  This paper proposes a novel profile likelihood method for estimating the
covariance parameters in exploratory factor analysis of high-dimensional
Gaussian datasets with fewer observations than number of variables. An
implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method
are implemented to develop a matrix-free framework for likelihood maximization.
Simulation results show that our method is substantially faster than the
expectation-maximization solution without sacrificing accuracy. Our method is
applied to fit factor models on data from suicide attempters, suicide ideators
and a control group.
