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How do I fit multilevel IRT models?
Here we consider multilevel IRT models for binary responses. See also the FAQ on singlelevel item response models for binary responses. Multilevel two parameter IRT models in gllamm
Now I consider a multilevel extension of the IRT models.
Suppose students are nested within schools and the school identifier is eq load: i1i15 constraint def 1 [pid1_1l]i2 = [sch2_1l]i2 constraint def 2 [pid1_1l]i3 = [sch2_1l]i3 constraint def 3 [pid1_1l]i4 = [sch2_1l]i4 constraint def 4 [pid1_1l]i5 = [sch2_1l]i5 gllamm y i1i15, nocons link(logit) family(binomial) i(pid sch) /// eqs(load load) constraints(1/4) adaptThis syntax is similar to the one for a simple twoparameter IRT model. Here for the multilevel two parameter IRT model, we need to specify loadings for levels 2 and 3 in the eqs() option.
In addition, note that
the discrimination parameters are assumed to be the same at levels 2 and 3 in the model.
I therefore defined
four constraints for the factor loadings (or item discrimnation parameters) using
constraint def .
Since the discrimination parameter for the first item (item 1) is constrained to 1 at both levels,
we constrain the factor loadings for items 2 to 4 to be the same at level 2 and level 3.
We then specify these constraints with the constraints(1/4) option,
where 1/4 means 1 to 4.
Instead of using parameter constraints, the model can also be estimated using the
Examples
References


