The variance theory of the mirror effect in recognition memory.

The mirror effect refers to a rather general empirical finding showing that, for two classes of stimuli, the class with the higher hit rates also has a lower false alarm rate. In this article, a parsimonious theory is proposed to account for the mirror effect regarding, specifically, high- and low-frequency items and the associated receiver-operating curves. The theory is implemented in a recurrent network in which one layer represents items and the other represents contexts. It is shown that the frequency mirror effect is found in this simple network if the decision is based on counting the number of active nodes in such a way that performance is optimal or near optimal. The optimal performance requires that the number of active nodes is low, only nodes active in the encoded representation are counted, the activation threshold is set between the old and the new distributions, and normalization is based on the variance of the input. Owing to the interference caused by encoding the to-be-recognized item in several preexperimental contexts, the variance of the input to the context layer is greater for high- than for low-frequency items, which yields lower hit rates and higher false alarm rates for high- than for low-frequency items. Although initially the theory was proposed to account for the mirror effect with respect to word frequency, subsequent simulations have shown that the theory also accounts for strength-based mirror effects within a list and between lists. In this case, consistent with experimental data, the variance theory suggests that focusing attention to the more difficult class within a list affects the hit rate, but not the false alarm rate and not the standard deviations of the underlying density, leading to no mirror effect.