Multivariate Priors, with a Focus on Factor and Structural Equation Models

A range of multivariate techniques are available for modeling multivariate collections of metric, binary, or count data, or for modeling multivariate random effects or regression residuals. These include data reduction (reduced dimension) methods, such as factor and principal component analysis (e.g., Hayashi and Arav, 2006; Lopes and West, 2004), discriminant analysis (e.g., Brown et al., 1999; Rigby, 1997), data mining, as well as direct (full dimension) modeling of the joint density of the observations or regression residuals (e.g., Chib and Winkelmann, 2001). Structured multivariate effects in the analysis of spatial or time-configured data raise additional issues, such as representing intervariable correlation within units as well as nonexchangeability between units (Song et al., 2005).