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This work is dedicated to the memory of Alain Lieury, who stimulated my interest in the use of factor analysis methods in differential psychology. First, we briefly discuss the theoretical status of factors and the nature of factor analytic inference. We then present the common and unique factor analysis model, and outline the various stages of the implementation of exploratory factor analysis. Lastly, the integration of factor analysis in the more general framework of structural equation models and certain extensions of confirmatory factor analysis are described. We highlight some aspects of the evolution of the model and techniques.