A unified theory of discrete and continuous responding.

Understanding the cognitive processes underlying choice requires theories that can disentangle the representation of stimuli from the processes that map these representations onto observed responses. We develop a dynamic theory of how stimuli are mapped onto discrete (choice) and onto continuous response scales. It proposes that the mapping from a stimulus to an internal representation and then to an evidence accumulation process is accomplished using multiple reference points or "anchors." Evidence is accumulated until a threshold amount for a particular response is obtained, with the relative balance of support for each anchor at that time determining the response. We tested this multiple anchored accumulation theory (MAAT) using the results of two experiments requiring discrete or continuous responses to line length and color stimuli. We manipulated the number of options for discrete responses, the number of different stimuli, and the similarity among them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate, faster, and more skewed distributions of responses near the ends of a response scale; lower accuracy and slower responses as the number of discrete choice options increases; and longer response times and lower accuracy when alternative responses are more similar to the target response. Our empirical and modeling results suggest that discrete and continuous response tasks can share a common evidence representation, and that the decision process is sensitive to the perceived similarity among the response options. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Accumulating advantages: A new conceptualization of rapid multiple choice.

Independent racing evidence-accumulator models have proven fruitful in advancing understanding of rapid decisions, mainly in the case of binary choice, where they can be relatively easily estimated and are known to account for a range of benchmark phenomena. Typically, such models assume a one-to-one mapping between accumulators and responses. We explore an alternative independent-race framework where more than one accumulator can be associated with each response, and where a response is triggered when a sufficient number of accumulators associated with that response reach their thresholds. Each accumulator is primarily driven by the difference in evidence supporting one versus another response (i.e., that response's "advantage"), with secondary inputs corresponding to the total evidence for both responses and a constant term. We use Brown and Heathcote's (2008) linear ballistic accumulator (LBA) to instantiate the framework in a mathematically tractable measurement model (i.e., a model whose parameters can be successfully recovered from data). We show this "advantage LBA" model provides a detailed quantitative account of a variety of benchmark binary and multiple choice phenomena that traditional independent accumulator models struggle with; in binary choice the effects of additive versus multiplicative changes to input values, and in multiple choice the effects of manipulations of the strength of lure (i.e., nontarget) stimuli and Hick's law. We conclude that the advantage LBA provides a tractable new avenue for understanding the dynamics of decisions among multiple choices. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

Integrating cognitive process and descriptive models of attitudes and preferences.

Discrete choice experiments--selecting the best and/or worst from a set of options--are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well-established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, multi-attribute discrete choice data. The fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best-worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator-based models of decision making used in response time research can also provide process-level instantiations for random utility models.

Stimulus-specific learning: disrupting the bow effect in absolute identification.

The bow effect is ubiquitous in standard absolute identification experiments; stimuli at the center of the stimulus-set range elicit slower and less accurate responses than do others. This effect has motivated various theoretical accounts of performance, often involving the idea that end-of-range stimuli have privileged roles. Two other phenomena (practice effects and improved performance for frequently-presented stimuli) have an important but less explored consequence for the bow effect: Standard within-subjects manipulations of set size could disrupt the bow effect. We found this disruption for stimulus types that support practice effects (line length and tone frequency), suggesting that the bow effect is more fragile than has been thought. Our results also have implications for theoretical accounts of absolute identification, which currently do not include mechanisms for practice effects, and provide results consistent with those in the literature on stimulus-specific learning.

Purely relative models cannot provide a general account of absolute identification.

Unidimensional absolute identification-identifying a presented stimulus from an ordered set-is a common component of everyday tasks. Laboratory investigations have mostly used equally spaced stimuli, and the theoretical debate has focused on the merits of purely relative versus purely absolute models. Absolute models incorporate substantial knowledge of the complete set of stimuli, whereas relative models allow only partial knowledge and assume that each stimulus is compared with recently observed stimuli. We test and refute a general prediction made by relative models, that accuracy is very low for some stimulus sequences when the stimuli are unequally spaced. We conclude that, although relative judgment processes may occur in absolute identification, a model must incorporate long-term referents to explain performance with unequally spaced stimuli. This implies that purely relative models cannot provide a general account of absolute identification.

