Towards Determinate Exploratory Factor Analysis

It is well-known that the classic exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative EFA model is proposed, which gives determinate factors. An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model and algorithm can be seen as a specific sparse PCA and as a low-rankplus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new EFA model, and the performance and behavior of its algorithmic implementation.