Single-factor analysis by minimum message length estimation

SUMMARY The minimum message length (MML) technique is applied to the problem of estimating the parameters of a multivariate Gaussian model in which the correlation structure is modelled by a single common factor. Implicit estimator equations are derived and compared with those obtained from a maximum likelihood (ML) analysis. Unlike ML, the MML estimators remain consistent when used to estimate both the factor loadings and the factor scores. Tests on simulated data show the MML estimates to be on average more accurate than the ML estimates when the former exist. If the data show little evidence for a factor, the MML estimate collapses. It is shown that the condition for the existence of an MML estimate is essentially that the log-likelihood ratio in favour of the factor model exceeds the value expected under the null (no-factor) hypotheses.