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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Joint regression analysis for discrete longitudinal data.

L Madsen1, Y Fang

  • 1Department of Statistics, Oregon State University, Corvallis, Oregon 97331, USA. madsenl@onid.orst.edu

Biometrics
|November 3, 2010
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Summary
This summary is machine-generated.

This study presents an approximation for Gaussian copula likelihood to estimate regression parameters in correlated discrete outcomes. For finite samples, generalized estimating equation (GEE) estimators showed higher efficiency than initially expected.

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Correlated discrete or mixed bivariate/trivariate outcomes present challenges in regression parameter estimation.
  • Existing Gaussian copula likelihood methods (Song et al., 2009) are limited in handling response vectors longer than three.
  • Accurate statistical modeling is crucial for analyzing complex biological and medical data.

Purpose of the Study:

  • To introduce a novel approximation to the Gaussian copula likelihood for estimating regression parameters.
  • To enable parameter estimation from response vectors of significantly larger lengths.
  • To compare the efficiency of the proposed method with generalized estimating equations (GEE) using real-world data.

Main Methods:

  • Developed an approximation to the Gaussian copula likelihood function.
  • Applied the approximation to estimate regression parameters for correlated discrete outcomes.
  • Utilized the toenail infection dataset (De Backer et al., 1996) comprising binary response vectors.
  • Conducted a simulation study to compare finite sample efficiencies.

Main Results:

  • The proposed approximation is asymptotically equivalent to the Gaussian copula likelihood.
  • For finite samples, generalized estimating equation (GEE) estimators demonstrated up to 20% greater efficiency compared to maximizing the Gaussian copula likelihood.
  • The method allows for parameter estimation with response vectors longer than three.

Conclusions:

  • The developed approximation offers a viable method for analyzing correlated discrete outcomes with longer response vectors.
  • While asymptotically efficient, the Gaussian copula likelihood may not outperform GEE in finite sample scenarios for this type of data.
  • The findings highlight the importance of considering sample size and specific data structures when choosing between statistical estimation methods.