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Calibration data often is often collected within schools. This illustration shows that random school effects for ability do not bias IRT parameter estimates or their standard errors. However, random school effects for item difficulty lead to bias in item discrimination estimates and inflated standard errors for difficulty and ability.
DeMars, C. E. & Jacovidis, J. N. (2016, April). Multilevel IRT: When is local independence violated? Electronic board presented at the annual meeting of the National Council on Measurement and Education, Washington, DC.