STRUCTURAL ALIGNMENT IN COMPARISON:

Abstract— Theories of similarity generally agree that the similarity of a pair increases with its commonalities and decreases with its differences. Recent research suggests that this comparison process involves an alignment of structured representations yielding commonalities, differences related to the commonalities, and differences unrelated to the commonalities. One counterintuitive prediction of this view is that it should be easier to find the differences between pairs of similar items than to find the differences between pairs of dissimilar items. This prediction is particularly strong for differences that are related to the commonalities. We tested this prediction in two experiments in which subjects listed a single difference for each of a number of word pairs. The results are consistent with the predictions of structural alignment. In light of these findings, we discuss the potential role of structural alignment in other cognitive processes that involve comparisons.     

Structure mapping in the comparison process

Carrying out similarity and analogy comparisons can be modeled as the alignment and mapping of structured representations. In this article we focus on three aspects of comparison that are central in structure-mapping theory. All three are controversial. First, comparison involves structured representations. Second, the comparison process is driven by a preference for connected relational structure. Third, the mapping between domains is rooted in semantic similarity between the relations that characterize the domains. For each of these points, we review supporting evidence and discuss some challenges raised by other researchers. We end with a discussion of the role of structure mapping in other cognitive processes.     

Structural Alignment during Similarity Comparisons

Similarity comparisons are a basic component of cognition, and there are many elegant models of this process. None of these models describe comparisons of structured representations, although mounting evidence suggests that mental representations are well characterized by structured hierarchical systems of relations. We propose that structured representations can be compared via structural alignment, a process derived from models of analogical reasoning. The general prediction of structural alignment is that similarity comparisons lead subjects to attend to the matching relational structure in a pair of items. This prediction is illustrated with a computational simulation that also suggests that the strength of the relational focus is diminished when the relational match is impoverished, or when competing interpretations lead to rich object matches. These claims are tested in four experiments using the one-shot mapping paradigm, which places object similarity and relational similarity in opposition. The results support the hypothesis that similarity involves the alignment of structured representations.     

Informativity and Asymmetry in Comparisons

We propose an account of comparison asymmetries based on viewing comparison as a process of structural alignment and mapping. Specifically, we hypothesize that (1) comparison asymmetries result from directional differences in informativity, and that (2) asymmetries can therefore be predicted from the relative degree of systematicity or conceptual coherence of the items being compared. In Experiment 1, we found a clear preference for placing the more systematic of two passages in the base position of a comparison. Experiments 1 and 2 further showed that structural alignability is crucial in obtaining such asymmetries. In Experiment 3, we found that asymmetries are predicted by the relative systematicity of the comparisons items rather than by the relative size of the distinctive feature sets. These results are inconsistent with accounts of asymmetry based on feature contrast or stimulus bias. In Experiments 4 through 6, we tested the functional implications of our account by examining inference projection and perceived informativity across asymmetric comparisons. Critically, comparisons having the more systematic item as the base were more likely to result in inference projection and other forms of target modification and were rated as more informative than reverse comparisons. We conclude by demonstrating that this account can explain comparison asymmetries without positing underlying asymmetries in subjective similarity, and that it offers a unified approach to the directionality of literal comparisons, analogies, and metaphors.     

What difference reveals about similarity

Detecting that two images are different is faster for highly dissimilar images than for highly similar images. Paradoxically, we showed that the reverse occurs when people are asked to describe how two images differ--that is, to state a difference between two images. Following structure-mapping theory, we propose that this disassociation arises from the multistage nature of the comparison process. Detecting that two images are different can be done in the initial (local-matching) stage, but only for pairs with low overlap; thus, "different" responses are faster for low-similarity than for high-similarity pairs. In contrast, identifying a specific difference generally requires a full structural alignment of the two images, and this alignment process is faster for high-similarity pairs. We described four experiments that demonstrate this dissociation and show that the results can be simulated using the Structure-Mapping Engine. These results pose a significant challenge for nonstructural accounts of similarity comparison and suggest that structural alignment processes play a significant role in visual comparison.     

Asymmetric Comparison in Choice Processes

Since Tversky's (1977) seminal paper on asymmetric comparisons was published, comparisons of different options are generally believed to be directional. Interestingly, the asymmetry involved in comparisons has not been considered systematically for choices between different options. This paper argues that, in decision situations, one of the options serves as a dominant standard against which the others are evaluated, which results in asymmetric comparisons and, in turn, has important and systematic consequences for the choice process. This paper outlines which conditions should result in asymmetric comparisons. Taking existing models of asymmetric comparisons into account, a process model will be presented using the loss of a previously available choice option as an example.     

