Here is Figure 1 from "A Paradigm for Developing Better Measures for Marketing Constructs". Gilbert A. Churchill, Jr., Journal of Marketing Research, 16:1. (Feb., 1979), pp. 64-73).
A Rasch equivalent to Churchill's raw-score procedure for test construction is explained in detail in Mark Wilson's book "Constructing Measures" (LEA, 2005) www.rasch.org/rmt/rmt183c.htm .
There is also Ben Wright's "The Road to Reason" www.rasch.org/rmt/rmt114o.htm.
An essential difference is that Churchill relies heavily on numerical indicators to improve the measures. Rasch focuses more on the meaning of the measures. Does the hierarchy of the items make sense (construct validity)? Do the measures indicate better performance by persons known to perform better (predictive validity)?
Churchill's Paradigm for Better Measures … G.A. Churchill, Rasch Measurement Transactions, 2008, 22:2 p. 1165
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