[Rasch] Comparison Rasch 3-parm IRT

Ricardo Primi rprimi at mac.com
Sat Sep 14 13:20:40 EST 2013

Thank you Mike for your prompt response. It helps a lot!
Indeed the average S. E. are very close to your calculations: (0.49/0.59)ˆ2 = .689 !! 
I run a scatterplot of the Rasch S.E. (Y) vs 3-PL S. E. (X) colored by estimated measures. In general high ability are estimated with higher S. E. because items are relatively easy for the sample.
Suppose two datasets A and B with everything equal but the discrimination in A is generally lower (low correlation theta-score) than dataset B. Does WINSTEPS will have different discrimination in each dataset maintaining it constant within datasets? or will it calibrate as 1 in both ? Does this differences will impact measures variance ?
And finally if the lower asymptote is really grater than zero for most of the items what estimate of reliability should we trust more ? Rasch or 3PL ? 
I know that we can use the real relaibility (that weight s. e. by the infit increasing it if we jhave more misfited person responses) but as shown in earlier plot 
 this correction lower the reliability but it is still higher then the 3PL. 

Thanks in advance for any comments 



Em 13/09/2013, às 01:55, Mike Linacre escreveu:

> Thank you for your questions about Rasch and 3-PL reliability, Ricardo.
> In general, the information in a response that fits the dichotomous 
> Rasch model contains more statistical information than an equivalent 
> response that fits the 3-PL model. This is because of the information 
> that is lost due to the lower asymptote, c parameter. For example, 
> suppose that the c parameter is 0.99, then there is almost no 
> information in the response. If the item-sample targeting is at 70% 
> success and c=2, we expect a 3-PL response to contain around 67% of the 
> information in a Rasch response.
> Rasch Reliability = 0.70. Measure S.D. = 0.79.  So, according to 
> Spearman(1910), RMSE (average S.E.) = 0.43
> 3PL Reliability=0.56. Theta S.D. = 0.79.  So, according to 
> Spearman(1910), RMSE (average S.E.) = 0.52
> Do these average S.E.s look like those reported by your software, 
> Ricardo? If so, your 3-PL responses have (0.43/0.52)^2 = 68% of the 
> information in your Rasch responses, and we expect that the average 
> person is scoring around 70% on the test.
> Hope this helps ....
> Mike L.
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