Recollection is Fast and Slow

Abstract

We implemented a new approach to measuring the relative speeds of different cognitive processes, one that extends multinomial models of memory and reasoning from discrete decisions to latencies. We applied it to the dual-process prediction that familiarity is faster than recollection. Relative to prior work on this prediction, the advantages of the new approach are that it jointly measures specific retrieval processes and their latencies, provides separate sets of latency-retrieval parameters for list items and related distractors, and supplies latency parameters for bias processes as well as retrieval processes. Six experiments were conducted using a design (conjoint recognition) in which subjects make traditional old/new decisions about probes, plus two other types of decisions (New but similar to old items? Old or new but similar to old items?). The relative speeds of context recollection, target recollection, familiarity, and bias processes were measured for old list items and for related distractors. Four patterns emerged in all experiments: (a) The speed of recollection did not differ from the speed of familiarity for list items. (b) The speed ordering was context recollection > target recollection = familiarity for related distractors. (c) Bias processes were slower than recollection and familiarity for both list items and related distractors. (d) Bias processes were faster in conditions in which list items were to be accepted than in conditions in which they were to be rejected. Overall, the results suggest that the relative speeds of different retrieval and bias processes are emergent properties of the efficiency of different retrieval cues.

In the present article, we implement a new methodology for answering a classic question about memory and reasoning: How do we determine the relative speeds of different cognitive processes? The essence of the methodology is that it extends existing multinomial models of memory and reasoning from discrete decisions to latencies. More explicitly, it extends those models in such a way that their core parameters, which measure the relative contributions of different cognitive processes to discrete decisions, are enriched with latency parameters, which measure the relative speeds of those processes. In this initial series of experiments, we investigated a well-known instance of the relative speed question from the sphere of episodic memory: Is familiarity faster than recollection?

We begin with a brief sketch of prior findings on this question and the procedures that were used to investigate it. Next, a new procedure is introduced whose key features are that it allows researchers (a) to directly measure the relative speeds of different retrieval processes (multiple forms of recollection and familiarity in this case), (b) to make those measurements for both studied items and distractors, and (c) to directly measure the relative speeds of retrieval processes versus bias processes. Finally, we report six experiments whose objective was to generate convergent evidence on all three of these topics.

Time Courses of Recollection and Familiarity

The time courses of different retrieval processes have customarily been studied with old/new recognition, which permits rigorous control of the retrieval cues that subjects respond to, as well as the amount of time that they have to retrieve. Atkinson and associates (e.g., Atkinson & Juola, 1973, 1974) proposed that in recognition, the global memory evidence that supports nonspecific feelings of familiarity is recovered more rapidly than the realistic details that support vivid recollection of particular items. For hits to list items, it follows that fast decisions are dominated by familiarity, whereas recollection makes increasing contributions as decision times lengthen. Mandler (1980) reiterated this proposal and added a theoretical hypothesis to explain the speed differential: Recollection is simply not activated unless familiarity fails to deliver evidence that exceeds a subjective decision criterion. Reder and Ritter (1988, 1992) then formulated some related proposals about the relative speeds of recollection and familiarity in solving arithmetic problems.

The question of whether recollection and familiarity actually follow different time courses has been studied by placing subjects under time pressure on recognition tests and measuring the effects on hit rates. In early experiments, effects that were predicted by the proposed difference in retrieval speed failed to materialize. Gillund and Shiffrin (1984) investigated how speeded versus non-speeded decisions were influenced by manipulations that are believed to enhance recollection (e.g., shorter lists, semantic orienting instructions, distinctive distractors). The logic behind their design was that if recollection is slower than familiarity, these manipulations’ effects on hit rates should be more pronounced with longer decision times, which allow adequate time for recollective evidence to accumulate. Interactions of that sort were not observed, however, and Mulligan and Hirshman (1995) subsequently reported further results in this vein. The authors concluded that their data could be explained by theories that did not posit a recollection-familiarity speed differential and, moreover, only posited a familiarity operation.

There is a sensitivity concern about such data—namely, that Retrieval Time X Treatment interactions would be difficult to detect if selectively strengthening the recollective component of recognition also increases its speed. To resolve that uncertainty, Brainerd, Reyna, Wright, and Mojardin (2003) reviewed findings from an alternative design in which recollection and familiarity support opposite decisions about certain types of distractor probes. The design has two principal features. First, three types of probes are administered: list items (e.g., couch, Pepsi, sea), related distractors (e.g., sofa, Coke, ocean), and unrelated distractors (e.g., garage, violin, shoe). Second, subjects make old/new decisions about these probes following various delays, using a response-signal procedure (Dosher, 1984). In that procedure, subjects must respond within some brief interval (e.g., 300 msec) following a signal, with the signal being presented at various lags after probe onset (e.g., 250, 500, 750, 1,000, and 1,500 msec).

The data of interest are speed/accuracy functions for related distractors; that is, plots of false alarm rates against retrieval time, with retrieval time being manipulated via signal lag. If familiarity is faster than recollection, these functions should be nonmontonic—specifically, inverted-U curves— because fast familiarity supports false alarms (subjects think that sofa is old because “household furniture” is familiar from the presentation of couch) but slow recollection supports correct rejections (subjects think that sofa is new because they clearly remember the appearance of couch on the study list). When retrieval time is extremely brief, little or no familiarity evidence can accumulate before the signal to respond. As retrieval time lengthens, more familiarity evidence accumulates prior to the signal, increasing the false alarm rate, and producing the left arm of the inverted U. As retrieval time lengthens further, recollective evidence is able to accumulate before the signal, suppressing false alarms and producing the right arm of the inverted U.

Several experiments have been conducted in which the relations between false alarm rates for related distractors and retrieval time were inverted Us (e.g., Basile & Hampton, 2013; Brainerd & Reyna, 2003; Dosher & Rosedale, 1991; Gronlund & Ratcliff, 1989; Hintzman & Curran, 1994; Matzen, Taylor, & Benjamin, 2011; Oztekin, Guengoer, & Badre, 2012; Rotello & Heit, 2000; for a review, see Brainerd & Reyna, 2005). Illustrations, from some experiments by Gronlund and Ratcliff (1989), are shown in Figure 1. Overall, these speed/accuracy results are consistent with the hypotheses that (a) recollection and familiarity both contribute to false alarm rates for related distractors, and (b) familiarity is faster than recollection. Rotello and Heit (2000) pointed out that the inverted Us in some experiments are compromised by the fact that raw false alarm rates were plotted rather than memory-discrimination statistics (d′, P_r, or A′) that eliminate the confounding influence of response bias. However, that confound was removed in other experiments (Brainerd et al., 2003).

Figure 1.

Inverted-U relations between retrieval time and false recognition of related distractors in two response-signal experiments reported by Gronlund and Ratcliff (1989).

A deeper uncertainty about inverted Us is that the hypothesis that familiarity is faster than recollection assumes that recollection is a univariate process, a notion that figures in all classic dual-process models of recognition (see Yonelinas, 2002). Although inverted-U functions for speed/accuracy are consistent with that hypothesis, there is an alternative explanation of those functions that falls out of dual-recollection theory (Brainerd, Gomes, & Moran, 2014). According to that explanation, such functions could be due to the different time courses of two distinct recollection processes, as well as the different time courses of recollection and familiarity. Specifically, dual-recollection theory posits that recollection is actually bivariate, consisting of distinct context recollection and target recollection processes. Context recollection consciously reinstates what, in perception, are ground-part features of stimuli but what, in memory research, are contextual details that accompanied list items’ presentation (e.g., conscious awareness of the font, color, size, or position of couch or Pepsi). Target recollection consciously reinstates what, in perception, is figure-whole information but what, in memory, are list items per se (e.g., conscious awareness of a specific item such as couch or Pepsi). Thus, the distinction between target and context recollection differs from a dual-recollection distinction that was proposed some years ago in connection with the process dissociation paradigm (Yonelinas & Jacoby, 1996). That distinction was between two forms of context recollection (criterial vs. non-criterial; see also, Gallo, 2013).

Brainerd et al. (2014) showed that the two recollections (a) are empirically separable because there are established phenomena that exemplify both context-recollection-without-target-recollection and target-recollection-without-context recollection and (b) are conceptually distinct because they should have opposite effects on false memory. Empirically, the recollection without remembering effect (e.g., Ball, DeWitt, Knight, & Hicks, 2014; Chen, Gomes, & Brainerd, in press; Kurilla & Westerman, 2010) is an example of context-recollection-without-target-recollection, and prior list intrusions in recall (e.g., Postman & Keppel, 1977) is an example of target-recollection-without-context-recollection. The former effect refers to subjects’ ability to recall contextual details that accompanied specific list items when they cannot remember the items themselves, on recognition or recall tests. With prior list intrusions, subjects are consciously aware of specific list items because they just read those items out of memory on a recall test, but obviously, they are not aware of contextual details that accompanied the items’ presentation because the items were not on the list that subjects are supposed to recall. Conceptually, in the false memory literature, context recollection provides realistic support for false memories, a phenomenon that is often called phantom recollection (“Yes, sofa was on the list because I can ‘hear’ the voice in which it was spoken”; Lampinen, Meier, Arnal, & Leding, 2005; for a review, see Arndt, 2012a). In contrast, target recollection provides realistic support for rejecting false memories, a phenomenon that is often called recollection rejection (“No, sofa was not on the list because I clearly remember reading couch instead”; Lampinen & Odegard, 2006; for a review, see Brainerd & Reyna, 2005).

