Assume \(\pmb{y}\), the response on \(P\) measured items, is centered *multivariate Gaussian* distributed with variance-covariance matrix \(\pmb{\Sigma}\):

\[ \pmb{y} \sim N_P\left( \pmb{0}, \pmb{\Sigma} \right) \]

- The goal is to find some model for \(\pmb{\Sigma}\) with
*positive degrees of freedom*in which \(\pmb{\Sigma}\) closely resembles the observed variance-covariance matrix- The number of parameters should be less than \(P(P+1)/2\)