# [Rasch] How to simulate data with error

Mike Linacre mike at winsteps.com
Fri Jun 28 09:50:35 EST 2013

```Stuart:

We could simulate dichotomous data this way with Excel:
1) assign item difficulties and person abilities
2) compute the expected value of the observation with the Rasch model = P
3) compute the square-root of model variance of the observation around
its expectation = sqrt(P*(1-P)) = S
4) multiply S by a unit-normal deviate = S*N(0,1) = D
5) half-round (P + D)  to 0 or 1 = X, the observation
6) repeat (2)-(5) for every observation

But simpler is to compare P with a uniform [0-1] random number, R.
X=1 if P>R, otherwise X=0.

Mike L.

On 6/27/2013 13:34 PM, Stuart Luppescu 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.

```