interpretation.
• The study advances LME methodology for practical, real-world applications.