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 Uwe Braut posted on Thursday, March 08, 2012 - 9:25 am
Is it possible with Mplus to estimate a Rasch model with random item and person effects?
 Tihomir Asparouhov posted on Thursday, March 08, 2012 - 10:11 am
Yes, use type=twolevel and estimator=wlsmv. It might be helpful to look at example 9.9 in the users guide (except you won't have a between level factor). You can also take a look at this paper and the simulation study in section 5.
http://statmodel.com/download/p2t1.pdf
 Tihomir Asparouhov posted on Thursday, March 08, 2012 - 11:43 am
Here is more on this topic ...

Model 1. This will give you a random component for the item and also a random component for the person

%within%
f by u1-u10;
%between%
u1-u10 with u1-u10@0;
u1-u10;

Model 2. This includes a group effect for the persons ability

%within%
f by u1-u10@1;
%between%
fb by u1-u10@1;
u1-u10;

Model 3. This is the 2-parameter model

%within%
f by u1-u10* (lam1-lam10);
f@1;
%between%
fb by u1-u10* (lam1-lam10);
fb;
u1-u10;
 Uwe Braut posted on Thursday, March 15, 2012 - 5:23 am
Thank you for you help! Could you perhaps suggest another parameterization that would allow the use of ML instead of wlsmv for the estimation of a Rasch model with random item effects?
 Linda K. Muthen posted on Thursday, March 15, 2012 - 10:41 am
I think you are running into the problem of too many dimensions of integration. With ML, you should fix the residual variances to zero, u1-u10@0; If you don't, each one requires one dimension of integration.
 Uwe Braut posted on Thursday, March 15, 2012 - 3:49 pm
Thank you again for the advice but, unfortunately, these commands do not seem to work. They do not give me a single random effect for the items difficulties.
 Bengt O. Muthen posted on Thursday, March 15, 2012 - 4:21 pm
Do you want only a single random effect for the item difficulties, or do you want as many random effects as there are items? In principle each item could have a random difficulty.

Is there a specific model in the literature that you want to capture?
 Uwe Braut posted on Thursday, March 15, 2012 - 6:06 pm
The notion of item-specific random effects is interesting but I want a single random effect for the item difficulties. This model is described, for example, by Van den Noortgate, W., De Boeck, P., & Meulders, M. (2003). Cross-classification multilevel logistic models in psychometrics.
Journal of Educational and Behavioral Statistics, 28, 369386.
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