[Rasch] Interpretation of Item Plot

Mike Linacre (RMT) rmt at rasch.org
Sat Mar 24 19:43:27 EST 2007


Thank you for asking us about your plot. Its shape certainly prompts 
further thought ....

In your five-category scale, categories 2 and 4 are a little below modal. 
This means that the category intervals on the latent variable (considered 
from a Rasch-Thurstone perspective) are slightly narrower than the .6 
logits (or so) necessary for ordered Rasch-Andrich thresholds. But is the 
rating scale defective? This depends on several considerations. Here are four:
1) Category meaning: Are the categories intended to be modal, or are 
categories 2 and 4 intended to be transitional (lower probability) states?
2) Model fit: Do the observations in each category fit in those categories?
3) Category inference: Do the average measures (corresponding to the 
observations in each category) advance with the categories?
4) Sampling variation: Is the non-modality of those two categories (this 
time) merely an accident of the data, rarely to be repeated?

The plot does not tell us enough to know whether a 3-category rating scale 
would function better (though it might), nor does it tell us which 
collapsing of the categories would be optimal.

Mike Linacre
rmt at rasch.org

At 3/23/2007, Petroski, Greg wrote:
>The item is ordinal with responses 0 to 4 with larger values indicating 
>greater ability.  Note that two of the five catagories do not ever have 
>the highest probability of being endorsed.  Am I correct in interpreting 
>this as suggesting a defective item -- one that might work as well with 
>only three categories?

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  20:4 Spring 2007
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