The mirror effect and mixture signal detection theory.

Abstract

The mirror effect for word frequency refers to the finding that low-frequency words have higher hit rates and lower false alarm rates than high-frequency words. This result is typically interpreted in terms of conventional signal detection theory (SDT), in which case it indicates that the order of the underlying old item distributions mirrors the order of the new item distributions. However, when viewed in terms of a mixture version of SDT, the order of hits and false alarms does not necessarily imply the same order in the underlying distributions because of possible effects of mixing. A reversal in underlying distributions did not appear for fits of mixture SDT models to data from 4 experiments.Keywords: mirror effect, signal detection theory, mixture modelsThe mirror effect (Glanzer & Adams, 1985, 1990) is a general phenomenon in recognition memory that has been studied with a number of variables, most often with word frequency. In that case, the mirror effect refers to the finding that low-frequency words have higher hit rates and lower false alarm rates than highfrequency words. This result is usually interpreted in terms of (unequal variance) signal detection theory (SDT), in which case it implies that the order of the underlying old item distributions mirrors the order of the new item distributions, just like the observed hit and false alarm rates. Figure 1 illustrates the interpretation of the mirror effect in terms of conventional SDT; note that the relative spacing and relative variances of the normal distributions shown in the figure are consistent with those found below (with the exception that the distributions in Figure 1 are spaced further apart for visual clarity). The figure shows that the mirror effect consists of two fundamental aspects (Glanzer & Adams, 1985). The first is that the distribution for high-frequency new (HN) words is to the right of that for low-frequency new (LN) words. This suggests that HN words are more familiar than LN words, as expected because highfrequency words are more commonly encountered. A second aspect of the mirror effect is that the distribution for low-frequency old (LO) words is to the right of that for high-frequency old (HO) words. Thus, when one studies the words, the less familiar lowfrequency words are strengthened more than the high-frequency words, with the result that the order of old item distributions mirrors that for new item distributions (i.e., the order is reversed); note that the SDT distance parameter dЈ is therefore larger for low-frequency words than for high-frequency words.It should be recognized that in order for the mirror effect to hold, both aspects noted above must be present-that is, the HN word distribution must be to the right of the LN distribution and the LO distribution must be to the right of the HO distribution. Simply finding a larger value of dЈ for low-frequency words is not sufficient to demonstrate the mirror effect, as was noted by Glanzer and Adams (1990), who gave examples in which the mirror effect does not appear. In on...

Examining the causes of memory strength variability: Recollection, attention failure, or encoding variability?

“…Indeed, the dual-process signal-detection model is a simplified version of a more complex mixture model (cf., DeCarlo, 2007). According to Onyper et al (2010), the λ parameter reflects the probability that an item is recollected.…”

Recognition memory models and binary-response ROCs: A comparison by minimum description length

“…3 Also note that in the present context, the MSD becomes mathematically equivalent to DPSD when μ o → + ∞ (see DeCarlo, 2007DeCarlo, , 2008. Decisions between mathematically equivalent models cannot be based on model selection criteria.…”

Some-or-none recollection: Evidence from item and source memory.

“…The value of d ′ R controls the difference between the intercepts of the liberal and conservative asymptotes and the value of R controls where the transition takes place. Notably, the VRDP can generate “kinked” zROC curves that resemble neither those predicted by the UVSD nor the DPSD (Sherman et al, 2003; DeCarlo, 2007, 2002). …”