Returning to the time course question, if recollection is bivariate, it is easy to see that there are at least two theoretical paths to inverted-U speed/accuracy functions. First, familiarity might be faster than both forms of recollection. Under that scenario, the left arm would be produced by a process that simply supports false alarms (familiarity), whereas the right arm would be produced by a mixture of two processes—one that supports correct rejections and one that supports false alarms (target and context recollection, respectively). Second, context recollection might be faster than either familiarity or target recollection. If so, the left arm would be produced by a different process that simply supports false alarms (context recollection), and the right arm would be produced by a different mixture of two processes that support correct rejections and false alarms (target recollection and familiarity, respectively). The difference between the two scenarios is that familiarity and context recollection have exchanged positions. The theoretical importance of the second path is that inverted-U functions can occur for related distractors even if familiarity is slower than one of the two forms of recollection. One aim of our experiments was to decide between the two scenarios.

Latency Model for Conjoint Recognition

In our experiments, we conducted the first investigation of the speed of recollective and nonrecollective retrieval processes in which their relative speeds were directly measured, rather than being inferred from speed/accuracy functions. In order to do that, we imposed two design criteria on our experiments. First, they had to deliver separate estimates of the context recollection, target recollection, and familiarity components of recognition decisions. Second, they had to deliver separate estimates of the relative speeds of decisions that were based on each of these components.

We used conjoint recognition designs to meet the first criterion. In such designs, subjects study lists of related items and then respond to recognition tests on which list items, related distractors, and unrelated distractors are the test cues. Additionally, subjects respond to these three types of cues under three types of instructions: verbatim (V: accept list items [couch] and reject related distractors [sofa] and unrelated distractors [violin]); gist (G: accept related distractors and reject list items and unrelated distractors); and verbatim + gist (VG: accept list items and related distractors and reject unrelated distractors). The parameters of the model that is fit to the data delivers statistically independent estimates of context recollection, target recollection, and familiarity for decisions about related distractors (Brainerd et al., 2014).

The second design criterion was met by implementing recent mathematical techniques for extending multinomial models from discrete responses (e.g., recognition decisions) to response latencies (for reviews, see Heck & Erdfelder, 2016, 2017). Once such an extension is effected, the relative speeds of different memory processes—the two recollections and familiarity in the present case—can be measured. The theoretical idea behind this technique is that latency distributions for discrete responses are mixtures of underlying latency distributions for the different cognitive processes that contribute to those responses. In order to avoid assumptions about the shapes of those underlying distributions, response latencies are treated in a distribution-free manner by sorting individual responses into fast and slow bins for each subject. This allows underlying latency distributions to be parameterized with the same types of probability parameters that are used in the core model of discrete responses. That leads to a highly tractable mathematical result—namely, that the same statistical machinery that is used to fit the core model, estimate its parameters, and compute significance tests can be used to perform those analyses for the extended latency model.

Next, we show how latency extension works for the conjoint recognition model. The parameters of the core model are defined in Table 1. It can be seen that there are two retrieval parameters for list items (T_R = combined target and context recollection; T_F = familiarity), three retrieval parameters for related distractors (RD_CR = context recollection, RD_TR = target recollection and RD_F = familiarity), and bias parameters for unrelated distractors for the three conditions (b_V, b_G, and b_VG). The retrieval parameters for related distractors are of focal interest because they measure, respectively, the probability that acceptance/rejection of these items is based on context recollection, target recollection, and familiarity, respectively. Because target and context recollection both support hits for list items, T_R is the total probability that hits are based on one or the other, and T_F is the probability that hits are based on familiarity.

Table 1.

Parameters of the Conjoint Recognition Model

Parameter	Definition
Related distractors:
RDTR	Target recollection: the probability that related distractors (e.g., sofa) provoke conscious reinstatement of corresponding list items (e.g., couch). Items that provoke target recollection are perceived to be related distractors, supporting acceptance of G and VG probes but rejection of V probes.
RDCR	Context recollection: the probability that related distractors provoke conscious reinstatement of contextual details that accompanied the presentation of corresponding list items. Items that provoke context recollection but not target recollection are perceived to be list items, supporting acceptance of V and VG probes and rejection of G probes.
RDF	Familiarity: the probability that related distractors’ meanings are so familiar that they are perceived to be either targets or related distractors. Items that provoke familiarity but not target or context recollection are accepted on V, G, and VG probes.
Targets:
TR	Target/context recollection: the probability that list items provoke conscious reinstatement of their prior presentations, conscious reinstatement of contextual details that accompanied those presentations, or both. Items that provoke target or context recollection are perceived to be list items, supporting acceptance on V and VG probes and rejection on G probes.
TF	Familiarity: the probability that list items’ meanings are so familiar that they are perceived to be either targets or related distractors. Items that provoke familiarity but not target or context recollection are accepted on V, G, and VG probes.
Unrelated distractors:
bV	Bias: high-threshold bias parameter for V probes
bG	Bias: high-threshold bias parameter for G probes
bVG	Bias: high-threshold bias parameter for VG probes

The question of the core model’s validity—the extent to which the parameters in Table 1 measure what they are assumed to measure—has been explored in prior articles that examined manipulations that ought to affect particular parameters in specific ways (Brainerd et al., 2014, 2015). In the present article, we focus on the latency extension of this model, which is shown in Figures 2 (list items), 3 (related distractors), and 4 (unrelated distractors). On the far left of the three trees in Figure 2 are the empirical probabilities of accepting list items in the V, G, and VG conditions [p(T|V), p(T|G), and p(T|VG), respectively]. On the far right are the four possible response outcomes after the latencies of accept/reject decisions have been binned (accept-fast, accept-slow, reject-fast, and reject-slow). The model’s retrieval parameters (T_R, and T_F), bias parameters (b_V, b_G, and b_VG), and latency parameters for the retrieval processes (L_TR and L_TF) and bias processes (L_bVT, L_bGT, and L_bVGT) appear along the paths from the empirical probabilities to the response outcomes. With respect to the latency parameters for the retrieval processes, L_TR and L_TF are the probabilities of fast acceptance/rejection due to target/context recollection and to familiarity, respectively. Based on traditional ideas about the time courses of recollection and familiarity, the magnitude order of these parameters should be L_TF > L_TR. (By convention, L_i is always the probability that a response for process i falls in the fast bin.)

Figure 2.

Latency-extended conjoint recognition model for list items. Definitions of the core retrieval and bias parameters appear in Table 1, and definitions of the latency parameters of the extended model appear in Table 3.

The latency extension for related distractors is displayed in Figure 3. The structure is the same as in Figure 2; that is, empirical probabilities on the far left, latency-binned response outcomes on the far right, and theoretical parameters for retrieval processes, bias processes, and their latencies populating the paths that map empirical probabilities with response outcomes. In particular, the latency parameters for the retrieval processes (L_RDCR, L_RDTR, L_RDF) and bias processes (L_bVRD, L_bGRD, L_bVGRD) appear along the paths. With respect to the latency parameters for the three retrieval processes, L_RDCR, L_RDTR, and L_RDF are the probabilities of fast acceptance/rejection due to context recollection, target recollection, and familiarity, respectively. Based on traditional ideas about the time courses of recollection and familiarity, the pairwise relations L_RDF > L_RDCR, and L_RDF > L_RDTR should be observed. Predictions about the relation between the two latency parameters for recollection are not possible, of course, because recollection is treated as a unitary operation in traditional dual-process theories.

Figure 3.

Latency-extended conjoint recognition model for related distractors. The core retrieval and bias parameters in Figure 2 are defined in Table 1, and the latency parameters of the extended model are defined in Table 3.

Thus far, the model provides five retrieval parameters, five latency parameters that correspond to each of these retrieval processes, and three bias parameters, for a total of 13 free parameters. As our aim was to study the time courses of recollection and familiarity, the developments in Figures 2 and 3 are the important ones. However, the model also contains latency parameters for bias processes. Although fit is the ultimate criterion for whether this model is acceptable, some preliminary decisions had to be made about how many latency-bias parameters to include, in order to avoid supersaturating the parameter space. Remember that the core factorial structure of a conjoint recognition experiment is 3 X 3, generating nine free empirical probabilities for discrete decisions. Once the accept/reject decisions in such an experiment are binned for fast-slow latency, the factorial structure expands to 3 (type of test item) X 3 (type of conjoint recognition instruction) X 2 (decision: accept vs. reject) X 2 (latency: fast vs. slow), for a total of 36 free empirical probabilities. We just saw that 13 of these degrees of freedom are used for the retrieval decision parameters, bias decision parameters, and retrieval-latency parameters, 23 degrees of freedom for the inclusion of bias-latency parameters and for model fitting.

