Analysis of skew normal factor analysis model with incomplete data

• Main Authors: Jou-Hsiao Lin, 林柔孝
• Other Authors: Dr. Tsung-I Lin
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/e4x3x4

碩士 === 國立中興大學 === 統計學研究所 === 101 === Missing data are a pervasive problem that arises in almost all statistical models. Factor analysis (FA) is among the most frequently used techniques to identify the underlying relationships among measured variables. This paper present novel methods for the fitting of the skew normal factor analysis (SNFA) model when missing values occur in the data. In the model, the latent factors is assumed to follow a restricted version of multivariate skew normal distribution with additional shape parameters allowing for accommodation of skewness. Under missing at random mechanisms, we formulate an analytically simple ECM algorithm for conducting parameter estimation and retrieving each missing value with a single-valued imputation. To facilitate the implementation, two auxiliary indicator matrices are incorporated into the estimating procedure for exactly extracting the location of observed and missing components of each observation. The practical usefulness of the proposed methodology is illustrated with real data examples and comparisons are made with those obtained from fitting the traditional FA counterparts.