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Weighted pairwise likelihood estimation for a general class of random effects models.

Vassilis G S Vasdekis1, Dimitris Rizopoulos2, Irini Moustaki3

  • 1Department of Statistics, Athens University of Economics and Business, 76 Patission Street, 10434, Athens, Greece vasdekis@aueb.gr.

Biostatistics (Oxford, England)
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This study introduces a novel weighted pairwise likelihood estimator to efficiently analyze complex multilevel models with latent variables. This method improves parameter estimation accuracy for multivariate data, outperforming simpler approaches.

Keywords:
Categorical dataComposite likelihoodGeneralized linear latent variable modelsLongitudinal data

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Multilevel and multivariate models with latent variables are crucial for analyzing complex data structures.
  • Estimating these models becomes computationally challenging with increasing numbers of latent variables due to high-dimensional integration.
  • Composite likelihood methods offer an alternative to full maximum likelihood estimation by using lower-order densities.

Purpose of the Study:

  • To propose a novel weighted pairwise likelihood estimator for models with random effects/latent variables.
  • To enhance the efficiency of parameter estimation in complex statistical models.
  • To provide a practical method for analyzing multivariate longitudinal data where full likelihood is intractable.

Main Methods:

  • Developed a weighted pairwise likelihood estimator by combining estimates from separate marginal pairwise likelihood maximizations.
  • Derived optimal weights to minimize the total variance of estimated parameters.
  • Applied the methodology to a multivariate growth model for binary outcomes.

Main Results:

  • The proposed weighted pairwise likelihood estimator demonstrated higher efficiency compared to estimators with equal weights.
  • The method effectively handled the estimation challenges in models with multiple latent variables.
  • Successful application to a real-world case study involving schistosomiasis indicators.

Conclusions:

  • The weighted pairwise likelihood approach provides a more efficient and practical estimation strategy for models with latent variables.
  • This method is particularly valuable for analyzing complex hierarchical and multivariate data, such as longitudinal health outcomes.
  • The findings suggest a robust alternative for statistical modeling in various scientific disciplines.