Considering that there are 3 instructional conditions, 5 retrieval processes, and 2 types of recognition decisions, it would have been possible to posit many more than 23 latency-bias parameters. In the end, it can be seen in Figures 2–4 that the model includes 12 latency-bias parameters: 3 for accepting unrelated distractors in the 3 instructional conditions, 3 for rejecting unrelated distractors in the three instructional conditions, 3 for accepting/rejecting list items in the in the 3 instructional conditions, and 3 for accepting/rejecting related distractors in the in the three instructional conditions. This meant that the model’s global fit test was a G²(11) statistic. This particular configuration of latency-bias parameters was based on two considerations: identifiability and pilot data. Concerning identifiability, even when a large number of free probabilities is available (23 in this case), some parameterizations of a model will not be identifiable, and hence, its parameters cannot be estimated (Brainerd, Howe, & Desrochers, 1982). That is true of the present latency model where, for instance, parameterizations that use the same latency-bias parameters for list items, related distractors, and unrelated distractors are not identifiable. Concerning pilot data, results from pilot studies showed that latencies were affected by decision condition and type of test cue but not by other variables. The ultimate criterion for any parameterization, however, is fit, and it will be seen that the parameterization in Figures 2–4 delivered good fits to the data of all of our experiments.

Figure 4.

Latency-extended conjoint recognition model for unrelated. The core bias parameters in Figure 3 are defined in Table 1, and the latency parameters of the extended model are defined in Table 3.

Summing up, direct measurement of the relative speeds of different retrieval processes is achieved via a latency extension of the conjoint recognition model. Although direct latency measurements are relative to the conjoint recognition model’s method of measuring the retrieval processes, that relation is not an arbitrary one that is posited without evidence: Both the core model and its latency extension must pass fit tests before latency measurements can be effected.

Method

In an attempt to secure stable data that would supply firm footing for future theoretical analysis, our strategy was to conduct multiple, independent experiments, using conventional conjoint recognition procedures and similar materials. We then fit the core model of recognition decisions to the data of all experiments, and once fit was established, we estimated the values of the retrieval and bias parameters in Table 1. Those values measured the relative contributions of the different retrieval and bias components to recognition decisions. Next, we fit the extended model to the latency-binned recognition decisions of all experiments, and once fit was established, we estimated the values of the latency parameters for the retrieval and bias processes in Figures 2–4. Those values measured the relative speeds of the different retrieval and bias components of recognition decisions. The hope was that across the independent experiments, a picture of latency ordering would emerge for the different retrieval processes and for bias. It did.

We report six conjoint recognition experiments, which are expansions of conventional false memory designs (Brainerd, Reyna, & Mojardin, 1999). Traditionally, subjects study lists of semantically related items and then respond to recognition tests that include list items, related distractors that preserve aspects of list items’ meanings, and unrelated distractors. Subjects simply make old/new decisions about each cue, which is the V condition of conjoint recognition. The hit rate for list items, the false alarm rate for related distractors, and the false alarm rate for unrelated distractors normally serve as measures of true memory, false memory, and response bias, respectively. Conjoint recognition methodology adds two elements to this basic paradigm—namely, two other recognition decisions (G and VG) and a retrieval model that is defined over all three types of recognition decisions (V, G, and VG).

The semantic relation between list items in the typical false memory design varies from experiment to experiment (e.g., category exemplars, synonyms, words with the same emotional valence). In recent years, Deese/Roediger/McDermott (DRM; Deese, 1959; Roediger & McDermott, 1985) lists have been far more common than any other type of material, and they were the study lists in our experiments. DRM lists have figured in many prior conjoint recognition experiments (cf. Brainerd et al., 2014), and the model in Table 1 has delivered good fits to the data. In our experiments, subjects (a) studied a large number of such lists, then (b) responded to conjoint recognition tests on which the three types of items were factorially crossed with the three types of decisions, and (c) the latencies of individual decisions were recorded. Experiments 1–5 were similar, differing in the details of some of the DRM lists that were administered, their presentation rate, some of the test cues that were administered, and of course, in their subject samples. Experiment 6 was quite different. Although the basic study-test procedure was preserved, it was administered while the subjects were lying in an MRI scanner, and their brains were being scanned.

Subjects

The experiments were conducted over a period of two years. All of them were drawn from a pool of undergraduate students who were enrolled in psychology or human development courses. The numbers of subjects who participated in the individual experiments were 19 (Experiment 1), 28 (Experiment 2), 59 (Experiment 3), 23 (Experiment 4), 31 (Experiment 5), and 25 (Experiment 6). All of the subjects participated in order to fulfill course requirements.

Materials and Procedures

As the materials and procedures for Experiments 1–5 were quite similar, we describe them together, noting specific differences among the experiments. We then describe Experiment 6.

Except for the measurement of response latencies, Experiments 1–5 were very similar to Experiment 1 of Brainerd, Reyna, and Aydin (2010). The full details of the conjoint recognition testing procedure that was used in the present experiment can be found in that article. To the best of our knowledge, Experiments 1–5 are the first conjoint recognition studies to measure response latencies.

In Experiments 1–5, each subject participated in three cycles of study lists followed by conjoint recognition tests. During the study phase of each cycle, the subjects viewed a total of 25 DRM lists that were presented on a computer screen (centered in 72-point black font). The lists were four-word DRM lists of a type that was originally developed by Reuter-Lorenz and associates (Atkins & Reuter-Lorenz, 2011; Flegal, Atkins, & Reuter-Lorenz, 2010). DRM lists are constructed using association norms to select the first several forward associates of a missing word, which is called the critical distractor or critical lure. For instance, the first 10 forward associates of sweet are sour, candy, sugar, bitter, good, taste, tooth, nice, honey, and soda. Levels of false memory are positively correlated with levels of backward associative strength (BAS) from list words to the critical distractor. Hence, four-word DRM lists are constructed by selecting the four forward associates that have the highest BAS. For the distractor sweet, for example, sour, sugar, bitter, and honey have a mean BAS of .43. The 75 DRM lists that were administered to the subjects in Experiments 1–5 were randomly selected from a pool of 200 lists that had been constructed in this manner. The mean BAS of the lists that were administered in individual experiments ranged from .41 to .46. During the study phase of each study-test cycle, the 25 DRM lists were presented in random order, with the words of each list being presented consecutively, one after the other, with a 3 sec fixation cross between each word. The presentation rates of individual list items were 1 sec (Experiments 3) and 2 sec (Experiments, 1, 2, 4 and 5).

During the test cycles of Experiments 1–5, subjects responded by pressing one of two keys of the computer keyboard, which had been labeled “yes” and “no.” Each subject responded to recognition probes for 75 cues: list items, related distractors, and unrelated distractors. For each cue, the subject made a V, G, and VG decision. Because 75 is not divisible by 9, there was an uneven distribution of each cue type in a single test cycle. However, across all three tests (225 cues), there were 75 list items (1 per list), 75 related distractors (the critical distractors for those same 75 lists), and 75 unrelated distractors. For the 75 cues of each type, subjects made 25 V decisions, 25 G decisions, and 25 VG decisions. The source of unrelated distractors varied somewhat from experiment to experiment. They were drawn from critical distractors from unpresented lists in the DRM list pool in Experiments 1, 2, and 3. In Experiment 4 and 5, they were high frequency abstract nouns drawn from the Toglia and Battig (1978) semantic word norms. A 3 min break was inserted between the first and second study/test cycles and between the second and third cycles, for two breaks in all. Finally, owing to programming errors, 5 related distractors were omitted from 1 of the test cycles in Experiment 4, 1 related distractor was added to Experiment 2, and 1 omitted from Experiment 5. Thus, a total of 70 related distractors were tested in Experiment 4, 76 were tested in Experiment 2, 74 were tested in Experiment 5, and 75 were tested in the other experiments.

Turning to Experiment 6, each subject also participated in three cycles of study lists followed by conjoint recognition tests, and the procedure was the same as Experiment 5, except for three changes. First, subjects were laying in an MRI scanner and their brains were being scanned throughout the experiment. Second, whereas Experiment 5 used high frequency abstract nouns as unrelated distractors, the unrelated distractors in Experiment 6 were critical distractors from unpresented lists in the DRM list pool. Third, the subjects responded to the recognition probes by pressing the left and right buttons of an MRI response box.

On the recognition tests in all six experiments, subjects were given a maximum of 4 sec to respond to each probe, after which the computer advanced to the next probe regardless of whether or not the subject had responded to the current one. The latencies of subjects’ responses to each probe were also recorded.

Latency Binning

In the latency extension of the conjoint recognition model, latencies to accept and to reject test cues are binned into fast and slow decisions, using the fast and slow bins for each of the nine observable response probabilities on the far left of the model trees in Figures 2–4. We used a binning procedure recommended by Heck and Erdfelder (2016), in which latency boundaries for binning are obtained from the overall latency data for the three types of test cues. Fast and slow bins were established for accept and reject decisions in each of the three decision conditions, for each of the three types of test cues (i.e., fast list item acceptance in the V condition, slow list item acceptance in the V condition, fast list item rejection in the V condition, slow list item rejection in the V condition, …, fast unrelated distractor rejection in the VG condition, slow unrelated distractor rejection in the VG condition). Next, the latency boundary was identified in order to create these fast and slow bins for each cue-condition combination. That was done by transforming the raw latencies across all of responses for all cues and conditions, locating the median of those data, transforming the median back to a raw latency value, and using that value to sort raw latencies into the fast and slow bins.

