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In the past few years, there have been a number of proposals for generalizingthe factor analysis (FA) model and its mixture version (known as mixtures offactor analyzers (MFA)) using non-normal and asymmetric distributions. Thesemodels adopt various types of skew densities for either the factors or theerrors. While the relationships between various choices of skew distributionshave been discussed in the literature, the differences between placing theassumption of skewness on the factors or on the errors have not been closelystudied. This paper examines these formulations and discusses the connectionsbetween these two types of formulations for skew factor models. In doing so, weintroduce a further formulation that unifies these two formulations; that is,placing a skew distribution on both the factors and the errors.

On formulations of skew factor models: skew errors versus skew factors