Q:

Item Response Models with Few Measures

Are there any problems with using Item Response Theory models such as the Graded Response Model when the number of measures is small? I don't know if there are any asymptotic results that would make a Graded Response Model undesirable with such a small number of measures.

A:

There are a number of issues, include convergence failures, biased parameter estimates, large standard errors, and difficulty in using the fitted model for predictive purposes (i.e., for scoring individuals by obtaining $\hat{\theta}$ estimates). 
These are all technical issues, though more philosophically you can think of other issues such as failure to sufficiently sample the domain, validity issues in selecting only certain kinds of response stimuli types, and so on. 
So yes, there are potentially many issues, though these depend of philosophical considerations as well as data characteristics. 

