# Testing for IRT assumptions with large samples and short scales

I’m using R’s mirt package to fit some (unidimensional) GPC models to a set of Likert-style items with five levels in each. I’m looking for some advice on how to test for the standard IRT assumptions.

Testing unidimensionality with a scree plot using fa.parallel() works fine. However, regarding local independence and item fit: since the sample is large (around 4,000) and the number of items in each scale is small (3-4) the correlations given by Yen’s Q3 (using residuals()) inevitably come out strongly negative (around -0.6), and the p-values for itemfit() come our very small.

Do people happen to know of any alternative (perhaps graphical) ways to evaluate local independence and item fit under these circumstances, preferably in ways that are well-integrated with mirt?

I don’t think switching to ltm will help me here: it would mean I could run a DIMTEST using sirt’s conf.detect(), but ltm’s item fit() and sirt’s Q3() are for dichotomous models only - and would likely have the same issues with large samples and small scales anyway.

Any advice would be greatly appreciated!

• Have you tried the residuals() function in the mirt package? philchalmers.github.io/mirt/html/residuals-method.html That sounds like what you are after. Also, itemfit() has more traditional graphical methods build in – philchalmers Mar 31 '19 at 21:56
• Thanks, Phil. The empirical.plot argument in itemfit() was indeed what I needed for item fit. On residuals(): that’s what I’ve used for Q3. Apologies if a stupid question, but what’s the way to evaluate local independence with residuals() in a manner that (unlike Q3) doesn’t inevitably yield strongly negative correlations for short scales/instruments? Do the X2 and G2 statistics not have the same issue? – kh_one Apr 1 '19 at 9:50
• Q3 is based on computing factor score estimates first, so it can be quite sub-optimal. This is why the defaults in mirt at the marginal LD statistic by Chen and Thissen, which average over the underlying distribution instead – philchalmers Apr 1 '19 at 13:24
• That’s helpful. Thanks, Phil! – kh_one Apr 3 '19 at 10:14