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Linear mixed models for multiple outcomes using extended multivariate skew-t distributions.

Binbing Yu1, A James O'Malley2, Pulak Ghosh3

  • 1Laboratory of Epidemiology and Population Sciences, National Institute on Aging Bethesda, MD 20904, U.S.A.

Statistics and Its Interface
|April 25, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces extended multivariate skew-t (MST) distributions to model complex data with varying tail heaviness. This flexible approach enhances robust modeling for clustered and longitudinal studies, improving analysis of biomedical data.

Keywords:
Multivariate skew-tRobust methodScale-mixture representation

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Multivariate outcomes with skewness and thick tails are common in clustered experiments and longitudinal studies.
  • Linear mixed models using multivariate skew-t (MST) distributions offer robust modeling for such data.
  • Traditional MST distributions assume a common degree of freedom, limiting their ability to model varying tail heaviness across outcomes.

Purpose of the Study:

  • To introduce a novel class of extended multivariate skew-t (MST) distributions.
  • To allow for heterogeneity in tail-heaviness across different outcomes by permitting distinct degrees of freedom.
  • To provide a more flexible and robust modeling framework for complex multivariate data.

Main Methods:

  • Development of extended multivariate skew-t (MST) distributions with varying degrees of freedom.
  • Utilizing the hierarchical representation of MST distributions for parameter estimation.
  • Application of Markov Chain Monte Carlo (MCMC) methods for computing parameter estimates.

Main Results:

  • The proposed extended MST distributions accommodate heterogeneity in tail-heaviness across outcomes.
  • This new class of distributions provides a more flexible family of models for multivariate outcomes.
  • The model was successfully applied to real-world biomedical data.

Conclusions:

  • Extended MST distributions offer a significant advancement in robust modeling for multivariate data with heavy tails and skewness.
  • The flexibility in degrees of freedom allows for more accurate modeling of heterogeneous tail behaviors.
  • The approach is effective for analyzing complex data from biomedical studies, including AIDS progression markers and longitudinal sexual behavior data.