Dissociating speed and accuracy in absolute identification: the effect of unequal stimulus spacing.

Identification accuracy for sets of perceptually discriminable stimuli ordered on a single dimension (e.g., line length) is remarkably low, indicating a fundamental limit on information processing capacity. This surprising limit has naturally led to a focus on measuring and modeling choice probability in absolute identification research. We show that choice response time (RT) results can enrich our understanding of absolute identification by investigating dissociation between RT and accuracy as a function of stimulus spacing. The dissociation is predicted by the SAMBA model of absolute identification (Brown, Marley, Dockin, & Heathcote, 2008), but cannot easily be accommodated by other theories. We show that SAMBA provides an accurate, parameter free, account of the dissociation that emerges from the architecture of the model and the physical attributes of the stimuli, rather than through numerical adjustment. This violation of the pervasive monotonic relationship between RT and accuracy has implications for model development, which are discussed.

Inverted-U effects generalize to the judgment of subjective properties of faces.

Researchers studying absolute identification have long known that it takes more time to identify a stimulus in the middle of a range than one at the extremes. That is, there is an inverted-U relation between mean response time and response position. In this task, an inverted-U relation also exists between response uncertainty and response position. Similarly, an inverted-U relation between mean response time and response position has been found for psychometric measures involving questions about the self. However, psychophysicists explain these inverted-U effects differently than do self-schema researchers. We propose an integrative framework in which task constraints explain these effects. To verify the generality of these inverted-U effects, we hypothesized that they would exist in three tasks having similar constraints--in this case, tasks involving the judgment of subjective properties of faces on a Likert-type scale. Our results are consistent with this hypothesis. We discuss the relevance of the results for other applications of Likert-type scales.

An integrated model of choices and response times in absolute identification.

Recent theoretical developments in the field of absolute identification have stressed differences between relative and absolute processes, that is, whether stimulus magnitudes are judged relative to a shorter term context provided by recently presented stimuli or a longer term context provided by the entire set of stimuli. The authors developed a model (SAMBA: selective attention, mapping, and ballistic accumulation) that integrates shorter and longer term memory processes and accounts for both the choices made and the associated response time distributions, including sequential effects in each. The model's predictions arise as a consequence of its architecture and require estimation of only a few parameters with values that are consistent across numerous data sets. The authors show that SAMBA provides a quantitative account of benchmark choice phenomena in classical absolute identification experiments and in contemporary data involving both choice and response time.

Is absolute identification always relative? Comment on Stewart, Brown, and Chater (2005).

N. Stewart, G. D. A. Brown, and N. Chater's relative judgment model includes three core assumptions that enable it to predict accurately the vast majority of "classical" phenomena in absolute identification choices, but not the time taken to make them, including sequential effects, such as assimilation and contrast. These core assumptions, coupled with the parameter values used in the above-mentioned article, lead to the prediction that identification accuracy is low when a large stimulus on 1 trial is followed by a small stimulus on the next trial and vice versa. Data do not support this prediction. The authors identify a set of parameters that allow the model to better fit the data, but problems remain when the data are analyzed with a version of the discrimination measure (d') from signal detection theory. The fundamental problem is that the model fits data on average but at the expense of making incorrect predictions in detail.

Choice and response time processes in the identification and categorization of unidimensional stimuli.

Lacouture and Marley (1991, 1995, 2001) have successfully modeled the probabilities of correct responses and the mean correct response times (RTs) in unidimensional absolute identification tasks for various stimulus ranges and stimulus/response set sizes, for individual and group data. These fits include those to a set of phenomena often referred to as end-anchor effects. A revised model, with the independent accumulator decision process replaced by a leaky competing accumulator decision process, fits the probabilities of correct responses and the full distributions of RTs in unidimensional absolute identification. The revised model is also applied successfully to a particular class of unidimensional categorization tasks. We discuss possible extensions for handling sequential effects in unidimensional absolute identification, and other extensions of the given class of categorization tasks that are of potential empirical and theoretical importance as a supplement to the study of multidimensional absolute identification tasks.