In factor factor analysis, it is critical to determine the number of factors. A new approach to select the number of factors based on unbiased risk estimation is introduced. This approach utilizes a concept, called generalized degrees of freedom (GDF), originally proposed for model selection in regression. A data perturbation technique is applied for estimating GDF. Simulation experiments show that the proposed method performs better than some commonly used methods. (C) 2009 Elsevier B.V. All rights reserved.