Skewed factor models using selection mechanisms

Abstract

Please cite this article as: H.-M. Kim, M. Maadooliat, R.B. Arellano-Valle, M.G. Genton, Skewed factor models using selection mechanisms, Journal of Multivariate Analysis (2015), http://dx.doi.org/10.1016/j.jmva. 2015.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Skewed Factor Models using Selection MechanismsHyoung Abstract Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skewt, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.

On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality

“…Finally, for the fourth data example, the performance of goodness-of-fit tests for MSN distribution are compared on the five variate open/closed book (OCB) dataset Mardia et al (1979). The OCB data are recently analyzed by Kim et al (2016), who considered three new skewed factor models, namely the SN, skew-t, and the generalized SN factor models, depending on a selection mechanism of the factors. The OCB data contain the results of five proficiency namely mechanics, vectors, algebra, analysis, and statistics tested on n = 88 students.…”

Mixtures of Factor Analyzers with Fundamental Skew Symmetric Distributions

“…Concerning (ii), for the case of a single factor analysis model, Montanari and Viroli (2010) considered the restricted skew normal distribution for its factors. Kim et al (2016) proposed the so-called generalised skew normal factor model which is equivalent to a FA model with the errors following a CFUSN distribution. In the case of mixtures of skew factor analyzers, we note that for the MSNFA and MSTFA models (Lin et al, 2016(Lin et al, , 2018 the factors follow a (restricted) skew normal and skew t-distribution, respectively.…”