The One-Parameter Logistic Model Can Be True With Zero Probability for a Unidimensional Measuring Instrument: How One Could Go Wrong Removing Items Not Satisfying the Model

Abstract

This note is concerned with the chance of the one-parameter logistic (1PL-) model or the Rasch model being true for a unidimensional multi-item measuring instrument. It is pointed out that if a single dimension underlies a scale consisting of dichotomous items, then the probability of either model being correct for that scale can be zero. The question is then addressed, what the consequences could be of removing items not following these models. Using a large number of simulated data sets, a pair of empirically relevant settings is presented where such item elimination can be problematic. Specifically, dropping items from a unidimensional instrument due to them not satisfying the 1PL-model, or the Rasch model, can yield potentially seriously misleading ability estimates with increased standard errors and prediction error with respect to the latent trait. Implications for educational and behavioral research are discussed.