This paper establishes theoretical bounds on GIRT parameter estimation error as a function of test length, item characteristics, and response category structure, providing insights for adaptive test design and sample size determination.
Key findings
Establishes fundamental lower and upper bounds on GIRT parameter estimation error.
Derives novel Cramér-Rao-type bounds for GPCM and GRM, characterizing Fisher information accumulation.
Shows estimation error scales as O((nIk(θ))−1/2) where n is the number of items and Ik(θ) is the per-item Fisher information.
Proves matching upper bounds via analysis of maximum likelihood estimation convergence.
Limitations & open questions
Theoretical bounds may not fully account for practical complexities in test administration.
Assumes standard regularity conditions for asymptotic tightness of bounds.