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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Multivariate regression models are crucial for analyzing complex datasets.
  • Handling missing data in skewed, positive-valued response vectors presents significant challenges.
  • Existing methods may not adequately capture associations among response vector components.

Purpose of the Study:

  • To propose and investigate a novel class of multivariate regression models.
  • To address ignorable missing data in skewed, positive-component response vectors.
  • To enable accurate marginal quantile estimation considering component associations.

Main Methods:

  • Development of multivariate regression models for skewed, positive data with missing values.
  • Application of a Markov Chain Monte Carlo (MCMC) Bayesian approach.
  • Utilizing a monotone data augmentation algorithm for missing data imputation.

Main Results:

  • The proposed models effectively handle ignorable missing data.
  • Accurate estimation of marginal quantiles is achieved, accounting for component associations.
  • Simulation studies confirm the satisfactory performance of posterior distributions and imputation.

Conclusions:

  • The developed models provide a robust framework for analyzing skewed, positive multivariate data with missing observations.
  • The Bayesian MCMC approach with data augmentation is effective for quantile estimation.
  • The methodology is validated through simulations and demonstrated on real-world anthropometric data.