A Single-System Model Predicts Recognition Memory and Repetition Priming in Amnesia

Reliability of the recognition and priming measures.

Prior research has shown that it is important to take into account the reliability of the tasks used to measure recognition and priming when comparing performance (Buchner and Wippich, 2000). Accordingly, the reliability of the recognition and priming measures was calculated using split-half correlations. Each participant's dataset was split into odd and even trials, and then P_r and priming measures were calculated for the trials in each of these halves. The split-half correlation for recognition/priming is the Pearson correlation of the recognition/priming measures for each half, across participants. Importantly, both recognition and priming were highly reliable (recognition: r₍₄₆₎ = 0.91, p < 0.001; priming: r₍₄₆₎ = 0.56, p < 0.001). The greater reliability of the recognition task is consistent with previous research (Buchner and Wippich, 2000); however, when each group was analyzed individually, the reliability of recognition was greater than that of priming only in the KOR group, and not the CON group (where the reliability of recognition and priming was approximately equal; KOR group: recognition, r₍₂₂₎ = 0.84, p < 0.001; priming, r₍₂₂₎ = 0.47, p = 0.02; CON group: recognition, r₍₂₂₎ = 0.50, p = 0.013; priming, r₍₂₂₎ = 0.58, p = 0.003).

Formal single-system and multiple-systems models.

Full details of the models are given in the study by Berry et al. (2012). The SS model is based on signal detection theory (Green and Swets, 1966) and assumes that during the test phase each item is associated with a memory strength value, f, which is a normally distributed, random variable with mean (μ) and SD σ_f [i.e., f ∼ N(μ, σ_f)]. The mean f of old items can be greater than of new items because of prior study (i.e., μ_old ≥ μ_new). The value of f for an item is used to derive its recognition judgment and its measure of priming. To generate a recognition judgment, random, normally distributed noise, e_r, is first added to f to produce the judgment measure J_r [i.e., J_r = f + e_r, where e_r ∼ N(0, σ_r)]. If J_r exceeds a particular threshold of strength, C, the item will be judged old, otherwise it will be judged new. For the priming task, greater values of f will tend to result in better performance in the task. For example, if the task is to identify fragmented versions of an object (fragment identification), the greater the value of f for an item, the greater the level of fragmentation at which it will be identified. Importantly, however, f is combined with another independent source of random normally distributed noise, e_p, to derive the priming measure [i.e., ID = b − sf + e_p, where ID is the level of fragmentation at which identification occurs; b and s are scaling parameters; b is the ID intercept; s is the rate of change in ID with f; and e_p ∼ N(0, σ_p)]. Both of the task-specific noise variables e_r and e_p have mean values equal to zero.

The SS model can be modified to create two “multiple-systems” versions of the model—the MS1 and MS2 models. The MS1 model is the same as the SS model except that one “explicit” memory strength signal, f_r, drives recognition [where f_r ∼ N(μ_r, σ_f)], whereas a separate “implicit” memory signal, f_p, drives priming [where f_p ∼ N(μ_p, σ_f)]. As in the SS model, f_r and f_p are combined with task-specific sources of noise (e_r and e_p) to produce the recognition judgment (i.e., J_r = f_r + e_r) and priming measure (i.e., ID = b − sf_p + e_p). Importantly, however, f_r and f_p are uncorrelated [i.e., r(f_r, f_p) = 0], and the mean explicit strength of old items (μ_r|old) can vary independently of the mean implicit strength of old items (μ_r|old) across individuals/conditions. This allows the model to produce dissociations at the level of individual items (e.g., stochastic independence; Tulving et al., 1982; Poldrack, 1996) and also at the level of group/condition (e.g., independent effects of a variable upon recognition and priming, such as the dissociation in amnesia). Thus, this model represents a relatively strong interpretation of the idea that explicit and implicit memory systems are independent (Tulving et al., 1982).

Another model, the MS2 model, represents a weaker interpretation of the idea that there is independence between systems (Berry et al., 2012). This model is identical to the MS1 model except that the explicit and implicit strengths of individual items may be positively correlated (with correlation w). A correlation could arise, for example, via distinctiveness: a more distinctive item may be better encoded into both the explicit and implicit memory systems. This gives the MS2 model greater flexibility, allowing it to reproduce associations between recognition and priming measures at the level of individual items (like the SS model). In fact, the MS2 model subsumes the SS and MS1 models as special cases of it, and the MS2 model can therefore, in principle, produce any result that the SS and MS1 models can achieve (Berry et al., 2012). When the correlation between f_r and f_p is 1 [i.e., r(f_r, f_p) = 1], and the mean f_r and f_p values of old items are equal (i.e., μ_r|old = μ_p|old), f_r = f_p, and so the model reduces to the SS model; when the correlation between f_r and f_p is zero [i.e., r(f_r, f_p) = 0], the model reduces to the MS1 model (Berry et al., 2012).

