Independence & Separability

Since Garner and Felfoldy (1974) introduced the notion of separability and integrality of dimensions in perception, researchers have usually reached for a finite number of canonical sets of object attributes that are characteristically separable (e.g., circles with radial lines) or characteristically integral (hue, saturation of a color) when constructing stimuli to study more advanced processes such as categorization or recognition memory. Most often, for separable dimensions, the circles were either semicircles with a radial line whose length varied with the circles size or full circles with the same property. In an unpublished study presented at an earlier meeting of this Society, Balakrishnan argued that due to the co-termination of the line length with the circle size, the physics of light propagation (modeled via a Poisson process) would render these dimensions not independent (even before perception) going against their prevailing use. We altered the traditional pattern to have the radial line be of a constant length that extended beyond the circle diameter to ensure that, at least in the physics, these attributes would be independently constructed. We present evidence that they are in fact perceptually separable and independent. We also gain insight into the mental architecture behind their identification by employing patterns defined by these dimensions in a combined systems factorial technology and general recognition theory framework.

Even after decades of attitude associations research, the cognitive processes underlying behavior on tasks that evaluate these associations remain elusive (Corneille & Hütter, 2020). Specifically, it remains unclear whether social categories, such as age, and valence information in Implicit Associations Tasks (IATs) are processed independently. Our research investigates this independence using a within-subjects two-part task designed to implement the analytical tools from Systems Factorial Technology (SFT) and General Recognition Theory (GRT) to an IAT and Sorted Pairs Features (SPF) task. In Part 1, we adapted the traditional IAT design to present both word and face stimulus pairs together. Across eight separate blocks, participants identified the presence of only age, word valence, or a combination of both stimulus categories. In Part 2, we adapted the SPF task to allow modeling of stimulus category confusions via General Recognition Theory (GRT). Data collection is ongoing at the University of Florida, with a target of two-hundred undergraduate students. We will compare standard IAT and SPF measures to our SFT and GRT based analyses. Specifically, we implement workload capacity analysis to the response time distributions collected in part 1, comparing the coefficients to the UCIP benchmark to infer processing independence between age and word valence channels. We model the category confusions from part 2 for each individual and hierarchically using the GRT framework to infer category-level independence and separability. We discuss the methodological approach, results, and implications of processing non/independence of implicit attitudes.

Response inhibition, the ability to stop ongoing responses when they are no longer appropriate, is commonly assessed using the stop-signal paradigm. The paradigm owes its popularity to the underlying horse-race model that enables estimation of the unobservable latency of stopping. The model conceptualizes performance as a race between a go and a stop process. A key assumption of the model is that the go process is unaffected by the presence or absence of a stop signal. Bissett et al. (2021) found that this “context independence” assumption is commonly violated, especially when the stop signal is presented shortly after the primary task. As violations of context independence invalidate nonparametric estimates of stopping latencies derived from the race model, they should not be taken lightly. In this talk, we present a systematic assessment of context independence through an extensive review of the literature. Our review uncovered 2090 stop-signal papers published between 2000 to 2021, resulting in 31 papers and 107 conditions with usable and openly available datasets included in our analysis. We found no systematic violations of context independence. In fact, our results generally align with the predictions of a version of the race model that accounts for attention lapses, formalized as failures to trigger the stop process. We discuss the implications of these findings for applied researchers as well as the broader stop-signal literature.

General Recognition Theory (GRT) demarcates various types of independence in the multidimensional perceptual decision process and provides empirical methods to detect violations of these independences. These methods are based on the pattern of errors made by participants and therefore require the experiment to be carefully designed so that the level of difficulty is appropriately matched to perceptual ability. The traditional approach to administering a GRT experiment is susceptible to individual differences in perceptual ability, which may cause more data to need to be collected than would otherwise be necessary. To address this problem, we developed an adaptive approach that calibrates the experiment to the individual participant. We previously conducted a simulation study to demonstrate proof of concept and gauge the adaptive method’s statistical properties. In the current work, we present a validation study using human participants. Twenty participants made judgments about separable or integral stimuli. During a short preliminary block, the adaptive algorithm fit a highly constrained Gaussian GRT model to each participant’s responses. Afterwards, the participants performed the typical complete identification task using stimuli predicted by the fitted model to yield a targeted level of accuracy. We observed more violations of marginal response invariance in the integral condition than in the separable condition. We compare the effectiveness of the adaptive approach to a control study where a single set of stimuli were determined via traditional pilot-testing and administered to all participants. Our adaptive approach improves the accessibility and efficiency of GRT studies and facilitates online and replication studies.