A Diagnostic Procedure to Detect Departures From Local Independence in Item Response Theory Models
Item response theory (IRT) is a widely used measurement model. When considering its use in education, health outcomes, and psychology, it is likely to be one of the most impactful psychometric models in existence. IRT has many advantages over classical test theory-based measurement models. For these advantages to hold in practice, strong assumptions must be satisfied. One of these assumptions, local independence, is the focus of the work described here. Local independence is the assumption that, conditional on the latent variable(s), item responses are unrelated to one another (i.e., independent). Stated another way, local independence implies that the only thing causing items to covary is the modeled latent variable(s). Violations of this assumption, quite aptly titled local dependence, can have serious consequences for the estimated parameters. A new diagnostic is proposed, based on parameter stability in an item-level jackknife resampling procedure. We review the ideas underlying the new diagnostic and how it is computed before covering some simulated and real examples demonstrating its effectiveness.