[Rasch] Sample free

Trevor Bond trevor.bond at jcu.edu.au
Wed Jul 23 15:58:32 EST 2008


What is meant by "Rasch is sample free" 
B&F 2nd Chap 10
"Those enamored with traditional principles might be 
more than a little skeptical of some claims made for the Rasch family of 
measurement 
models. Often, the most difficulty is expressed concerning the assertion that 
the Rasch family of models produces what are commonly referred to as 
“personfree” 
estimates of item difficulties and “item-free” estimates of person abilities. 
This is, of course, a direct consequence of the development of invariant, 
intervalscale 
fundamental measures: The use of the shorthand descriptors, “person-free” 
and “item-free” estimates raises some eyebrows in social science circles. 
Invariant 
Rasch measures can be seen as the natural consequence of two complementary 
Rasch measurement principles. The first is the calculation of item difficulty 
estimates that are independent of the distribution of abilities in the particular 
group of persons for whom the items are appropriate. The complement is the 
calculation 
of person ability estimates that are independent of the distribution of difficulties 
of the particular set of items used for the estimation. In that case, we 
should prefer “person-distribution-free” over “person-free” and “item- 
distribution- 
free” over “item-free” because some, rather tendentiously, seem to understand 
“person-free” to mean that no empirical person responses are required. 

B&F 2nd Chap 13
MEASUREMENT AND ITEM RESPONSE THEORY
Of the few textbooks that deal with the Rasch model, most tend to lump it 
together
with two- and three-parameter models under the general heading, Item 
Response
Theories. In that context, the Rasch model is referred to as the one-parameter 
item
response theory (IRT) model. But the 1-PL, 2-PL, 3-PL models are so called 
because
the test items are characterized by one, two, or three parameters, and the 
sample of
persons by a distribution. The persons are not individually parameterized as in 
the
Rasch model. This has important implications for the concept of measurement
invariance, because those IRT models are not “person-distribution-free” (see 
chap.
10).


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