This procedure allows the members of certain sets of latency parameters to be directly compared because their values are on the same scale of measurement (i.e., the same test cue in the same decision condition). Specifically, the latency parameters in each of the following sets can be directly compared: (a) the latency-retrieval and latency-bias parameters for list items (L_TR, L_TF, L_bVT, L_bGT, L_bVGT); (b) the latency-retrieval and latency-bias parameters for related distractors (L_RDCR, L_RDTR, L_RDF, L_bVRD, L_bGRD, L_bVGRD); and (c) the latency-bias parameters for accepting versus rejecting unrelated distractors (L_bVUA, L_bGUA, L_bVGUA, L_bVUR, L_bGUR, L_bVGUR). The ability to compare the latency-retrieval parameters in the first two sets to each other allows classic questions about the time courses of recollection and familiarity to be answered. Further, the ability to be able to compare the latency-retrieval parameters to the latency-bias parameters in these two sets allows questions about the relative speeds of retrieval versus bias to be answered. That is important because in traditional theoretical conceptions, bias should be slower than recollection or familiarity because it operates when retrieval processes fail to deliver decisions about test cues. However, it is quite conceivable that bias operates in parallel with retrieval processes, sometimes generating decisions while information is still being retrieved from memory. If so, the speeds of latency-retrieval and latency-bias parameters could have similar values.

Finally, the ability to compare latency-bias parameters for accepting versus rejecting unrelated distractors is also useful theoretically. Some theories of recognition (e.g., Bayen, Murnane, & Erdfelder, 1996) posit a detect-new process that yields fast, confident rejections of some unrelated distractors, although most do not posit such a process. Under the detect-old hypothesis, bias-driven rejections of such cues should be faster than bias-driven acceptances because the detect-old processes operates with rejections but not acceptances. That becomes an empirical question in the extended model.

Results

Descriptive Statistics: Recognition Decisions and Latencies

Descriptive statistics for the six experiments are reported in Table 2, for three types of data. First, in the upper portion of the table, mean acceptance probabilities are displayed for the 9 cells of the 3 (type of item) X 3 (type of conjoint recognition decision) factorial structure of each experiment. Second, in the middle third of the table, mean acceptance latencies are displayed for the 9 cells of each experiment. Third, in the lower third of the table, mean rejection latencies are reported for the 9 cells of each experiment. Although the data in Table 2 are not of primary interest in the present research, we make four general comments about them before proceeding to the process-level results.

Table 2.

Mean Acceptance Probabilities (SDs) and Mean Accept and Reject Latencies (SDs) for the 9 Item X Probe Combinations of Experiments 1–5

	Experiment
Item|probe type	1	2	3	4	5	6
	critical UDs 2s presentation 0.41 BAS 75 RDs	critical UDs 2s presentation 0.41 BAS 76 RDs	critical UDs 1s presentation 0.41 BAS 75 RDs	abstract UDs 2s presentation 0.46 BAS 74 RDs	abstract UDs 2s presentation 0.46 BAS 70 RDs	fMRI study	Means
Probability:
RD|V	.31(.46)	.34(.47)	.38(.49)	.57(.49)	.51(.50)	.46(.50)	.43
RD|G	.53(.50)	.58(.49)	.63(.48)	.65(.48)	.64(.48)	.72(.45)	.63
RD|VG	.70(.46)	.70(.46)	.74(.44)	.77(.42)	.68(.47)	.80(.40)	.73
T|V	.68(.47)	.77(.42)	.78(.42)	.80(.40)	.65(.48)	.72(.45)	.73
T|G	.29(.45)	.29(.46)	.30(.46)	.25(.43)	.52(.50)	.44(.50)	.35
T|VG	.77(.42)	.78(.42)	.82(.39)	.83(.37)	.68(.47)	.80(.40)	.78
UD|V	.16(.37)	.19(.39)	.16(.36)	.20(.40)	.27(.44)	.24(.42)	.20
UD|G	.32(.47)	.29(.45)	.26(.44)	.34(.47)	.34(.47)	.36(.48)	.32
UD|VG	.36(.48)	.34(.47)	.30(.46)	.38(.49)	.37(.48)	.39(.49)	.36
Latency-accept:
RD|V	1.80(.69)	1.82(.66)	2.10(.77)	2.08(.83)	2.20(.71)	2.18(.71)	2.03
RD|G	2.06(.66)	2.15(.59)	2.31(.70)	2.36(.75)	2.25(.75)	2.34(.75)	2.25
RD|VG	1.86(.60)	1.92(.61)	2.06(.67)	2.04(.71)	2.24(.74)	2.12(.72)	2.04
T|V	1.51(.56)	1.59(.54)	1.69(.68)	1.71(.69)	1.90(.77)	1.75(.69)	1.69
T|G	1.89(.75)	1.99(.65)	2.20(.83)	2.23(.73)	2.12(.80)	2.14(.78)	2.10
T|VG	1.67(.54)	1.72(.57)	1.81(.66)	1.75(.62)	2.02(.78)	1.86(.68)	1.81
UD|V	1.65(.64)	1.83(.60)	2.10(.77)	2.10(.82)	2.35(.76)	2.46(.75)	2.08
UD|G	2.04(.66)	2.22(.57)	2.41(.72)	2.33(.77)	2.46(.77)	2.67(.72)	2.36
UD|VG	1.88(.65)	1.97(.59)	2.22(.73)	2.24(.74)	2.29(.78)	2.55(.73)	2.19
Latency-reject:
RD|V	1.81(.60)	1.94(.57)	2.17(.68)	2.13(.69)	2.28(.73)	1.69(.94)	2.00
RD|G	2.03(.76)	2.05(.66)	2.35(.73)	2.41(.74)	2.39(.80)	2.56(.68)	2.30
RD|VG	1.72(.73)	1.91(.67)	2.19(.74)	2.29(.76)	2.33(.74)	2.44(.75)	2.15
T|V	1.67(.75)	1.85(.59)	2.08(.69)	2.12(.71)	2.24(.69)	2.28(.69)	2.04
T|G	1.94(.67)	2.01(.57)	2.23(.71)	2.20(.72)	2.41(.73)	2.36(.73)	2.19
T|VG	1.69(.79)	1.89(.59)	2.25(.69)	2.10(.73)	2.28(.77)	2.42(.66)	2.10
UD|V	1.70(.59)	1.81(.55)	1.93(.65)	1.90(.64)	2.21(.72)	2.16(.70)	1.95
UD|G	2.02(.71)	2.08(.62)	2.35(.73)	2.39(.75)	2.41(.73)	2.46(.73)	2.29
UD|VG	1.99(.72)	2.01(.67)	2.21(.71)	2.12(.72)	2.33(.74)	2.28(.73)	2.16

Note. RD = related distractors, T = list items, UD = unrelated distractors, V = verbatim recognition, G = gist recognition, and VG = verbatim + gist recognition.

The first concerns the behavior of the acceptance probabilities in the upper portion of Table 2. As the chief goal was to identify general trends in the relative speeds of different retrieval processes, it is important to know whether these probabilities were well behaved, by which we mean whether their relative magnitudes resembled the general picture that has emerged from prior conjoint recognition experiments with similar material. In that connection, Brainerd et al. (2014) reviewed a corpus of 297 conjoint recognition data sets in which subjects studied semantically related material and responded to test lists containing list items, semantically related distractors, and unrelated distractors. Across this corpus, the order of acceptance probabilities for V, G, and VG decisions was p(VG) > p(V) > p(G) for list items, p(VG) > p(G) > p(V) for related distractors, and p(VG) = p(G) > p(V) for unrelated distractors. Visual inspection of the acceptance probabilities for Experiments 1–6 reveals that these patterns were present in our experiments. The grand means were p(VG) = .78, p(V) = .72, and p(G) = .35 for list items, p(VG) = .73, p(G) = .63, and p(V) = .43 for related distractors, and p(VG) = .36, p(G) = .32, and p(V) = .20 for unrelated distractors. Concerning unrelated distractors, although the grand mean of p(VG) was slightly larger than the grand mean of p(G), the difference between them was not reliable in any of the individual experiments.

The other three comments are concerned with the mean response latencies in the middle and lower portions of Table 2. To the best of our knowledge, latency data have not been previously reported for conjoint recognition experiments, but such data have been reported for list items and distractors in old/new recognition, which corresponds to the V condition. The first latency comment concerns the standard finding that latencies are shorter to accept list items than to accept distractors in old/new recognition. That result was obtained here, too: Over the six experiments, the grand mean latencies to accept list items, related distractors, and unrelated distractors in the V condition were 1.87 sec, 2.11 sec, and 2.21 sec, respectively.

The other two latency comments are about variability in latency as a function of type of acceptance/rejection and decision condition (V, G, VG), and they are relevant to the parameter space of the extended model. In order to generate an identifiable model, we restricted the number of latency parameters for response bias to the 12 that are displayed in Figures 2–4. We noted in that connection that our selection of these 12 parameters grew out of pilot data showing that latency varies as a function of decision condition and type of test cue. The latency data in Table 2 are congruent with that impression. On one hand, the grand latency means for the three decision conditions over items, experiments, and accept-reject decisions were V = 1.96 sec, G = 2.24 sec, and VG = 2.08 sec. On the other hand, the grand means for the three types of items over decision conditions and experiments were list items = 1.99 sec, related distractors = 2.13 sec, and unrelated distractors = 2.17 sec.

Fit of the Core Model and Retrieval Parameter Estimates

First, the fit of the core conjoint recognition model (Table 1) must be evaluated. For each experiment, the model is fit in the usual way, by maximizing its likelihood function for data that have been aggregated across the subjects. This delivers a value of the G²statistic, which has a critical value of ≥ 3.84 rejects the null hypothesis of model fit at the .05 level. In the corpus of data that Brainerd et al. (2014) reviewed, fits were consistently good, with mean values falling well below this critical value. Similarly, the observed values of the G²(1) statistic were .24, 2.60, .02, .08, .44, and .99 for Experiments 1–6, respectively.

