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 skew- t , 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.
Highlights
Factor models are among the most used and useful statistical techniques
We demonstrate how to use the EM-type algorithm for maximum likelihood (ML) estimation of the skew-normal factor model
Similar to Theorem 2, we find that [x|η] =d [y|f > 0, η] follows a unified skew-normal distribution, SU N p,k(μ, 0, 1p, W (η)Ω∗), where Ω∗ is given in Theorem 2
Summary
Factor models are among the most used and useful statistical techniques. They date back to the seminal paper of Spearman (1904) and are mainly applied in two major situations: (i) data dimension reduction; and (ii) identification of underlying structures. Yung (1997) developed a confirmatory factor analysis model to handle data such that observations are drawn by several sub-populations In this case, data are not normally distributed. Montanari & Viroli (2010) devised a skew-normal factor model for the analysis of student satisfaction in university courses They assumed that the factors follow a skew-normal distribution and the error term follows a normal distribution. Bagnato & Minozzo (2014) proposed a spatial latent factor model to deal with multivariate geostatistical skew-normal data.
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