Influence diagnostics in constrained general linear models

ABSTRACT

Constrained general linear models (CGLMs) have wide applications in practice. Similar to other data analysis, the identification of influential observations that may be potential outliers is an important step beyond in the CGLMs. We develop multiple case-deletion diagnostics for detecting influential observations in the CGLMs. The diagnostics are functions of basic building blocks: studentized residuals, error contrast matrix, and the inverse of the response variable covariance matrix. The basic building blocks are computed only once from the complete data analysis and provide information on the influence of the data on different aspects of the model fit. Computational formulas are given which make the procedures feasible. An illustrative example with a real data set is also reported.

Keywords:

• Case deletion
• Cook’s distance
• Log-likelihood function

Mathematics Subject Classification:

• 62J20
• 62J05

Acknowledgment

The authors would like to thank the editor and anonymous referees for several helpful comments and suggestions, which resulted in a significant improvement in the presentation of this article.