In trying to respond to your critique regarding whether factor analysis or the Rasch approach can resolve the "mixture" problem, I find it unclear about what meaning of "mixture" you are using in this context. Are you asking, e.g, whether the wide range of symptoms that we observe in depression, is the result of a mixture of the underlying syndromes of major depressive and generalized anxiety disorders, as against in the other case, the results of the interaction of independent dimensions, uncovered through factor analysis?
Also, on a related issue, what do you mean by "intensive analysis"
It would be useful if you could clarify these concepts so that I can try to provide an intelligible reply. One problem in regard to discussing the mixture issue may be the several meanings we encounter in psychometrics for factor analysis. When using Hotelling's principal components, I would restate that of the factor analytic techniques involved, principal components is characterized as a strictly mathematical approach, based on deriving dimensions generated by the intercorrelations of the factored variables, with investigators confined to minimal interpretation, i.e., interpreting the meaning underlying the most highly "loaded" variables of an extracted component. Factor analysis, in general, in psychometrics can, as we know however,take several forms, several of the techniques relying more heavily on the investigator's choice of the form and on his interpretations at several stages of the procedure.. So that the role of factor analysis in relation to the mixture problem may differ as a function of the specific factor analytic approach referred to.
Martin M. Katz
April 17, 2014