Statistics of this sort are called sufficiency tests because they evaluate whether a model, as specified, is adequate to account for the data or whether some more complex model is required (cf. Brainerd et al., 1982; Brainerd, Stein, & Reyna, 1998). They do not evaluate whether some simpler model will also account for the data. Tests of the latter sort are called necessity tests. Considering the long-standing controversy over whether recognition is governed by a single familiarity process or by both familiarity and recollection processes, the necessity tests of interest are (a) statistics that evaluate whether one or the other of the two retrieval parameters for list items (T_R or T_F) can be deleted without compromising fit, and (b) statistics that evaluate whether one or two of the three retrieval parameters for related distractors (RD_CR, RD_TR, or RD_F) can be deleted without compromising fit (cf. Brainerd et al., 2014). Whenever a parameter is deleted, the G²(1) statistic becomes a G²(2) statistic, with a critical value of 5.99 to reject the null hypothesis that the simplified model fits the data.

We computed that test for the null hypotheses T_R = 0 and T_F = 0, for all six experiments, and all tests produced values of the G²(2) statistic that exceeded the critical value. To determine if any of the retrieval processes could be deleted for related distractors, we computed the same test for the null hypotheses RD_CR = 0, RD_TR = 0, and RD_F = 0. All tests in all experiments produced values of the G²(2) statistic that exceeded the critical value. In short, the necessity tests showed that none of the retrieval processes could be deleted experiments without compromising fit.

Maximum likelihood estimates of the retrieval and bias parameters for each experiment are reported in the upper portion of Table 3. The internal behavior of these parameters resembles their behavior in the larger conjoint recognition literature. The mean values of the parameters in the corpus of data that Brainerd et al. (2014) were T_R = T_F for list items, RD_F > RD_TR > RD_CR for related distractors, and b_VG = b_G > b_V for unrelated distractors. The means of these parameters for Experiments 1–6 appear in the column on the far right of Table 3, were it can be seen that the inter-parameter relations in the Brainerd et al. (2014) corpus were also present in these experiments.

Table 3.

Maximum Likelihood Estimates of the Conjoint Recognition Model’s Retrieval, Bias, and Latency Parameters for Experiments 1–5

	Experiment
Parameter	1	2	3	4	5	6
	critical UDs 2s presentation 0.41 BAS 75 RDs	critical UDs 2s presentation 0.41 BAS 76 RDs	critical UDs 1s presentation 0.41 BAS 75 RDs	abstract UDs 2s presentation 0.46 BAS 74 RDs	abstract UDs 2s presentation 0.46 BAS 70 RDs	fMRI study	Means
Retrieval-related distractors:
RDTR	.28	.29	.32	.14	.12	.28	.24
RDCR	.21	.14	.12	.14	.03	.09	.12
RDF	.15	.26	.39	.56	.41	.49	.38
Retrieval-list items:
TR	.46	.49	.51	.60	.16	.34	.43
TF	.31	.40	.46	.40	.42	.47	.41
Bias:
bV	.16	.19	.16	.18	.27	.23	.20
bG	.32	.29	.26	.33	.34	.36	.32
bVG	.37	.33	.30	.38	.36	.39	.36
Latency-retrieval:
LRDTR	.30	.44	.50	.47	.52	.56	.47
LRDCR	.54	.86	1.00	1.00	.89	1.00	.88
LRDF	.47	.42	.37	.43	.53	.53	.46
LTR	.72	.71	.72	.71	.71	.75	.72
LTF	.69	.67	.67	.63	.70	.82	.70
Latency-bias (accept unrelated distractors):
LbVUA	.60	.53	.50	.67	.42	.37	.52
LbGUA	.31	.28	.30	.28	.35	.26	.30
LbVGUA	.40	.44	.44	.38	.49	.35	.42
Latency-bias (reject unrelated distractors):
LbVUR	.63	.58	.62	.59	.49	.53	.57
LbGUR	.44	.38	.34	.33	.39	.34	.37
LbVGUR	.43	.42	.44	.44	.43	.48	.44
Latency-list items
LbVT	.63	.57	.53	.54	.54	.49	.55
LbGT	.02	.00	.00	.00	.32	.00	.06
LbVGT	.69	.54	.43	.53	.49	.39	.51
Latency-related distractors
LbVRD	.68	.50	.40	.45	.44	.27	.46
LbGRD	.50	.33	.15	.00	.40	.06	.24
LbVGRD	.64	.52	.44	.44	.42	.36	.47

Note. The eight retrieval and bias parameters at the top of the table are defined in Table 1. The five latency-retrieval parameters are the probabilities of fast recognition decisions about related distractors that are based on target recollection, context recollection, or familiarity and the probabilities of fast recognition decisions about list items that are based on recollection or familiarity. The remaining 12 parameters are all latency parameters for bias-driven decisions in the V, G, and VG conditions. The first six are two trios of parameters, one for accepting unrelated distractors and one for rejecting unrelated distractors. The next three are a trio for accepting and rejecting list items. The final three are a trio for accepting and rejecting related distractors.

Fits of Extended Model and Latency Parameter Estimates

Next, we evaluate the fit of the extended model to the latency data of Experiments 1–6. Once decision latencies have been binned, the factorial structure of each experiment becomes 3 (type of item) X 3 (type of conjoint recognition decision) X 2 (response: accept vs. reject) X 2 (latency: fast vs. slow), for a total of 36 free empirical probabilities. Returning to Figures 2–4, the extended model contains a total of 25 free parameters: the 8 decision parameters of the core model (Table 1) + 5 latency parameters for the 5 retrieval processes + 12 latency parameters for bias processes. Thus, the extended model is fit with 11 degrees of freedom, so that G² ≥ 19.65 rejects the null hypothesis of fit at the .05 level. The model gave an excellent account of the data of Experiments 1, 2, 5 and 6, with a mean G² value (6.58) that was less than half of the critical value. For Experiments 3 and 4, the G² statistic exceeded the critical value.

When initial fit tests such as those for Experiments 3 and 4 fail, there are two main explanations—the obvious one, that the model is wrong for the target data, or that there are substantial individual differences in its parameter values. In the present case, the second explanation is a more plausible working hypothesis, for two reasons. First, model fits were excellent for four of the six experiments. That cannot be due to major differences in procedures because, except for Experiment 6 where fit was good, the methodologies of the experiments did not differ in major respects. The only notable differences among the other experiments is that they were conducted during different semesters with different subject samples. Second, individual differences in latency are ubiquitous in the cognitive psychology literature, and certain procedures are routinely used to control their influence (e.g., trimming outliers when computing descriptive statistics and significance tests). Therefore, we evaluated the working hypothesis that individual differences caused the fit failures in Experiments 3 and 4 by (a) testing that hypothesis statistically and then (b) computing further model fit tests that determined whether the model could account for the data of individual subjects.

The model fit tests reported above were standard ones in which data were aggregated over subjects, on the hypothesis that individual differences are small enough that fit will not be seriously affected. That is the first move in model fitting, rather than beginning with models that allow different parameter values for individual subjects because such models tend to over fit noise in the data (Myung & Pitt, 1997). Thus, if models that allow different parameter values for individual subjects are fit first, the ultimate results may be misleading because a statistical justification is lacking for fitting them rather than more parsimonious aggregate models. A more appropriate sequence of events is (a) to fit aggregate models, (b) to compute Smith and Batchelder’s (2008) omnibus test for individual differences in parameter values when fit fails, and (c) only to fit models that permit individual differences in parameter values when that test rejects the null hypothesis.

As the aggregate model did not produce acceptable fits in Experiments 3 and 4, we evaluated whether there was statistical evidence of significant individual differences in parameter values. This is done with Smith and Batchelder’s test (2008). For data such as ours, in which recognition decisions and latencies are scored dichotomously, the test is the χ² statistic

$${\mathrm{\chi }}^2(\mathrm{N}-1)={\mathrm{\sum }}_i[\{{(R_i-R_e)}^2÷R_e\}+\{{(M-R_i-R{\ast }_e)}^2÷(M-R{\ast }_e)\}],$$ (1)

where N is the number of subjects, R_i is the total number of acceptances for a particular cue type/decision combination for a particular response latency (e.g., fast acceptances for list items in the V condition), R_e is (Σ R_i) ÷ N, M is the total number of examples of that cue type/decision combination that subjects respond to (M = 25 in our experiments), and R*_e = M − R_e. For Experiments 3 and 4, N = 62 and 22, respectively, so that the critical values of χ² to reject the null hypothesis of no individual differences at the .05 level were 81.38 and 33.9.

As expected, this test showed that the hypothesis of no individual differences in parameter values could be rejected at high levels of confidence. The values of the χ² statistic were 243.16 (Experiment 3), and 84.57 (Experiment 4). This means that the extended model may fit the data of individual subjects quite well. Hence, the next step was to fit the extended model to the data of the individual subjects in Experiment 3 and 4. If the model is wrong, it still will not fit, of course. A design feature of the present experiments allows such individualized fit tests to be computed: Each subject participated in all nine cells of the conjoint recognition procedure. If, on average, the extended model delivers accurate accounts of the data of individual subjects, the mean value of the individualized G²(11) statistics for an experiment will be < 19.68. They were. The mean values were 16.91 and 11.56 for Experiments 3 and 4, respectively. In addition, the percentages of the subject samples for which G²(11) < 19.68 were 80% (Experiment 3) and 91% (Experiment 4).

