Computationally Stable Estimation Procedure for the Multivariate Linear Mixed-Effect Model and Application to Malaria...

Area of Science:

• Statistics
• Biostatistics
• Computational Biology

Background:

• Multivariate linear mixed-effects models are crucial for analyzing complex data structures.
• Consistent estimation of random effects covariance is vital for model accuracy.
• Existing methods like the EM algorithm may yield non-consistent estimates.

Purpose of the Study:

• To develop and present Maximum Likelihood (ML) and Restricted ML (REML) criteria for consistent estimation in multivariate linear mixed-effects models.
• To generalize existing estimation procedures for one-dimensional models to the multivariate case.
• To provide a robust and numerically consistent method for estimating the random effects covariance matrix.

Main Methods:

• Factorization of the random effects covariance matrix.
• Reparameterization of the model to derive an explicit expression of the profiled deviance.
• Comparison of the proposed method with the EM algorithm via a simulation study.

Main Results:

• The proposed method provides a numerically consistent estimate of the random effects covariance matrix.
• The approach is robust regarding starting points for estimation.
• Simulation studies demonstrate the performance of the new method compared to the EM algorithm.

Conclusions:

• The developed ML and REML criteria offer a consistent and robust approach for estimating multivariate linear mixed-effects models.
• The method generalizes existing techniques and provides a reliable alternative to classical algorithms.
• The approach was successfully applied to a real-world study on immune response to Malaria.