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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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PC program for obtaining orthogonal polynomial regression coefficients for use in longitudinal data analysis.

Thomas R Ten Have1, Charles J Kowalski2, Emet D Schneiderman3

  • 1Department of Biostatistics, The University of Michigan, Ann Arbor, Michigan 48109.

American Journal of Human Biology : the Official Journal of the Human Biology Council
|May 20, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a PC program for generating orthogonal polynomials, simplifying dimensionality reduction in polynomial growth curve models. The program aids in estimating regression coefficients for longitudinal data analysis, especially with unequally spaced time points.

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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.