Influential observation in the growth curve model with unstructured covariance matrix

Jian-Xin Pan*, Kai Tai Fang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


Under a normal assumption, Liski (Biometrics 47 (1991) 659-668) gave some measurements for assessing influential observations in the growth curve model (GCM) with a known covariance. For the GCM with an unstructured covariance matrix (UCM), i.e., the covariance is an arbitrary positive definite matrix, the problems of detecting influential observations are discussed in this paper. Based on the empirical influence function of the regression coefficient, a generalized Cook's distance is proposed to measure the influence of a subset of observations on the MLE's fit. In order to make comparison with the generalized Cook's distance, some other diagnostic measurements for assessing the influence are investigated too, which are based on the change of the confidence ellipsoid's volume after deleting the observation's subset. In addition, the influences on some linear combinations of the regression coefficient are discussed. For illustration purpose, a numerical example is provided and the analysis results show that the approaches presented in this paper are useful in practice.

Original languageEnglish
Pages (from-to)71-87
Number of pages17
JournalComputational Statistics and Data Analysis
Issue number1
Publication statusPublished - 14 Jun 1996

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discordant outlier
  • Growth curve model
  • Influential observation
  • Leverage point
  • Statistical diagnostics


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