Identification constraints and inference in factor models

The choice of constraints used to identify a simple factor model can affect the shape of the likelihood. Specifically, under some nonzero constraints, standard errors may be inestimable even at the maximum likelihood estimate (MLE). For a broader class of nonzero constraints, symmetric normal approximations to the modal region may not be appropriate. A simple graphical technique to gain insight into the relative location of equivalent modes is introduced. Implications for estimation and inference in factor models, and latent trait models more generally, are discussed.