Structural alignment in similarity and difference judgments

Similarity is a central construct in models of cognitive processing, and as such has been the focus of psychological inquiry. This work has revealed that similarity and difference judgments are not always inverses. One explanation for this effect is that similarity judgments focus on matching relations between the items, while difference judgments focus on the mismatching attributes. A second explanation is that both similarity and difference judgments involve a process of structural alignment, and that they use the output of this process differently. These views are contrasted by using the one-shot mapping technique that places attribute similarity and relational similarity in competition. The results suggest that similarity and difference judgments both involve structural alignment.     

MAC/FAC: A Model of Similarity-Based Retrieval

We present a model of similarity-based retrieval that attempts to capture three seemingly contradictory psychological phenomena: (a) structural commonalities are weighed more heavily than surface commonalities in similarity judgments for items in working memory; (b) in retrieval, superficial similarity is more important than structural similarity; and yet (c) purely structural (analogical) remindings e sometimes experienced. Our model, MAC/FAC, explains these phenomena in terms of a two-stage process. The first stage uses a computationally cheap, non-structural matcher to filter candidate long-term memory items. It uses content vectors, a redundant encoding of structured representations whose dot product estimates how well the corresponding structural representations will match. The second stage uses SME (structure-mapping engine) to compute structural matches on the handful of items found by the first stage. We show the utility of the MAC/FAC model through a series of computational experiments: (a) We demonstrate that MAC/FAC can model patterns of access found in psychological data; (b) we argue via sensitivity analyses that these simulation results rely on the theory; and (c) we compare the performance of MAC/FAC with ARCS, an alternate model of similarity-based retrieval, and demonstrate that MAC/FAC explains the data better than ARCS. Finally, we discuss limitations and possible extensions of the model, relationships with other recent retrieval models, and place MAC/FAC in the context of other recent work on the nature of similarity.     

Consuming now or later? The interactive effect of timing and attribute alignability

Decisions are often temporally separated from their outcomes. Using theories of structural alignment and temporal construal, we examined how temporal distance and the associated shift in decision processes moderate susceptibility to context effects. Specifically, in two experiments (one hypothetical, one with real outcomes), we demonstrated that people attend more to nonalignable differences when the outcome of the decision is in the distant future than when it is in the near future. This shift in decision processes was found in preference and choice data, as well as coded written protocols. We further show that this temporal shift cannot be explained by differential involvement with the decision or by the feasibility and desirability of the attributes. Our findings establish temporal distance as an important moderator of structural alignment effects and also extend the implications of temporal construal theory beyond the nature of the attributes to the structural relationships among attributes.     

Speeded verbal responding in adults who stutter: are there deficits in linguistic encoding?

Linguistic encoding deficits in people who stutter (PWS, n=18) were investigated using auditory priming during picture naming and word vs. non-word comparisons during choice and simple verbal reaction time (RT) tasks. During picture naming, PWS did not differ significantly from normally fluent speakers (n=18) in the magnitude of inhibition of RT from semantically related primes and the magnitude of facilitation from phonologically related primes. PWS also did not differ from controls in the degree to which words were faster than non-words during choice RT, although PWS were slower overall than controls. Simple RT showed no difference between groups, or between words and non-words, suggesting differences in speech initiation time do not explain the choice RT results. The findings are consistent with PWS not being deficient in the time course of lexical activation and selection, phonological encoding, and phonetic encoding. Potential deficits underlying slow choice RTs outside of linguistic encoding are discussed. EDUCATIONAL OBJECTIVES: The reader will be able to (1) describe possible relationships between linguistic encoding processes and speech motor control difficulties in people who stutter; (2) explain the role of lexical priming tasks during speech production in evaluating the efficiency of linguistic encoding; (3) describe the different levels of processing that may be involved in slow verbal responding by people who stutter, and identify which levels could be involved based on the findings of the present study.     

A maximum likelihood method for fitting the wandering vector model

After introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data, an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed. The possibility of testing various hypotheses by means of likelihood ratio tests is discussed. Finally, the algorithm is applied to some existing data sets for illustrative purposes.     

