Sternberg Paradigm

[Rita Seliba]

Despitethe wide variety of different formal models of short-term memory search that have been considered, it is surprising that there have been relatively few attempts to contrast them by considering their ability to account for RT distribution data. Indeed, we are not aware of any studies that have engaged in competitive testing of fully parameterized versions of the models with respect to their ability to account for detailed forms of RT distribution data in the Sternberg task. In light of major advances in the field in the development of formal RT models and methods for evaluating them, our main aim in the present research was to fill that gap. As is described more fully below, in addition to considering some of the major classes of models, a closely related goal was to determine the types of parameter variation within the models that seem crucial to capturing performance in the task.

Before turning to the candidate models and describing the key issues in greater detail, we first provide a brief review of some previous studies that did involve analysis of RT distribution data in the Sternberg task.

In this research, we decided to consider three main candidate models defined by different information-processing architectures. Within each architecture, a variety of different parametric assumptions were considered. The goal was both to investigate whether some architectures provided superior quantitative accounts of the RT distribution than did others and to evaluate the parsimony of the alternative accounts. To help interpret the resulting quantitative fits, we also evaluated them on a battery of their qualitative predictions.

As is explained in detail in the next section, we chose to use a linear ballistic accumulator (LBA) approach (Brown & Heathcote, 2008), rather than a diffusion approach, for modeling the elementary match/mismatch decisions. Both approaches to modeling elementary decision processes have received considerable support in the literature, and we do not believe that our main conclusions are influenced by this specific choice. Because there is now a good deal of consensus that the LBA approach provides a reasonable description of the time course of elementary decision processes, it serves as a suitable building block for the information-processing architectures that we will investigate. Furthermore, simple analytic expressions are available for computing the likelihood of RT distributions predicted by the LBA model, thereby easing considerably the computational burden in the present investigations.

To begin, we should emphasize that the aim of our investigation was to discriminate among fairly general versions of the alternative architectures for short-term memory recognition. Therefore, the models we develop do not specify detailed cognitive mechanisms that underlie the overall process. For example, we make no specific assumptions about the ways in which items are maintained or retrieved or by which similarity comparisons are made. Instead, we adopt a descriptive approach in which the outcome of these detailed mechanisms is summarized in the form of the evidence accumulation parameters of the LBA decision process. Fast evidence accumulation, for example, would arise because of some (unspecified) combination of effective maintenance, retrieval, and similarity comparison. By adopting this approach, we seek to contrast versions of the information-processing architectures that are framed at a reasonably general level.

Within each architecture, we model the elementary decision processes using the LBA model (Brown & Heathcote, 2008).Footnote 2 The LBA model is based on an evidence accumulation framework, in which evidence for potential responses is accumulated until a threshold amount is reached. In the LBA, evidence is accrued at a linear rate and without noise (ballistically) toward a response threshold. Observed RT is a combination of the time taken for the decision process and the time taken for other aspects of RT not involved in the decision process, such as the time taken for the encoding of the stimuli and the motor response.

There are a variety of ways that LBA accumulators can be arranged in order to produce a decision (for analogous issues in the domain of multidimensional classification, see Fific, Little, & Nosofsky, 2010). We consider the three architectures that correspond to the aforementioned models of short-term memory scanning: global familiarity, parallel self-terminating, and serial exhaustive. We now discuss each of the model architectures in turn. Figure 1b, c provide a visual summary. Note that whereas the present section discusses only the general architectures, a subsequent Model Parameterizations section provides more detailed assumptions for specifying the accumulation rates and response thresholds in each architecture.

In addition to investigating the multiple model architectures, we consider a number of different parameterizations of the models. Within each of the model architectures, we fit a range of models in which drift rate and response threshold parameters are differentially allowed to vary across experimental conditions (such as the lag between a studied item and when it is probed, and the length of the study list). There are two reasons for investigating multiple parameterizations. The first is that the adequacy of an architecture may depend critically on the parameterization that is assumed. In addition, by investigating different parameterizations, we may discover which model provides the most parsimonious account of performance.

The second reason for investigating multiple parameterizations is that we can use the estimated parameters to better understand short-term memory-scanning performance. The parameters of the LBA have interesting psychological interpretations, and the way in which various empirical factors influence those parameters can be particularly revealing. For example, the rate of accumulation of evidence for the match between a study item and a probe provides an indication of the strength of the memory for that study item. Therefore, the way in which factors such as the number of items in the study list or the lag between study and probe influence the parameters of the LBA accumulators can be highly revealing of the processes underlying short-term memory.

We now present an overview of the considerations we made regarding how empirical factors may influence response thresholds and drift rates. The details of these parameterizations are provided in the Appendix.

It seems likely that participants will set different thresholds for deciding whether there is a match or a mismatch between the probe and a study item. For example, participants may require less evidence to decide that a probe does not match a study item than to decide that the probe does match a study item. It is also possible that the length of the study list could influence the amount of evidence required to make a decision. Indeed, Nosofsky et al. (2011) found evidence that participants increase their response thresholds as the size of the study list grows. Note that, like Nosofsky et al., we assumed that when response thresholds were allowed to change with set size, they did so as a linear function of set size. (Our main conclusions are unchanged if more flexible functions are allowed.)

In our second (more general) drift rate parameterization, we allowed for the possibility that the rate of evidence accumulation is also influenced by the size of the memory set. Again, we allowed for the possibility that drift rates are driven by the lag between study and probe. However, in this parameterization, we also allowed that there may be a systematic effect of memory set size on the drift rates as well. For example, the short-term memory store presumably has some capacity that may be strained as the size of the study list increases, thus reducing the rate at which study and probe items can be matched.

For simplicity, in the case of the parallel self-terminating and global-familiarity models, we modeled the nondecision time component of RT using a single parameter, t 0, and this parameter was held fixed across all conditions. Because of historical precedent, in the case of the serial-exhaustive model, we allowed different nondecision times for targets and lures (Sternberg, 1975). Also, we found that fits of the serial-exhaustive model to the RT distribution data improved considerably when we made allowance for between-trial variability in the nondecision time. Thus, for the serial-exhaustive model, we modeled nondecision time as a log-normal distribution, with two separate mean nondecision times for targets and lures (T POS and T NEG) and a common log-normal scale parameter (S T ). (Note that in the special case in which T POS = T NEG and S T = 0, the nondecision time in the serial-exhaustive model is identical in form to what is assumed for the other models.) Finally, as is explained later in our article, to address past hypotheses advanced by Sternberg (1975) that involve encoding-time issues, we also fitted elaborated versions of the serial-exhaustive model in which nondecision time was allowed to vary across other conditions as well.

Nosofsky et al. (2011, Experiment 2) reported RT distributions for 4 participants, each of whom completed multiple sessions of short-term memory scanning. Memory set size ranged from one to five items, and all serial positions within each set size were tested. Two participants (1 and 2) completed 9 sessions (days) of 500 trials per session. Participants completed an equal number of trials in each memory set size condition, with the serial position probed on each trial selected randomly from within the relevant memory set. Two participants (3 and 4) completed 16 sessions of 300 trials in which each unique combination of serial position and set size was presented equally often. (Thus, for these 2 participants, smaller set sizes were tested less often than were larger ones.) Within each block of testing, the probe was a target item (a member of the study list) on half of the trials and was a lure item on the other half of the trials. Presentation orders were random within the constraints described above.

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