Thou shalt identify! The identifiability of two high-threshold models in confidence-rating recognition (and super-recognition) paradigms

Abstract

Model identifiability i.e., the possibility to determine the ’true’ parameters of a model in a unique manner based on an empirical dataset, is a vital property of any scientific model. Indeed, the absence of this property undermines the model’s use qua measurement and inference tool. Here, I examined the identifiability of different variants of the successful two-high threshold model (2HTM) in the confidence-rating recognition paradigm. Traditionally, 2HTM has adopted the certainty assumption according to which, detected test-probes receive only the highest correct confidence rating. Modern variants, however, allow responses for detected items to distribute across all correct confidence levels (Detect–Correct; DC) or even across erroneous confidence levels (Free Response Mapping, FRM). Here, I present identifiability proofs for the certainty variant and, when there are multiple target conditions, for DC. Additionally, I present non-identifiability proofs for DC when there is a single target condition and for FRM. One important advantage of identifiability proofs over fitting-based methods for testing identifiability is that they highlight the mathematical principles that are instrumental for a deeper understanding of models. Based on these principles, I present a novel extended super-confidence paradigm, which includes super-strong targets and lures and that identifies FRM. I illustrate the perils of non-identifiability by reanalyzing a recent model comparison study of Chen et al. (2015). Finally, solutions for non-identifiability problems are discussed. While the current study focuses on identifiability in the context of recognition-memory, it should serve as a universal reminder for the importance of identifying models in any domain of research.