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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 single-level 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: i1-i15 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 i1-i15, nocons link(logit) family(binomial) i(pid sch) /// eqs(load load) constraints(1/4) adaptThis syntax is similar to the one for a simple two-parameter 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
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