The detection of residual serial correlation in linear mixed models

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• The empirical semi-variogram is useful for identifying serial correlation in stationary linear mixed models.
• Existing methods may not adequately capture complex correlation structures in non-stationary models.

Purpose of the Study:

• To extend the empirical semi-variogram approach for analyzing non-stationary linear mixed models.
• To improve the estimation of covariance structures in models with random effects beyond intercepts.
• To apply this extended method to real-world data, specifically prostate cancer data from the Baltimore Longitudinal Study of Aging.

Main Methods:

• Extension of Diggle's (1988) empirical semi-variogram method.
• Application to linear mixed models with non-stationary covariance structures and random effects.
• Utilizing prostate cancer data from the Baltimore Longitudinal Study of Aging.
• Conducting a simulation study to validate the method's effectiveness.

Main Results:

• The extended empirical semi-variogram effectively suggests appropriate covariance structures for non-stationary linear mixed models.
• The method demonstrated improvement in covariance structure estimation compared to standard approaches.
• Application to prostate cancer data yielded insights into disease progression modeling.

Conclusions:

• The extended empirical semi-variogram is a valuable tool for modeling complex correlation structures in non-stationary linear mixed models.
• This approach enhances the accuracy of statistical models used in longitudinal studies.
• The findings have implications for analyzing health data, such as that from the Baltimore Longitudinal Study of Aging.