Model fitting.

Models were fit using maximum likelihood estimation (full details are given in Berry et al., 2012). The likelihood of each identification level (ID) and judgment (Z) combination is given by the following function: where X = old, new; Φ is the cumulative normal distribution function; φ is the normal density function; σ_ID² = s²σ_f² + σ_p²; μ_Jr|ID,X; and σ_Jr|ID² are the mean and variance of the conditional distribution of J_r given ID, j = 1 when Z = “new” (N), and j = 2 when Z = “old” (O); C₀ = −∞, C₁ = C and C₂ = ∞. μ_Jr|ID,X and σ_Jr|ID² are calculated as follows: and where μ_r|new = 0 when X = new, and μ_r|old ≥ 0 when X = old; μ_p|new = 0 when X = new, and μ_p|old ≥ 0 when X = old. In the SS model, μ_r|old = μ_p|old = μ_old, and w = 1. In the MS1 model, w = 0; in the MS2 model, 0 ≤ w ≤ 1.

In fitting the models to the data, an automated procedure was used to find the parameter values that maximize the summed log likelihood across trials. A full list of parameters (both free and fixed) is given in Table 1. The values of certain parameters are nonidentifiable and were therefore fixed such that they act as scaling parameters (Berry et al., 2012), as follows: SS model, μ_new = 0; MS1/MS2 models, μ_r|new = μ_p|new = 0; M(e_p) = M(e_r) = 0; σ_f = σ_r = √0.5; finally, the value of s in the MS1 and MS2 models was fixed to that of the SS model. Fixing σ_f and σ_r to √0.5 means that the SD of J_r is equal to 1 (because σ_Jr = √(σ_f² + σ_r²)), and μ_r|old can therefore be interpreted as d′. We have previously shown that whether s is fixed or free to vary in the MS1 and MS2 models does not affect their fit (Berry et al., 2012).

This leaves the following five free parameters in the SS model: μ_old, the mean strength of the old item distribution; C, the old judgment criterion; b, the ID intercept; s the rate of change in the ID level with changes in f; and σ_p, the variance of e_p, the noise associated with the priming task. The MS1 model also has the following five free parameters: μ_r|old, the mean explicit memory strength of the old item distribution; μ_p|old, the mean implicit memory strength of the old item distribution; C, the old judgment criterion; b, the ID intercept; and σ_p, the variance of e_p. The MS2 model has the following six free parameters: μ_r|old, the mean explicit memory strength of the old item distribution; μ_p|old, the mean implicit memory strength of the old item distribution; C, the old judgment criterion; b, the ID intercept; σ_p, the variance of e_p; and w, the correlation between f_r and f_p.

It is usually preferable to fit the models to each participant's data; however, this was not possible for all participants because the model parameters could not be estimated for participants who did not make at least one hit, miss, false alarm, or correct rejection response. Accordingly, the models were fit to (1) the data aggregated across the 24 participants within each group and (2) to each individual's data, providing that the individual made at least one hit, miss, false alarm, and correct rejection response (CON group, n = 19; KOR group, n = 15). We report the Akaike information criterion (AIC, Akaike, 1973) and the Bayesian information criterion (BIC, Schwarz, 1978) measures of fit because both are frequently reported in model comparisons. We place more emphasis on the AIC because our previous investigations indicated that the true generative model can be more reliably identified with this measure (Berry et al., 2012).

Given the best-fitting parameter values for a model, the expected model results can be calculated analytically as follows: P(hit) = 1 − Φ(C − μ_r|old); P(false alarm) = 1 − Φ(C); d′ = μ_r|old; E[ID|new] = b; E[ID|old] = b − sμ_p|old; priming effect = sμ_p|old.

The expected values of ID conditional on judgment Z are given by the following function: where σ_Jr = √(σ_f² + σ_r²); j = 1 when Z = N; and j = 2 when Z = O; C₀ = −∞; C₁ = C; and C₂ = ∞. Thus, the equation gives the expected ID of hits (E[ID|H]) when X = old and Z = O; it gives the expected ID of false alarms (E[ID|F]) when X = new and Z = O. Similarly, the equation gives the expected ID of misses (E[ID|M]) when X = old and Z = N; and it gives the expected ID of correct rejections (E[ID|CR]) when X = new and Z = N.

In the data, because the mean ID for items judged old/new are weighted means, the expected ID for items judged old/new are given by the weighted expected IDs to hits and false alarms (items judged old), or misses and correct rejections (items judged old), hence: and The overall fluency effect (see below) can be calculated as E[ID|Z = N] − E[ID|Z = O].

