Diagnostics analysis for skew-normal linear regression models: Applications to a quality of life dataset

Abstract

The skew-normal distribution has been used successfully in various statistical applications. The main purpose of this paper is to consider local influence analysis, which is recognized as an important step of data analysis. Motivated to simplify expressions of the conditional expectation of the complete-data log-likelihood function, used in the EM algorithm, diagnostic measures are derived from the case-deletion approach and the local influence approach inspired by Zhu et al. [Biometrika 88 (2001) 727–737] and Zhu and Lee [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 111–126]. Finally, the results obtained are applied to a dataset from a study to evaluate quality of life (QOL) and to identify its associated factors in climacteric women with a history of breast cancer.