Metric Stability in Item Response Models

In item response theory, uncertainty associated with estimated item parameters can lead to greater uncertainty in subsequent analyses, such as estimating trait scores for individual examinees. Most existing methods to characterize or correct for item parameter uncertainty implicitly assume that the latent trait continuum is fixed across the posterior distribution of item parameters. However, the latent trait continuum can also be understood as an artifact of the fitted model, such that the location of this continuum is determined with error. In other words, item parameter estimation error implies uncertainty about the location of the metric. This article uses Ramsay's (1996) geometry of the latent trait metric to develop a quantitative measure of metric stability, that is, the sampling variability of the latent trait continuum implied by errors in item parameter estimation. Through a series of illustrations, it is clarified how metric stability is related to other item response model evaluation outcomes (e.g., test information, model fit), and how metric stability can be useful in identifying well-determined regions of the latent trait continuum, making sample size recommendations, and selecting a model. Overall, the proposed measure of metric stability provides meaningful and highly interpretable information to aid in item response model evaluation.