We should note that the ID response variable is discrete but is modeled here as continuous (because f_p ∼ N(μ_p, σ_f) and ID = b − sf_p + e_p). To justify this way of modeling ID, parameter recovery simulations were performed. In these simulations, first, recognition judgment and ID data (for 10,000 old/new items) were simulated from a given model. The parameter values used for this were the mean estimated parameter values for the KOR group (given on the right-hand side of Table 1). The simulated ID values were then rounded to the nearest integer; if the value was <1 or >10, then it was rounded to 1 or 10, respectively, thereby producing discretized ID data. The simulated ID and judgment data were then fit by the models as described above, and the estimates of the free parameters were compared with the values of the parameters that were originally used to simulate the data (i.e., the true parameter values). For all models, the estimated parameter values matched the true parameter values. This demonstrates that the parameters of the models can still be recovered, even though the ID data are discrete.

Another issue concerns the function used to relate f_p to ID level. The amount of a test picture revealed across levels varies by an exponential function, whereas the equation relating ID level to f_p in the models is linear. It is possible that an alternative function relating ID to f_p would provide a more complete characterization of the ID data and improve the performance of all of the models. However, most important for current purposes is that ID is modeled as a monotonically decreasing function of f_p in all models. We chose to model the ID variable in this way for consistency with previous applications of the models, and for ease of model specification.

Model predictions.

Three key predictions are made by the SS model. These predictions follow from the assumption that greater values of f tend to lead to a greater likelihood of an old judgment and also better performance in the priming task (i.e., greater values of J_r and lower values of ID; Fig. 2). Prediction 1 is that, given a deficit in recognition in amnesic individuals, a deficit in priming should also be evident. This is because changes in μ_old will tend to affect overall levels of both recognition and priming. However, the effect on priming can be smaller in magnitude than for recognition because of the greater variance of the noise associated with the priming task that is typically assumed (Berry et al., 2006). The MS1 and MS2 models can reproduce any pattern of recognition and priming, and so do not make this prediction in advance.

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Figure 2.

Model representations and Predictions 2 and 3. The top panels illustrate the relationship between the ID (identification level) and J_r variables in the models. The ellipses represent bivariate normal distributions of each class of item (old or new), cut horizontally and centered on a point that represents the mean J_r and ID for that class of item. Prediction 2 concerns whether ID levels are facilitated for items judged old within new and old items, that is, whether the mean ID of false alarms is less than that of correct rejections [CRs; i.e., CR − false alarm (FA)], and whether the mean ID of hits is less than of misses (i.e., MISS − HIT), where a correct rejection is a new judgment to a new item, a false alarm is an old judgment to a new item, a miss is a new judgment to an old item, and a hit is an old judgment to an old item. Prediction 3 concerns whether the priming effect overall (across all items) is greater than the priming effect for items judged new. Priming is calculated as mean ID(new items) − mean ID(old items); priming for items judged new is calculated as mean ID(CR) − mean ID(FA). The SS model predicts positive differences between ID(CR) − ID(MISS), ID(MISS) − ID(HIT), and priming − priming items judged new. The MS1 model predicts no differences. The MS2 model predicts positive differences when the explicit and implicit strengths of an item are positively correlated (i.e., w > 0), and predicts no differences when there is no correlation (i.e., w = 0).

Predictions 2 and 3 concern performance in the priming task when broken down by recognition response (Fig. 2). Prediction 2 is that, within old and new items, items that are judged old are likely to be identified at greater levels of fragmentation than items judged new (this is often referred to as a “fluency effect”; Conroy et al., 2005): Items with values of J_r that exceed the criterion C are judged old and tend to have larger f values than items judged new. Because the same f value drives identification, items judged old will tend to be identified at more fragmented levels. Prediction 3 concerns the priming effect for items judged new. This effect has been reported in numerous studies, and on the surface appears to indicate that recognition and priming have distinct memorial bases since priming occurs in the absence of overt recognition (Berry et al., 2008a). The SS model predicts that the magnitude of the priming effect (i.e., the identification advantage of all old items relative to new items) will be greater than the priming effect within the subset of items judged new (i.e., the identification advantage for old items judged new relative to new items judged new). This is because values of J_r tend to be greater for old items than new items, even within the subset of items judged new. However, the difference in J_r between all old and new items is greater than the difference in J_r between old and new items within the subset of items judged new (Fig. 2). Because differences in J_r tend to reflect differences in f, the priming effect across all items will tend to be greater than the priming effect within the subset of items judged new. (Though differences in J_r do not always reflect differences in f, as is the case, for example, with false-alarm and miss responses; Berry et al., 2008a.) Predictions 2 and 3 are not made by the MS1 model because ID and J_r are uncorrelated within item type (Fig. 2). The MS2 model can produce the same results as the SS model with regard to Predictions 2 and 3, but the greater flexibility of this model means that it does not make these predictions in advance.