Summing up the fit results for the extended model, it delivered acceptable levels of fit to the data of all six experiments. For four experiments, individual differences were small enough so that fit was established with conventional aggregate tests. For two experiments, individual differences in parameters were statistically reliable, making it necessary to fit the model to the data of individual subjects. Because the experiments were conducted in the same laboratory with the same materials, the vagaries of different subject samples (different years, different semesters) are the most plausible explanation for individual differences being reliable in two experiments but unreliable in four.

Parameter Analyses for the Extended Model

Estimates of the extended model’s latency parameters for retrieval and bias processes are reported in the lower portions of Table 3. Remember that each of these values is the probability that the indicated process produced a fast rather than a slow decision. We are chiefly concerned with the latency parameters for the five retrieval processes because their values can answer questions about the relative speeds of recollection and familiarity. We report results for those parameters first and then move on to results for the latency-bias parameters.

Speed of retrieval processes

There are three latency-retrieval parameters that measure the speed of decisions about related distractors—one apiece for decisions that are based on context recollection (L_RDCR), target recollection (L_RDTR), and familiarity (L_RDF), respectively. There are two latency-retrieval parameters that measure the speed of decisions about list items— one for decisions that are based on either target or context recollection (L_TR) and one for the speed of decisions that are based on familiarity (L_TF). The mean values of the five latency-retrieval parameters for all six experiments appear in the far right column of Table 3.

Taking the latency-retrieval parameters for related distractors first, two patterns are immediately apparent in the mean values of L_RDCR, L_RDTR, and L_RDF, neither of which are consistent with the traditional view that familiarity is fast and recollection is slow. First, note that conscious reinstatement of contextual details was very fast, relative to both conscious reinstatement of list items per se and familiarity. Numerically, the mean value of L_RDCR was .88, which is roughly twice the mean vales of L_RDTR and L_RDF (.47 and .46, respectively). Second, note that there was no evidence that familiarity is faster than target recollection because the mean values of L_RDTR and L_RDF were virtually the same. In short, one form of recollection was much faster than familiarity, and the other was equally fast.

In each experiment, we tested the numerical differences between the estimates of L_RDCR, L_RDTR, and L_RDF for statistical significance in the usual way, with likelihood ratio tests. In each instance, the tests consisted of two steps: (a) a likelihood ratio test of the omnibus null hypothesis L_RDCR = L_RDTR = L_RDF, which produced a G²(3) statistic with a critical value of 7.82 to reject this null hypothesis, and (b) if this null hypothesis was rejected, likelihood ratio tests of the pairwise hypotheses L_RDCR = L_RDTR, L_RDCR = L_RDF and L_RDTR = L_RDF, which each produced a G²(2) statistic with a critical value of 5.99 to reject the null hypothesis. Concerning the first step, the omnibus test produced a null hypothesis rejection in five of the six experiments, with the individual G²(2) values being 14.42 (Experiment 1), 8.59 (Experiment 2), 60.54 (Experiment 3), 37.18 (Experiment 4), 19.84 (Experiment 5), and 17.58 (Experiment 6). Concerning step b, in the five experiments for which the omnibus null hypothesis was rejected, pairwise tests (a) rejected the null hypothesis that L_RDCR = L_RDTR in five experiments (Experiment 5 was the exception), (b) rejected the null hypothesis that L_RDCR = L_RDF in three experiments (Experiment 1, 2, and 5 were exceptions), and (c) did not reject the hull hypothesis that L_RDTR = L_RDF in five experiments (Experiment 3 was the exception). Across the experiments, then, the indicated speed ordering of the three retrieval processes was that context recollection was faster than either target recollection or familiarity, but the speeds of the latter did not differ.

Next, we consider the relative speeds of recollection and familiarity for list items. As the two recollections do not produce different recognition decisions for list items, there is a single recollection parameter, in addition to the familiarity parameter. Therefore, in order to establish whether the speeds of recollection and familiarity differed in a given experiment, it is only necessary to compute a likelihood ratio test of the pairwise null hypothesis L_TR = L_TF, which yields a G²(2) statistic. When that hypothesis was tested, it was not rejected in any of the six experiments. The most reasonable conclusion, then, is that for list items, the retrieval processes that are measured by these two parameters operate at approximately the same speed.

That suggests an important further conclusion, which is that the speeds of recollection and familiarity depends on whether the test cue is a related distractor or a list item. Remember that (a) L_TR is a mixture of the speeds of target and context recollection, (b) that context recollection was much faster than familiarity in decisions about related distractors, and (c) target recollection operated at roughly the same speed as familiarity in decisions about related distractors. If that ordering holds regardless of whether the test cue is a related distractor or a list item, the finding that L_TR = L_TF could not have occurred. Instead, the ordering would have to be L_TR > L_TF, regardless of the particular mixture of proportions of target and context recollection that figured in the recollection parameter. The only circumstance in which L_TR = L_TF could be expected is if context recollection makes no contribution to T_R, which seems highly unlikely considering the extensive literature on how context manipulations affect other measures of recollection for list items (for a review, see Yonelinas, 2002). The more likely scenario is that the relative speeds of recollection and familiarity is influenced by the nature of the test cues.

Speed of bias processes

Prior experiments on the relative speeds of recollection and familiarity have not considered similar questions about bias processes, and hence, our experiments provide the first systematic evidence on such questions. Bias processes are assumed to produce decisions about unrelated distractors because such cues preserve neither the surface form nor the semantic content of list items. Further, they deliver decisions about list items and related distractors, in addition to decisions that are supported by the two recollections and familiarity. Here, we report two types of findings about the latency-bias parameters—namely, findings about the relative speeds of different types of bias-driven decisions, and findings about the relative speeds of decisions that are based on bias versus recollection or familiarity.

1. Comparisons of bias processes

As mentioned, pilot data indicated that latencies vary as a function of decision condition. There were four trios of latency-bias parameters that take that influence into account: A trio that indexes the speed of decisions about list items in the V, G, and VG conditions, a trio that indexes the speed of decisions about related distractors in these conditions, a trio that indexes the speed of accept decisions about unrelated distractors in these conditions, and a trio that indexes the speed of reject decisions about unrelated distractors in these conditions. The values of these parameters for each experiment are displayed at the bottom of Table 3.

Inspection of those values reveals two major patterns. First, the speed of bias-based decisions did not depend noticeably on whether the decision was to accept or reject: For unrelated distractors, the mean values of the three latency-bias parameters for acceptances and the three latency bias parameters for rejections were virtually the same (.37 and .39, respectively). Second, as the pilot data indicated, the speed of bias-based decisions did depend on the decision condition. More narrowly, it depended most strongly on whether the subjects were told that list items should be accepted (V and VG conditions) or rejected (G condition). This pattern is clearly discernable in the mean parameter values that appear in the far right column of Table 3. Across the six experiments and across the four trios of latency-bias parameters, the grand means of the latency-bias parameters were roughly twice as large when list items were to be accepted (M_V = .52 and M_VG = .42) as when they were to be rejected (M_G = .24). Another way of saying this is that bias-driven decisions slowed markedly when subjects were told to screen out items from the study phase. To avoid misinterpretation, it is important to stress that this is a decision condition effect rather than a test cue effect because it holds for all three types of cues.

A second finding that merits comment concerns the latency-bias parameters for V versus VG. Although list items are accepted with both types of decisions, additional items (related distractors) are accepted in the VG condition. In light of the familiar finding that decision criteria become more liberal as the pool of to-be-accepted items expands (e.g., Starns et al., 2008), it would be natural to expect that bias-based decisions would be faster in the VG condition because the baseline probability that any random cue should be accepted is higher in that condition. Actually, the reverse was true overall because we saw that the mean estimates of V and VG latency-bias parameters were .52 and .42, respectively. As might be expected, given the small size of this difference, it was reliable in some experiments but not in others, as will be seen in the significance tests that follow.

The procedure for detecting reliable differences among the latency-bias parameters in each experiment consisted of two steps. First, a likelihood ratio test of the omnibus null hypothesis that the values of all three parameters in each of the four trios were equal (e.g., L_bVT = L_bGT = L_bVGT) was computed for a given experiment, which produced a G²(3) statistic for each of the four trios. Second, when that null hypothesis was rejected for a given trio (e.g., for the trio L_bVT, L_bGT, and L_bVGT), likelihood ratio tests of the three possible pairwise hull hypotheses (L_bVT = L_bGT, L_bVT = L_bVGT, and L_bGT = L_bVGT in the example) were computed, which each produced a G²(2) statistic. The overall results of these tests were as follows.

First, the trio-level omnibus tests produced some null hypothesis rejections in all of the experiments, which confirms the suggestion in the far right column of Table 3 that there were differences between the latency-bias parameters for the G condition versus the other two conditions. Four of the trio-level tests produced null hypothesis rejections in all Experiments except for Experiment 5. Experiment 5 produced 3 null hypothesis rejections. Second, in the four trios of Experiments 1, 2, 3, 4, and 6, 19 out of 20 pairwise tests of the null hypothesis that the latency-bias parameters for the V and G conditions were equal produced rejections, as did 17 of the pairwise tests of the null hypothesis that latency-bias parameters for the VG and G conditions were equal. In addition, six of the pairwise tests of the null hypothesis that latency-bias parameters for the V and VG conditions were equal produced rejections. Turning to Experiment 5, for which one of the trio-level null hypotheses were rejected, pairwise tests rejected the null hypothesis that the latency-bias parameters for the V and G conditions were equal in three of those tests, and pairwise tests rejected the null hypothesis that the latency-bias parameters for the VG and G conditions were equal in two of those tests. In those same experiments, pairwise tests did not reject the null hypothesis that the latency-bias parameters for the V and VG conditions were equal in any of the trios.

