The flexibility of models of recognition memory: The case of confidence ratings

The normalized maximum likelihood (NML) index is a model-selection index derived from the minimum-description length principle. In contrast to traditional model-selection indices, it also quantifies differences in flexibility between models related to their functional form. We present a new method for computing the NML index for models of categorical data that parameterize multinomial or product-multinomial distributions and apply it to comparing the flexibility of major models of recognition memory for confidence-rating based receiver-operating-characteristic (ROC) data. NML penalties are tabulated for datasets of typical sizes and interpolation functions are fitted that allow one to interpolate NML penalties for datasets with sizes between the tabulated ones. Recovery studies suggest that the NML index performs better than traditional model-selection indices in model selection from ROC data. In an NML-based meta-analysis of 850 ROC datasets, versions of the dual-process signal detection models received most support followed by the finite mixture signal detection model and constrained versions of two-high threshold models.