I've checked two textbooks about EFA, one is the seminal work of Gorsuch (1974, 'Factor Analysis') and the other 'Exploratory and Confirmatory Factor Analysis' by Thompson (2004). Both described determination of number of factors to be extracted as a stage before choosing factor extraction method in the EFA decision sequence. But I'm wondering that all criteria for determination of the number of the factors (e.g. Kaiser criterion, Scree test, etc) need some sort of factor extraction to be done before. So are these authors wrong ? or am I missing something ?
Ehsan: eigenvalues, upon which the Kaiser rule, parallel analysis, and other empirical factor-retention criteria are based (empirical factor retention decisions being data-driven, rather than driven by preferences regarding number of factors, or theoretical motivations, which may inform other retention approaches), can be extracted initially using principal components or common factor analysis (or iterated factor analysis), and a retention decision made about the underlying dimensionality (number of components or number of common factors). Subsequent to a retention decision, full-on factor analysis (rotation, extracted factors using ML factor analysis, interpretation of eigenvectors, etc.) can take place. The authors you cite are fully correct.