Summing up the results for latency-bias parameter comparisons, the speed of bias-driven decisions can potentially vary as function of decision condition (V, G, VG), type of test cue (list item, related distractor, unrelated distractor), and type of response (accept, reject). In the event, the results had two themes, a major one and a minor one, both of which involved decision condition. The major theme was robust evidence that bias-driven decisions are slowest when list items must be rejected, regardless of the type of test cue. The minor theme was the weaker evidence that when list items had to be accepted, bias-driven decisions were slower than when related distractors also had to be accepted.

2. Comparison of retrieval and bias processes

For related distractors, the trio of latency-bias parameters can be compared to the trio of latency-retrieval parameters, and for list items, the trio of latency-bias parameters can also be compared to the pair of latency-retrieval parameters. Naturally, the aim is to identify any general trends in the relative speeds of bias versus retrieval. That, in turn, bears on the theoretical question of whether bias operates after recollection and familiarity have failed to deliver a decision, or whether it operates in parallel with them. Unlike the relative speeds of recollection and familiarity, the answer to that question did not depend on the type of test cue that subjects responded to.

It can be seen in Table 3 that the mean value of the two latency-retrieval parameters for list items (.71) is roughly twice as large as the mean value of the three latency-bias parameters for these cues (.37). This is consistent with the notion that for list items, bias operates after context recollection, target recollection and familiarity have run their courses. Similarly, it can be seen in Table 3 that the mean value of the three latency-retrieval parameters for related distractors (.62) is more than twice as large as the mean value of three latency-bias parameters for these cues (.24). That is consistent with the notion that for related distractors, bias also operates after all three retrieval processes have run their courses.

Significance testing to verify these two findings is rather cumbersome, although the findings themselves are obvious from the means in Table 3. That is due to the large number of pairwise null hypotheses that bear on each finding. For related distractors, there are nine pairwise null hypotheses in each experiment: L_RDCR = L_bVRD, L_RDCR = L_bGRD, L_RDCR = L_bVGRD, …, L_RDF = L_bVGRD. Across the 6 experiments, then, there were 54 likelihood ratio tests of such null hypotheses (18 apiece for L_RDCR, L_RDTR, and L_RDF), each producing a G²(2) statistic. The null hypothesis was rejected for 11 of the 18 L_RDCR tests, for 7 of the18 L_RDTR tests, and 7 of the18 L_RDF tests. The latency-retrieval parameter was larger than the corresponding latency-bias parameter for all 11 of the L_RDCR rejections, 4 of the 7 L_RDTR rejections, and all 7 of the L_RDF rejections. Overall, then, the pairwise significance tests were consistent with the impression that had been formed by comparing the mean values of the latency-retrieval and latency-bias parameters for related distractors.

Turning to list items, there are six pairwise null hypotheses in each experiment: L_TR = L_bVT, L_TR = L_bGT, …, L_TF = _bVGT. Therefore, across the 6 experiments, there were 36 likelihood ratio tests of such null hypotheses (18 apiece for L_TR and L_TF), each producing a G²(2) statistic. The null hypothesis was rejected for 16 of the 18 L_TR tests and 13 of the 18 L_TF tests. The latency-retrieval parameter was larger than the corresponding latency-bias parameter for all 16 of the L_TR rejections and all 13 L_TF rejections. Thus, as was the case for related distractors, the pairwise significance tests were consistent with the impression that had been formed by comparing the mean values of the latency-retrieval and latency-bias parameters.

General Discussion

In the present article, we implemented a new approach to measuring the relative speeds of different cognitive processes via latency extensions of established multinomial models and used it to investigate relative speed predictions of classic dual-process accounts of recognition (Atkinson & Juola, 1973; Mandler, 1980). In those accounts, an ostensible point of separation between recollection and familiarity is that the latter is faster than the former. Early experiments failed to confirm that difference, using designs in which hit rates were compared under speeded versus non-speeded testing for manipulations that supposedly strengthen recollection (Gillund & Shiffrin, 1984; Mulligan & Hirshman, 1995). However, this null result might be due to that fact that manipulations that strengthen recollection also speed it up (Brainerd et al., 2003). Response-signal designs control for that possibility by varying testing speed from very fast to quite slow and plotting speed/accuracy functions for related distractor false alarms as well as for hits. Distractor functions should separate recollection and familiarity because, theoretically, recollection supports correct rejections, whereas familiarity supports false alarms (Matzen, Taylor, & Benjamin, 2011). Distractor functions should be inverted Us when the fastest speeds are so brief that familiarity retrieval cannot be completed before a decision is required.

Such inverted Us have been detected in several experiments (e.g., Gronlund & Ratcliff, 1989), and they are more likely to occur under conditions that ensure target recollection, in particular (e.g., Rotello & Heit, 2000). However, such results are limited in multiple ways. First and most foremost, inferences about the relative speeds of recollection and familiarity are indirect, which opens the door to alternative process interpretations (see Brainerd et al., 2003). By indirect inference, we simply mean that speed/accuracy designs do not directly measure these retrieval processes and map them with their respective latencies. Second, inverted-U functions for related distractors supply no information about the relative speed of recollection and familiarity for list items. Even if we accept the hypothesis that familiarity is faster than recollection with related distractors, the same may not be true when the test cue is a list item, unless we are willing to assume that speed is independent of cue type. That seems hazardous because, by the law of encoding variability, both absolute and relative speed could be influenced by the fact that retrieved information was stored for list items, not distractors. Third, inverted-U functions for related distractors do not necessarily show that familiarity is faster than recollection because that conclusion assumes a univariate recollection operation. Recent work suggests that recollection is bivariate, with one operation supporting correct rejections, but the other supporting false alarms. Because retrieval processes are not directly measured, the same inverted-U functions would result if context recollection is fast, relative to target recollection and familiarity. Fourth, speed/accuracy designs provide no information about the speed of bias processes. That is an important consideration because bias contributes to decisions about both list items and related distractors, and inverted-U functions could result from a single familiarity process if bias decreases as testing speed slows (Goethe & Oberauer, 2008; Rotello & Heit, 1999).

The approach that we implemented removed all four limitations via a latency extension of the conjoint recognition model: It directly measured retrieval processes and their respective latencies; provided separate sets of latency-retrieval parameters for related distractors and list items; provided separate context recollection, target recollection, and familiarity parameters for related distractors; and provided latency parameters for bias processes as well as retrieval processes. Four patterns emerged—one for the time course of retrieval processes for list items, one for the time course of retrieval processes for related distractors, one for the cue dependency of retrieval speed, and one for the time course of bias. To conclude, we comment briefly on the theoretical significance of each of these patterns.

Time Course of Retrieval Processes for List Items

A striking outcome of our experiments is the degree to which they supplied converging support for findings that were reported more than three decades ago by Gillund and Shiffrin (1884). Those authors used speeded recognition designs to pit the search of associative memory (SAM) model’s one-process view of recognition against dual-process models. Their method was to compare the effects of a series of conditions (e.g., deep versus shallow encoding) that are thought to selectively affect the recollection component of hits under speeded versus non-speeded testing. If recollection is slow, relative to familiarity, the straightforward prediction is Retrieval Time X Treatment interactions, such that treatment effects are larger for non-speeded than for speeded tests. Interactions of that sort were not observed, and that outcome held up in subsequent work by others.

Although such interactions would not be expected if recollection-enhancing manipulations speed up this process (Brainerd et al., 2003), our results argue against that explanation. Instead, they favor the obvious explanation: no speed differential between recollection and familiarity for hits. The parameter T_R measures the size of the recollection component of hits, the latency parameter L_TR measures its speed, the parameter T_F measures the size of the familiarity component of hits, and the latency parameter L_TF measures its speed. Over the six experiments, the grand means of T_R and T_F (.43 and .41) revealed that hits were equally likely to be based on recollection and familiarity. Then, the grand means of L_TR and L_TF (.72 and .70) indicated that the speeds of recollection- and familiarity-based decisions were the same. The picture was the same at the level of individual experiments because the values of L_TR and L_TF did not differ reliably in any experiment. In short, when the speeds of the recollection and familiarity components of hits were measured in six different experiments, there was no evidence that they differed. Obviously, that is consistent with the lack of Retrieval Time X Treatment interactions in prior studies.

Although there was no evidence of a recollection-familiarity speed differential for list items, it might be thought that our procedure could not detect it for the following reason: Familiarity evidence might accumulate first, but in order to ensure accuracy, subjects might withhold a decision until stronger recollective evidence becomes available. That would make it appear that there is no speed differential, when there is. Note, however, that the hypothesized strategy would be unnecessary in the VG condition because familiarity alone is sufficient to ensure accuracy. Thus, the retrieval processes would operate differently in the V and G conditions than in the VG condition, which means that the core model’s parameter invariance assumption would be wrong and fit would fail (Brainerd et al., 1998). As we saw, however, fits of the core model were uniformly acceptable.

