[Rasch] One model for three constructs

Mike Linacre rmt at rasch.org
Mon Jun 6 13:49:34 EST 2011

Thank you for your questions, Juanito.

You asked: What shall I do with my three constructs? How to justify my boss 
that the three constructs are considered as one dimension?

Reply: Are your three constructs truly three dimensions (as different as 
height, weight, temperature)? Or are they three strands (as similar as 
addition, subtraction, multiplication in an arithmetic test)? If your three 
constructs all relate to the same thing in the same way, then they are 
probably three strands. If so, organize the items on the item map according 
to their strands.

You wrote:
>Further, I followed your suggestion that I should do a Principal Component 
>Analysis of the Residuals with Winsteps, then do a "shop" DIF analysis for 
>the items by comparing the four shops in pairs.  My question is: What does 
>it mean when DIF test is significant for several items  and nonsignificant 
>for other items?  Can I still use the instrument for the four shops in the 
>future ?

Reply: Let's think about an example. Suppose the manager of one shop 
emphasizes "friendliness". Then "friendliness" will be rated relatively 
highly by customers of that shop. So, in a DIF report, the "friendliness" 
item will have significant DIF for that shop. We would be unlikely to 
change the instrument or its administration because of this DIF. Instead, 
this DIF becomes part of our report about the shop. We want the same 
instrument to be administered in the same way in all 4 shops, so that we 
can see that "friendliness" performance is relatively higher (or the 
"friendliness" item is relatively easier) in one shop.

You wrote: Using Winsteps, how to construct customer-item map in four 
columns, one for each shop?

Reply: Here is one way. Do separate analyses of each of the four shops. 
Output the four person-item maps (Table 1). Then use the rectangular-copy 
function in Word (alt+mouse) to place the maps next to each other.


Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  24:4 Spring 2011
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