Bayesian Covariance Structure Modeling of Multi-Way Nested Data

Stephanus Petrus Reinardus Baas, Richard J. Boucherie, Jean-Paul G.J.A. Fox

Research output: Working paperProfessional

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A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the well-known dependence structure implied by random effects. A conjugate shifted-inverse gamma prior is proposed for the covariance parameters which ensures that the covariance matrix remains positive definite under posterior analysis. A numerically efficient Gibbs sampling procedure is defined for balanced nested designs, and is validated using two simulation studies. For a top-layer unbalanced nested design, the procedure requires an additional data augmentation step. The proposed data augmentation procedure facilitates sampling latent variables from (truncated) univariate normal distributions, and avoids numerical computation of the inverse of the structured covariance matrix. The Bayesian multivariate (linear transformation) model is applied to two-way nested interval-censored event times to analyze differences in adverse events between three groups of patients, who were randomly allocated to treatment with different stents (BIO-RESORT). The parameters of the structured covariance matrix represent unobserved heterogeneity in treatment effects and are examined to detect differential treatment effects.
Original languageEnglish
Number of pages30
Publication statusPublished - 25 Jan 2022


  • Bayesian probit model
  • Covariance structure model
  • Interval-censored times
  • Multi-way nested design
  • Shifted-inverse gamma distribution


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