Time Course of Retrieval Processes for Related Distractors

Turning to the findings that have previously provided the most compelling support for fast familiarity followed by slower recollection, inverted-U speed/accuracy functions for related distractors, these results could also be due to fast context recollection followed by slower target recollection and familiarity. The results of our experiments converged on this second explanation. On the one hand, the average value of the latency parameter for context recollection over experiments (.88) was nearly twice the corresponding averages of the latency parameters for target recollection (.47) and familiarity (.46). On the other hand, the values of the last two latency parameters revealed no speed differential between target recollection and familiarity. The indicated explanation of inverted-U functions runs as follows.

Such functions consist of two arms, an initial increase in false alarms followed by a subsequent decrease (Figure 1). Our data imply that the first arm is due to fast context recollection. The explanation of the second arm may seem less obvious because although target recollection supports correct rejections, familiarity, like context recollection, supports false alarms. The reason for the decrease in false alarms is that the combined effect of the two processes must be to decrease such responses, relative to context recollection: Context recollection supports false alarms with probability 1, whereas target recollection and familiarity support false alarms with probabilities 0 and 1, respectively. Consequently, as retrieval time lengthens and the latter two processes come on-line, their respective effects will yield lower false alarm rates than context recollection. Across our experiments, the average values of the retrieval parameters for these processes (RD_TR = .24 and RD_F = .38) suggests a mixture that is approximately 40% target recollection and 60% familiarity, which would substantially reduce the false alarm rate, relative to context recollection alone. Based on our results, then, the indicated explanation of inverted-U functions for related distractors is that as decision time lengthens, retrieval switches from a process that only supports false alarms to a mixture of processes that support correct rejections as well as false alarms.

Cue Dependency

The question of whether the speeds of recollection and familiarity differ as a function of whether the test cue is a list item or a related distractor has not figured centrally in prior research. In one respect, that is surprising inasmuch as such differences would be expected on various theoretical grounds, the most obvious one being the venerable encoding variability principle (Tulving & Thomson, 1971). Encoding variability makes a straightforward prediction: Because some of the information that is retrieved on recognition tests was encoded for list items but none of it was encoded for related distractors, the latter ought to be less efficient cues for recovering it, slowing both recollection and familiarity. Moreover, this slowing effect might be more pronounced for some types of information than for others, altering the relative speeds of different retrieval processes. Regardless of the theoretical reasons, our results showed that the relative speeds of different retrieval processes was indeed cue dependent.

This cue dependency emerged from the manner in which the values of the latency-retrieval parameters for list items versus related distractors fell out. On the one hand, the values of the parameters for related distractors showed that context recollection was far faster than either familiarity or target recollection, whereas there was no speed differential between familiarity and target recollection. On the other hand, the values of the parameters for list items were nearly equal, pointing to no speed differential between either form of recollection and familiarity for such cues. Note that this pattern could not have occurred if the speed ordering for related distractors had been preserved by list items. Although the core recollection parameter for list items combines the influences of both recollection processes, if the context recollection component had been faster than familiarity, as it was for related distractors, the net effect, when the latencies of the two recollections were combined in the L_TR parameter, would have been L_TR > L_TF rather than L_TR = L_TF.

This cue dependency raises an intriguing theoretical possibility—namely, that the relative speed of different retrieval processes is an emergent property of the efficiency of the retrieval cue. Assuming that a list item is the most efficient possible cue because some of the to-be-retrieved information was encoded in connection with that cue, our data suggest that highly efficiency cues are equally good at accessing different types of information. Assuming that a related distractor is a less efficient cue because none of the to-be-retrieved information was encoded in connection with that cue, it is reasonable to think it would be better at accessing some aspects of that information than others. In particular, our data suggest that related distractors are better cues for retrieving contextual details that accompanied list items than for retrieving other types of information. We will avoid the temptation to speculate about why this might be so.

Bias

Some of the most novel results were findings about the speed of bias-based decisions, relative to each other and relative to decisions that were based on the two forms of recollection or on familiarity. This is another issue that has not been prominent in prior research on the relative speed of different retrieval processes. Here, the extended model in Figures 2–4 supplies latency-bias parameters for all three types of test cues, and those parameters revealed three patterns of theoretical significance: (a) The speed of bias-based decisions was affected by the type of decision that had to be made about list items; (b) the speed of bias-based decisions did not increase when the decision was to reject rather than accept unrelated distractors; and perhaps most importantly, (c) decisions that were based on any of the retrieval processes were faster than decisions that were based on bias.

Concerning the first pattern, the episodic state of a list item can be thought of in two ways that are logically but not psychologically equivalent: It is old, and it is not new. In conjoint recognition, subjects must make both types of decisions about list items; old in the V and VG conditions and not-new in the G condition. In each of these conditions, the extended model provides four parameters that measure the speed of bias-driven decisions, and the grand means of these three quartets of parameters told a simple story. They showed that those decisions were slower when list items were to be rejected as not-new than when they were to be accepted as old, with the values of the latency-bias parameters for the G condition being half as large as those for the other two conditions. It should be stressed that this was a pure decision condition effect inasmuch as it depended on whether subjects were told to accept or reject list items, but not on the type of test cue that subjects responded to.

Concerning the second pattern, there are theoretical reasons for expecting that bias-based decisions will be faster when rejecting than when accepting unrelated distractors and will be faster in the presence of more liberal decision criteria. However, our findings ran against both of these notions. With respect to the former, Egan (1958) seems to have been the first to propose a formal recognition model containing a detect-new process, which yields rapid, confident rejections of unrelated distractors. In recent years, since the appearance of an article by Bayen et al. (1996), models of source memory have assumed that a detect-new process operates when subjects make old/new decisions (as opposed to source decisions) about unrelated distractors. Because this process produces rejections of some unrelated distractors but is not involved in acceptances, it follows that rejections should be faster, on average, than acceptances. They were not. The extended model contains three latency-bias parameters apiece for rejection and acceptance of unrelated distractors, and over the six experiments, their average values were virtually the same.

Turning to the third and final pattern, that decisions were faster when they were produced by any of the retrieval processes than when they were bias-driven, the theoretical significance of this finding is that it bears on whether bias operates concurrently with retrieval processes and on the larger question of whether the time courses of retrieval and bias processes are such as to maximize accuracy. Obviously, for the sake of accuracy, the temporal relation should be serial for list items, with forms of bias (e.g., guessing, item preference) being used to generate decisions only after retrieval processes have failed to generate them. That is because the combined target/context recollection process and the familiarity process both support “old” decisions about list items, whereas bias sometimes supports “old” and sometimes supports “new.” If, in contrast, bias operates concurrently with retrieval processes, guessing and other irrelevant strategies would often produce incorrect decisions before subjects have finished recovering memories that were stored during the study phase. Our results overwhelmingly favored the first scenario over the second. With list items, the grand means of the latency-retrieval parameters, over experiments, for combined target/context recollection and familiarity processes were .72 and .70, respectively, whereas the corresponding grand mean of the latency-bias parameters was only .37. Thus, the time courses of retrieval and bias processes appear to optimize accuracy for list items.

The picture is different for related distractors, where “new” is the correct decision in old/new recognition. There is no single temporal ordering of bias relative to the three retrieval processes that optimizes accuracy because although target recollection supports “new” decisions, context recollection and familiarity both support erroneous “old” decisions. Thus, the bias ordering that optimizes accuracy depends, first, on the temporal ordering of the three retrieval processes and on how much each contributes to recognition decisions. On the latter two points, our data showed that the temporal ordering was context recollection > target recollection = familiarity, and their relative contributions to recognition decisions were familiarity > target recollection > context recollection. With this particular temporal ordering, it is easy to see that there is no single positioning of bias that would be best for accuracy. Some positions would obviously be worse than others, however. For instance, if bias were as fast as context recollection, the result would be much higher rates of erroneous “old” decisions than if it were slower than context recollection. In the event, the temporal ordering of bias relative to the retrieval processes resembled the order for list items: The grand means of the latency-retrieval parameters were .88 (context recollection), .47 (target recollection), and .46 (familiarity), whereas the grand mean of the latency-bias parameters was .39. Similar to list items then, retrieval processes had usually run their courses before bias came on-line, but the lag was much greater for context recollection that for target recollection or familiarity.

Concluding Comments

We have seen how easily this new procedure generates latency extensions of existing cognitive models and how such an extension can deliver a rich assortment of novel findings on fundamental theoretical questions. In the episodic memory sphere, a latency extension of the conjoint recognition model delivered five instructive patterns in connection with the relative speeds of recollective and non-recollective retrieval processes. First, although differences in relative speed were detected in all experiments, they depended on the nature of the test cue—with the same pattern of differences always being detected for related distractors but no differences ever being detected for list items. Second, differences in retrieval speed never conformed to the classic hypothesis that familiarity is faster than recollection because one form of recollection was always faster than familiarity. Third, regardless of the nature of the test cue, bias processes were always slower than retrieval processes, suggesting the theoretically important conclusion that subjects do not resort to guessing, preference, and other non-memorial strategies unless retrieval processes fail to produce a decision. Fourth, the speed of bias processes depended on the type of memory decision that subjects were asked to make, whereas the speed of retrieval processes did not. Fifth, relative speed can be added to the growing list of phenomena that dissociate target recollection from context recollection.