Robust modeling of multivariate longitudinal data using modified Cholesky and hypersphere decompositions

Anbin Rhee, Min Sun Kwak, Keunbaik Lee

Research output: Contribution to journalArticlepeer-review

Abstract

Due to the convenience of the statistical interpretation and parameter estimation, a normal distribution is typically assumed for multivariate longitudinal data analysis. However, this assumption may be questionable in practice, because it is possible that outliers exist or that the underlying data will show heavy tails. In addition, since the covariance matrix should explain complex correlation structures, it must be positive-definite, and as it is also high-dimensional, the modeling of the covariance matrix is not easy. To solve these problems, we propose the robust modeling of multivariate longitudinal data by considering multivariate t distribution, and we exploit modified Cholesky and hypersphere decompositions to model the covariance matrix. The estimation of the models is shown to be robust when the data include outliers and exhibit heavy tails. The performance of our proposed model and algorithm is illustrated using a nonalcoholic fatty liver disease data set and several simulation studies.

Original languageEnglish
Article number107439
JournalComputational Statistics and Data Analysis
Volume170
DOIs
StatePublished - Jun 2022
Externally publishedYes

Keywords

  • Autoregressive
  • Correlation matrix
  • Heterogeneity
  • Innovation variance
  • Positive definite
  • t distribution

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