Two-stage method of estimation for general linear growth curve models

Area of Science:

• Statistics
• Biostatistics
• Growth Curve Analysis

Background:

• Linear random-effects growth curve models (REGCM) are standard for analyzing longitudinal data.
• Analyzing population covariate effects on specific growth curve characteristics often requires complex reparameterization.
• Existing methods can be cumbersome and less robust to model misspecification.

Purpose of the Study:

• To extend the REGCM to directly study population covariate effects on linear combinations of growth curve parameters.
• To develop a more flexible and robust estimation method for growth curve analysis.
• To apply the new method to a biological growth model where standard techniques are insufficient.

Main Methods:

• A two-stage estimation method is implemented, building upon the two-stage growth curve model.
• Generalized least squares (GLS) is used to estimate population parameters.
• The method is designed to be robust to model misspecification.

Main Results:

• The GLS estimator is consistent, asymptotically efficient, and multivariate normal for large sample sizes.
• The proposed method is more robust to model misspecification than maximum likelihood with standard REGCM.
• The method successfully analyzes factors affecting the growth rate of salmonellae in a cubic growth model.

Conclusions:

• The extended REGCM with the two-stage GLS estimator provides a powerful and flexible tool for analyzing covariate effects on growth curves.
• This approach simplifies the analysis of complex growth characteristics and offers improved robustness.
• The method is particularly valuable for biological and other scientific applications with non-standard growth patterns.