Journal of Experimental Psychology: Learning, Memory, and Cognition 1994, Vol. 20, No. 1,201-205 Copyright © 1994 by the American Psychological Association, Inc. 0278-7393/94/S3.00 OBSERVATIONS On Explaining the Mirror Effect Douglas L. Hintzman Two points are made in relation to the recent article by K. Kim and M. Glanzer (1993). First, the attention-likelihood model is more complex than these authors and others suggest. In particular, 2 kinds of quantities—(a) parameters representing the true state of the subject's memory and (b) the subject's estimates of those parameters—have been referred to using the same symbols. This obscures the essential role of metamemory in the model's predictions. Second, log-likelihood rescaling is not needed to explain the mirror effect. An alternative rescaling scheme is described, which can be added to a variety of memory models. This new rescaling method estimates a test item's learnability by learning it. Simulations show that the method is consistent with Kim and Glanzer's experimental results. The mirror effect in recognition memory is the tendency for variables to affect hit and false-alarm rates in opposite direc- tions. Thus, if correct "old" responses are more common in Condition A than in Condition B, incorrect "old" responses will be less common in Condition A than in Condition B. Interest in this phenomenon once focused almost exclusively on differences between high- and low-frequency words; how- ever, Glanzer and Adams (1985, 1990) have argued convinc- ingly that many variables can produce a mirror effect. They have also pointed out that, in the context of a signal-detection analysis of recognition decisions, the mirror effect implies that the underlying distributions are ordered as follows: new A < new B < old B < old A. The attention-likelihood model, as developed and applied to data by Glanzer and his colleagues (Glanzer & Adams, 1990; Glanzer, Adams, & Iverson, 1991; Kim & Glanzer, 1993), offers an approach to understanding why distributions might be ordered in this way. Less obviously, it suggests an answer to the question of how recognition criteria are set. Both of these problems have proved difficult for memory theorists to solve. If important lessons are going to be extracted from the attention-likelihood model, however, as much clarity as pos- sible is needed about what assumptions it makes and how its predictions are derived. In this comment, I first clarify some aspects of the model that are obscure in Kim and Glanzer's (1993) article and in previous articles (Glanzer & Adams, 1990; Glanzer et al., 1991). I then describe an alternative way to explain Kim and Glanzer's results, without assuming that likelihoods are computed or known. The Attention-Likelihood Model The attention-likelihood model assumes that each item consists of N features and that prior to learning, a certain This article is based on research supported by National Science Foundation Grant BNS-90-08909. Correspondence concerning this article should be addressed to Douglas L. Hintzman, Department of Psychology, University of Oregon, Eugene, Oregon 97403. Electronic mail may be sent to hintzman@oregon.uoregon.edu. proportion, p mvi , of those features are "marked." 1 During study, the proportion of marked features is increased accord- ing to the expression, p M (i,stndy) = n(t,study)j N J (1) The greater n(t,study) is—that is, the more attention is paid to items of type i—the more of the item's features become marked. At retrieval, n(j',test) features of the test item are sampled at random. The number of these features that are marked is x, which constitutes a strength measure. The distribution of x is binomial. If the test item is new, the distribution of x is P(x|new) = n(i,test)\ x I • Pl^'Tr, If the test item is old, the distribution is P(x\old) = n(i,test)\ x J • <? ol d0\test)'<ft to '>~ (2) (3) Here,/? oW (/,test) indicates that/> oM (i,study) has been decre- mented as a result of forgetting. 2 When there has been more forgetting in one condition than in another, p o ^(i.test) for the two conditions will be different, even if p o id(/,study) was the same. For other experiments, such as Kim and Glanzer's (1993) Experiment 2, j> oW (2,test) differs between conditions because jPoM^'.study) was different, even though the proportion forgotten has been the same. Note that Equations 2 and 3 are 1 This treatment of the attention-likelihood model adopts slightly different notations from the one previously used (Glanzer & Adams, 1990; Glanzer, Adams, & Iverson, 1991; Kim & Glanzer, 1993). The primary differences are that I consistently differentiate between study and test parameters in parentheses, move "old" and "new" from parentheses to subscripts, and consistently use q in place of 1 — p. As shall be described, I also distinguish subjects' estimates of parameters from the parameters themselves. 2 Glanzer, Adams, and Iverson (1991, Equation 4) referred to this as p(i,old,t), where t was the amount of time since study. 201