ABSTRACT
In Chapter 8, we discussed the model of common-factor analysis, pointing out that its chief defect lies in the indeterminacy of the common and unique portions of variables. In this chapter, we consider several models of factor analysis which keep some of the essential ideas of the common-factoranalysis model while introducing new ideas to provide more determinacy. Speci cally we will consider (1) the model of component analysis, which makes no distinction between common and unique variance before analyzing variables into components; (2) image analysis, which de nes the common part of a variable as that part predictable by multiple correlation from all the other variables in the analysis; (3) canonical-factor analysis, which seeks to nd the particular linear combinations of the original variables that would be maximally correlated with a set of common factors for the variables; (4) image-factor analysis; (5) models that control for doublets, and (6) alpha factor analysis, which is a variant of the common-factor-analysis model which rescales the variables before analysis into the metric of the common parts of the variables. We will also consider the question of psychometric inference in factor analysis, because this will have some bearing on our evaluation of these different models.
