Skew-normal factor analysis models with incomplete data

Abstract

Traditional factor analysis (FA) rests on the assumption of multivariate normality. However, in some practical situations, the data do not meet this assumption; thus, the statistical inference made from such data may be misleading. This paper aims at providing some new tools for the skew-normal (SN) FA model when missing values occur in the data. In such a model, the latent factors are assumed to follow a restricted version of multivariate SN distribution with additional shape parameters for accommodating skewness. We develop an analytically feasible expectation conditional maximization algorithm for carrying out parameter estimation and imputation of missing values under missing at random mechanisms. The practical utility of the proposed methodology is illustrated with two real data examples and the results are compared with those obtained from the traditional FA counterparts.

Keywords:

• ECM algorithm
• imputation
• missing data
• rMSN distribution
• skewness

Acknowledgments

We gratefully acknowledge the chief editor, the associate editor and three anonymous referees for their insightful comments and suggestions, which led to a much improved version of this article. We would also like to thank Ms Jou-Hsiao Lin and Mr Tzu Hung Hsu for their skillful assistance in the initial experimental study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research was supported by MOST [103-2118-M-005-001-MY2] awarded by the Ministry of Science and Technology of Taiwan.