[Georg] Rasch was strongly against exploratory factor analysis, for two reasons. Not only because it was based on unrealistic assumptions like linearity and normality, but also because it was exploratory. He therefore always stressed that Rasch analysis is confirmatory. That it does require a theory of the construct and that the purpose of the analysis was both to check the theory and to check the items.
And Rasch never talked about interval scales. To Rasch, the constructs that we measure by Rasch models are constructs on ratio scales with absolute zeros and arbitrary units. Taking the logarithm of a ratio scale measure ["for practical purposes", Rasch, 1980, p.80] creates something similar to an interval scale since the arbitrary unit of the ratio scale is transformed into an arbitrary origin of the logit scale. An arbitrary unit on the logit scale corresponds to an arbitrary power transformation on the ratio scale, which is rarely taken to be part of the definition of ratio scales.
Item Characteristic Curves: Model and Empirical.
Figure 3 in Rashid et. al (2008) WSEAS Transactions on Advance in Engineering Education, 8, 5, 591-602
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