This article pursues the hypothesis that a scale-invariant representation of history could support performance in a variety of learning and memory tasks. This representation maintains a conjunctive representation of what happened when that grows continuously less accurate for events further and further in the past. Simple behavioral models using a few operations, including scanning, matching and a "jump back in time" that recovers previous states of the history, describe a range of behavioral phenomena. These behavioral applications include canonical results from the judgment of recency task over short and long scales, the recency and contiguity effect across scales in episodic recall, and temporal mapping phenomena in conditioning. A growing body of neural data suggests that neural representations in several brain regions have qualitative properties predicted by the representation of temporal history. Taken together, these results suggest that a scale-invariant representation of temporal history may serve as a cornerstone of a physical model of cognition in learning and memory.

In a classic 1978 Memory &Cognition article, Geoff Loftus explained why noncrossover interactions are removable. These removable interactions are tied to the scale of measurement for the dependent variable and therefore do not allow unambiguous conclusions about latent psychological processes. In the present article, we present concrete examples of how this insight helps prevent experimental psychologists from drawing incorrect conclusions about the effects of forgetting and aging. In addition, we extend the Loftus classification scheme for interactions to include those on the cusp between removable and nonremovable. Finally, we use various methods (i.e., a study of citation histories, a questionnaire for psychology students and faculty members, an analysis of statistical textbooks, and a review of articles published in the 2008 issue of Psychology andAging) to show that experimental psychologists have remained generally unaware of the concept of removable interactions. We conclude that there is more to interactions in a 2 × 2 design than meets the eye.

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S. Dennis and M. S. Humphreys (see record 2001-17194-007) proposed a model with the strict assumption that recognition memory is not affected by interference from other items. Instead, confusions are due to noise generated by prior contexts in which the test item appeared. This model seems disparate from existing models of recognition memory but is similar in many ways that are not superficially obvious. One difference is the order in which item and context information are used as retrieval cues. A more critical difference is the assertion that only an item's history, and not other items, affects recognition memory. Conceptual arguments along with the results of 2 experiments make a persuasive case that both types of noise affect recognition. To illustrate the approach, the authors fit experimental data with a version of the retrieving effectively from memory model (R. M. Shiffrin & M. Steyvers, 1997) incorporating both sources of noise.

In differentiation models, the processes of encoding and retrieval produce an increase in the distribution of memory strength for targets and a decrease in the distribution of memory strength for foils as the amount of encoding increases. This produces an increase in the hit rate and decrease in the false-alarm rate for a strongly encoded compared with a weakly encoded list, consistent with empirical data. Other models assume that the foil distribution is unaffected by encoding manipulations or the foil distribution increases as a function of target strength. They account for the empirical data by adopting a stricter criterion for strongly encoded lists relative to weakly encoded lists. The differentiation and criterion shift explanations have been difficult to discriminate with accuracy measures alone. In this article, reaction time distributions and accuracy measures are collected in a list-strength paradigm and in a response bias paradigm in which the proportion of test items that are targets is manipulated. Diffusion model analyses showed that encoding strength is primarily accounted for by changes in the rate of accumulation of evidence (i.e., drift rate) for both targets and foils and manipulating the proportion of targets is primarily accounted for by changes in response bias (i.e., starting point). The diffusion model analyses is interpreted in terms of predictions of the differentiation models in which subjective memory strength is mapped directly onto drift rate and criterion placement is mapped onto starting point. Criterion shift models require at least 2 types of shifts to account for these findings.