Estimation in Factor Analysis Under Various Initial Assumptions

The object of the following paper is to investigate how far it is practicable to adopt the principle of maximum likelihood for the estimation of factor loadings, when some of the loadings are assumed a priori to be zero. Both the orthogonal and the oblique case arc considered; and the solutions obtained are illustrated by applying them to a simple example. Owing to the need for an iterative procedure the labour involved increases enormously as the number of factors increases. It is concluded that one possibility would be to use methods which, though not fully efficient, would entail only fairly simple calculations. To devise such methods is comparatively easy, but it is far more difficult to assess their efficiency.