Rolf Sundberg: Fitting the standard factor analysis model, when there are more variables than observations (p>n)

First the standard factor analysis model is introduced, and the classical likelihood equations under normality, valid for p < n. It can be shown that covariance matrix properties for this model, without the need to assume normality or even p < n, lead to estimating equations which are the same, but valid also for p>n. A natural iterative method for solving them is seen (and illustrated) to converge without problems when p > n, in contrast to the case p < n. Another result says that for any fixed n, the factor scores are precisely predicted/estimated as p increases. In all, it may be stated that there is no "curse of dimensionality" in this case - the nice properties do not hold despite p > n, but because p > n.

This is joint work with Uwe Feldmann, Univ. of Saarland, see also Departmental Research Report 2013:10.