PC program for obtaining orthogonal polynomial regression coefficients for use in longitudinal data analysis

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal data analysis often requires dimensionality reduction to P parameters from T observations.
• Polynomial growth curve models are a common approach for analyzing such data.
• Estimating regression coefficients for these models involves selecting an appropriate design matrix (W).

Purpose of the Study:

• To advocate for the use of orthogonal polynomials in the design matrix (W) for polynomial growth curve models.
• To present a PC program (written in GAUSS) for computing orthogonal polynomials and regression coefficients.
• To facilitate the analysis of longitudinal data, particularly when time points are not equally spaced.

Main Methods:

• Focus on polynomial growth curve models for one-sample data matrices.
• Utilize orthogonal polynomials to construct the design matrix (W).
• Develop and present a GAUSS program for calculating orthogonal polynomials and regression coefficients (α).

Main Results:

• The presented GAUSS program efficiently computes orthogonal polynomials, serving as an alternative to tables or manual calculations.
• The program computes orthogonal polynomial regression coefficients (α) for subsequent analyses.
• Demonstrates the program's utility with examples for comparing growth profiles.

Conclusions:

• Orthogonal polynomials offer a robust method for dimensionality reduction in growth curve modeling.
• The GAUSS program simplifies the computation of necessary components for longitudinal data analysis.
• This tool enhances the ability to compare growth profiles across different groups.