Adaptive Fitting of Linear Mixed-Effects Models with Correlated Random-effects

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Linear mixed-effects models are standard for longitudinal data.
• Convergence failures occur due to boundary issues in random-effects covariance matrix G (near-singular, non-positive definite).
• Existing algorithms are suboptimal, increasing matrix G's condition number with non-zero random-effects correlations.

Purpose of the Study:

• To propose a novel adaptive fitting (AF) algorithm to address convergence issues in linear mixed-effects models.
• To improve computational efficiency and stability by optimizing the estimation of the random-effects covariance matrix G.
• To reduce the condition number of matrix G by minimizing random-effects correlations.

Main Methods:

• Developed an adaptive fitting (AF) algorithm utilizing an optimal linear transformation of the random-effects design matrix.
• The procedure adaptively reduces random-effects correlation estimates to zero in a transformed estimation space.
• Implementation demonstrated using the R package (nlme) with real-world Insulin-like Growth Factor (IGF) protein data.

Main Results:

• Simulations demonstrate that the AF algorithm significantly enhances convergent properties compared to existing methods.
• Improvements are particularly notable under conditions of small sample size, high noise, and high correlation.
• The algorithm effectively manages boundary issues associated with the random-effects covariance matrix G.

Conclusions:

• The proposed adaptive fitting (AF) algorithm offers a robust and computationally efficient solution for linear mixed-effects model fitting.
• AF improves convergence rates and model stability, especially in complex data scenarios.
• This method provides a valuable tool for longitudinal data analysis, as illustrated by the IGF protein data example.