Message/Author 

Uwe Braut posted on Thursday, March 08, 2012  3:25 pm



Is it possible with Mplus to estimate a Rasch model with random item and person effects? 


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 


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 u1u10; %between% u1u10 with u1u10@0; u1u10; Model 2. This includes a group effect for the persons ability %within% f by u1u10@1; %between% fb by u1u10@1; u1u10; Model 3. This is the 2parameter model %within% f by u1u10* (lam1lam10); f@1; %between% fb by u1u10* (lam1lam10); fb; u1u10; 

Uwe Braut posted on Thursday, March 15, 2012  10:23 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? 


I think you are running into the problem of too many dimensions of integration. With ML, you should fix the residual variances to zero, u1u10@0; If you don't, each one requires one dimension of integration. 

Uwe Braut posted on Thursday, March 15, 2012  8:49 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. 


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  11:06 pm



The notion of itemspecific 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). Crossclassification multilevel logistic models in psychometrics. Journal of Educational and Behavioral Statistics, 28, 369–386. 

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