The single factor analysis model for data is

where , is an i.i.d. zero-mean multivariate Gaussian random variable with a symmetric, positive definite variance-covariance matrix ; that is, for all . It is thus assumed that each data vector follows a -variate Gaussian distribution with moments

The aim of single factor analysis is to estimate the unknown factor scores , the mean , the variance-covariance matrix and the factor loadings .

I’ve written this note to show how one may derive the Fisher information for the single factor model. This turns out to be a fairly involved task requiring a lot of linear algebra and matrix differential calculus identities. I’ve uploaded a document describing all the necessary mathematical steps to the Publications section. Anyone interested in matrix differential calculus and linear algebra should find it useful.