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Gepubliceerd in:

25-11-2022 | Original Article

A comparative investigation of integral- and separable-dimension stimulus-sorting behavior

Auteurs: Charles A. Doan, Ronaldo Vigo

Gepubliceerd in: Psychological Research | Uitgave 6/2023

Abstract

Studies focusing on unsupervised categorization and sorting behavior have traditionally identified and empirically isolated a few select strategies frequently employed by observers, one-dimensional (SD), family resemblance (FR), and exclusive-or (XOR). To date, these investigations have mostly involved creating sets of multidimensional stimuli that directly contrast utilization of these strategies coupled with task or stimulus property manipulations to see their effects on categorization and sorting behavior. Currently, we extend on this methodological approach by having observers sort integral-dimension stimuli for two recently developed constrained unsupervised categorization tasks employing three-dimensional Boolean category structures. These structures instantiate six different sorting strategies, including the aforementioned SD, FR, and XOR strategies. Additionally, we connect the prevalence of the strategies observed across both tasks to previous investigations employing separable stimuli with the same tasks and underlying Boolean category structures. In comparison, our results indicate significant reductions in rule-like sorting behavior (SD or XOR) across multiple structures with the integral stimuli. Associated with this decrease in SD and XOR behavior was a corresponding increase in FR and FR-related sorting behavior. Finally, we assess how well generalized representational information theory and the simplicity model can account for the pattern of results across both experimental paradigms and stimulus sets. In general, a formal model derived from “GRIT” outperforms the simplicity model, accounting for nearly the entire range of unsupervised sorting behavior (SD, FR, XOR) observed across the separable and integral tasks.

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The category structure design of the stimulus set involved each of the two prototypical stimuli being maximally dissimilar to the other prototypical stimulus (e.g., Prototype A = {diamond, rectangle, arrow, x-octagon}; Prototype B = {rounded-diamond, oval, rounded-arrow, rounded-x-octagon}). To illustrate FR sorting, observers will place the following stimuli underneath Prototype A: {diamond, rectangle, arrow, rounded-x-octagon}, {diamond, rectangle, rounded-arrow, x-octagon}, {diamond, oval, arrow, x-octagon}, and {rounded-diamond, rectangle, arrow, x-octagon). By necessity, the other four “one-away” stimuli would be placed underneath Prototype B.

Note the lower percentage of selections for the deconstruction task compared to the construction task with these separable stimuli. This pattern, along with higher response times for the deconstruction task (Doan & Vigo, 2016), indicate that the deconstruction task was more difficult than the construction task.

It is important to note that both approaches account for 11/12 of the results from our experiments equally. The result that is not well accounted for involved participants using the XOR relation more often than the OA-FR relation during the construction task with the integral stimuli. This pattern of XOR behavior, however, is not robust with the color stimuli when considering that the effect size associated with this structure type (3₂[3] – II) is rather small (\(V=0.13\)) and when considering that the profile of behavior switched to OA-FR over XOR with the same structural relation in the deconstruction task (\(V=0.09\)). Thus, it is not clear whether this XOR result will replicate or if the prevalent OA-FR behavior will gradually emerge.

Each category type consists of a number of objects ([p]; in our case, [3]) defined over the same binary-valued dimensions (D_n; in our case, 3₂). This D_n[p] notation (Vigo, 2013b, 2015) is useful for delineating among categorical stimuli varying in dimensionality, number of dimensional values, and size. In fact, although there are 56 different ways of making 3 object categories defined over three binary-valued dimensions (8 total objects choose 3), these 56 ways can be logically reduced to a mere 3 logically distinct arrangements (3₂[3] – I, 3₂[3] – II, and 3₂[3] – III; Feldman, 2003; Higgonet & Grea, 1958; Vigo, 2013b). Once reduced, we find that there are 24 unique ways (instances) to form 3₂[3] – I, 24 unique ways (instances) to form 3₂[3] – II, and 8 unique ways (instances) to form 3₂[3] – III.

As mentioned earlier, the labeling of SD behavior with integral dimensions is a misnomer, as substantial evidence shows that integral dimensions are not processed independently (Garner, 1976; Nosofsky, 1987, 1992). Thus, even if one engages in SD behavior in the current tasks, it is not clear to what extent they were focused on the single diagnostic dimension. Despite this caveat, a main goal of the MDS procedure used by Nosofsky and Palmeri (1996) was to maximize the discrimination between the dimensional values of the color patches. Currently, we think about them in the same way even though they are not fully separable.

It is important to note that this increase in sorting behavior when the same structure types are repeatedly presented (~ 4% increase with SD sorting and ~ 11% increase with C-3D-sorting) was not observed for the XOR structures. This result could be due to a variety of factors, two that come to mind are the relative difficulty in expressing a verbalizable rule for XOR structures or the relatively few unique structure instances associated with C-3D-sorting (8 instances) compared to XOR-sorting (24 instances). Notwithstanding, the current investigation mirrors the design of Doan and Vigo (2016) and involves randomly presenting instances of all three of the 3₂[3] structures.

Unfortunately, one cannot perform the exact same post-hoc analysis of 24 instances for this type as each dimension is diagnostic in relation to another dimension being diagnostic. Despite this limitation, we did correlate the orders produced by the dimensions that lead to more exclusive-or behavior and this analysis is provided in Appendix A.

We thank an anonymous reviewer for suggesting we clarify and discuss further this distinction with regards to the current modification tasks.

Note that in the hardcover edition, which was published in 2015, there is a typographical error on page 173, where the second occurrence of “|F|” in the numerator of Eq. 9.7 and the “|F|” in the denominator of Eq. 9.7 should both appear instead as “|F´|”.

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Titel: A comparative investigation of integral- and separable-dimension stimulus-sorting behavior
Auteurs: Charles A. Doan
Ronaldo Vigo
Publicatiedatum: 25-11-2022
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 6/2023
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-022-01753-0

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