The Fisher information function and scoring in binary ideal point item response models: a cautionary tale

This article examines the Fisher information functions, I ( θ ) , and explores implications for scoring of binary ideal point item response models. These models typically appear to have I ( θ ) that are bimodal and identically equal to 0 at the ideal point. The article shows that this is an inherent property of ideal point IRT models, which either have this property or are indeterminate and thus violate the likelihood regularity conditions. For some models, the indeterminacy can be resolved, generating an effectively unimodal I ( θ ) , albeit with violated regularity conditions. In other cases, I ( θ ) diverges. All reasonable ideal point IRT models exhibit this behaviour. Users should exercise caution when relying on asymptotics, particularly for shorter assessments. Use of simulated plausible values or prediction from a fully Bayesian estimation is recommended for scoring.