[Rasch] [Semi-OT] How to simulate data with error

Rense Lange rense.lange at gmail.com
Fri Jun 28 06:49:09 EST 2013

I am not sure I understand. But, I would define some items (i.e., their difficulty parks) and then estimate the student score (I am assuming) from there …. So, the procedure is:

1. Define item parms as needed (e.g., normal, uniform, …)
2. Randomly draw student parameter from normal distribution (or any other you need)
3. Generate random 0-1 "raw" observations based on 1 and 2 above
4. Use UCON to find estimated value of student parameter and the associated SE
5. Repeat 2-4 as needed

You now have raw observations, and thus raw sums, actual student parms and "recovered" ones, and their difference conditional on student ability will closely follow a normal distribution in my experience that has excellent agreement with the SE from step 4. The simulation part comes in at step 3 where random raw observations are generated (well, conditional on student ability).

If you have a particular dataset you want to simulate, you can do Winsteps to generate files of random 0-1 according to the item difficulties.

Rense Lange

On Jun 27, 2013, at 5:34 PM, Stuart Luppescu <slu at ccsr.uchicago.edu> wrote:

> Hello all, this is not directly related to Rasch analysis but I can't
> think of a better group of people to put this problem to.
> I want to simulate measure data with error; the kind of data you get as
> the result of Rasch analysis. I was thinking of generating simulated
> measures and standard errors, and then including error by adding to the
> generated measures values sampled from a normal distribution with mean
> 0.0 and standard deviation = the simulated standard errors.
> Does this sound reasonable?
> Thanks.
> -- 
> Stuart Luppescu <slu at ccsr.uchicago.edu>
> University of Chicago
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