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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Flexible marginalized models for bivariate longitudinal ordinal data.

Keunbaik Lee1, Michael J Daniels, Yongsung Joo

  • 1Department of Statistics, Sungkyunkwan University, Seoul 110-745, Korea. keunbaik@skku.edu

Biostatistics (Oxford, England)
|February 1, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new Kronecker product covariance structure for analyzing bivariate longitudinal ordinal data. This method effectively models complex correlations, improving analysis of health-related factors.

Keywords:
Kronecker productMetabolic syndromePartial autocorrelation

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Random effects models are standard for longitudinal categorical data.
  • Marginalized random effects models estimate marginal means and serial correlation.
  • Existing models often use autoregressive structures for correlation.

Purpose of the Study:

  • To propose a novel Kronecker product (KP) covariance structure for bivariate longitudinal ordinal data.
  • To model both within-process serial correlation and between-process correlation.
  • To extend correlation modeling beyond standard autoregressive approaches.

Main Methods:

  • Utilized a Kronecker product (KP) covariance structure.
  • Employed partial autocorrelations for re-parameterizing correlation matrices.
  • Proposed maximum marginal likelihood estimation with quasi-Newton and quasi-Monte Carlo integration.
  • Assessed KP structure reasonableness using a score test.

Main Results:

  • The proposed KP structure effectively captures complex correlation patterns in bivariate longitudinal ordinal data.
  • The score test confirmed the reasonableness of the KP structure.
  • The maximum marginal likelihood estimation provided a robust method for parameter estimation.

Conclusions:

  • The novel Kronecker product covariance structure offers a flexible and effective approach for analyzing bivariate longitudinal ordinal data.
  • The method allows for a more comprehensive understanding of correlation structures.
  • This approach can be applied to health studies, such as examining demographic factors on metabolic syndrome and C-reactive protein.