A relational differential outcomes effect: pigeons can classify outcomes as “good” and “better”

In a conditional discrimination each of two sample stimuli indicates which of two comparison stimuli is correct. When correct choice following each conditional stimulus is followed by a different outcome (one kind of food following one, a different kind of food following the other) it often facilitates acquisition and improves memory. In transfer designs, in which two different conditional discriminations are followed by the same two differential outcomes, outcome expectation can be shown to be sufficient for comparison choice. That is, the samples from one conditional discrimination are matched to comparisons from the other conditional discrimination based on the common outcomes alone. In the present study we asked if for pigeons the relative value of the differential outcomes (higher versus lower value) can serve as the basis for comparison choice, independent of other characteristics of the outcomes and of differential sample responding. That is, would different outcomes that could be described as “good” and “better” form two stimulus classes. For one conditional discrimination, the differential outcomes involved differential probability of reinforcement for choice of the correct comparison stimulus (0.80 vs. 0.20 for correct choice of the two comparisons, respectively). For the other conditional discrimination, the differential outcomes involved differential responding to the two comparison stimuli (5 pecks vs. 20 pecks to the correct comparisons, respectively). On test trials, when conditional stimuli from the two conditional discriminations were interchanged and the relative value of the differential outcomes could serve as the only basis for comparison choice, we found positive transfer. The results indicate that relational attributes of outcomes can serve as effective cues for comparison choice.     

Construal Level Theory and Consumer Behavior

The three commentaries on our paper “Construal Levels and Psychological Distance: Effects on Representation, Prediction, Evaluation, and Behavior” offer insightful theoretical extensions and practical applications of construal level theory (CLT). We were inspired and challenged by the commentaries to elaborate on a number of issues, although our elaboration more often raises questions and speculations than provides definite answers. Owing to space limitations, however, we could discuss only some of the issues raised in the commentaries. The first set of issues concerns our theoretical framework, namely, similarities and differences among distance dimensions, the question of additional distances, the nature of the interaction among distances, and the relationship between psychological distance and construct of stimulus information sampling. The second set of issues concerns applications of CLT to consumer choice, namely, how to make better decisions, the nature of regret, and how people construct and process choice sets.     

偶然情绪对延迟选择的影响机制

本研究旨在探讨偶然情绪对延迟选择的影响及影响机制。本研究包括两个实验, 在被试进行决策前, 分别采用图片和短片诱发其与当前决策任务无关的偶然情绪, 然后要求被试完成选择任务, 并从决策结果和决策过程两个角度考察偶然情绪对延迟选择的影响及影响机制。结果发现, 当可选项中不存在1个优势选项时, 与正性情绪相比, 个体在负性情绪下会更倾向于延迟选择, 而个体对决策信息的加工深度在偶然情绪对延迟选择的影响中具有中介作用。这可能是因为相比于正性情绪, 个体在负性情绪下会采用更深入的加工策略, 增加了决策难度, 进而提高了个体的延迟选择倾向。     

Using Marginal Structural Modeling for Grade Retention Effects

Vandecandelaere, Vansteelandt, De Fraine, and Van Damme (this issue) described marginal structural modeling (MSM) and used it to estimate the effects of a time-varying intervention, retention (holding back) in school grades, on students' math achievement. This commentary supplements Vandecandelaere et al. (this issue) and discusses several topics in retention studies and MSM. First, we discuss the importance of equating time-varying confounders in retention studies. Second, we discuss same-grade and same-age comparisons in retention studies. Third, we discuss one important section in the authors' overview of MSM: why standard methods (e.g., ANCOVA, propensity score analysis) cannot properly adjust for time-varying confounders. Finally, using the grade retention analyses in Vandecandelaere et al. (this issue) as an example, we provide our insights on four aspects of MSM: (a) covariate selection, (b) estimation of weights, (c) evaluation of balance properties, and (d) missing data handling.     

Intentional self-regulation, ecological assets, and thriving in adolescence: a developmental systems model

The positive youth development (PYD) perspective emphasizes that thriving occurs when individual ?context relations involve the alignment of adolescent strengths with the resources in their contexts. The authors propose that a key component of this relational process is the strength that youth possess in the form of self-regulatory processes; these processes optimize opportunities to obtain ecological resources that enhance the probability of PYD. They use the selection, optimization, and compensation (SOC) model of intentional self-regulation to discuss the role of self-regulation in the PYD perspective among diverse youth.     

Extensions of the Finitist Point of View

Hilbert developed his famous finitist point of view in several essays in the 1920s. In this paper, we discuss various extensions of it, with particular emphasis on those suggested by Hilbert and Bernays in Grundlagen der Mathematik (vol. I 1934, vol. II 1939). The paper is in three sections. The first deals with Hilbert's introduction of a restricted ω -rule in his 1931 paper ‘Die Grundlegung der elementaren Zahlenlehre’. The main question we discuss here is whether the finitist (meta-)mathematician would be entitled to accept this rule as a finitary rule of inference. In the second section, we assess the strength of finitist metamathematics in Hilbert and Bernays 1934. The third and final section is devoted to the second volume of Grundlagen der Mathematik. For preparatory reasons, we first discuss Gentzen's proposal of expanding the range of what can be admitted as finitary in his esssay ‘Die Widerspruchsfreiheit der reinen Zahlentheorie’ (1936). As to Hilbert and Bernays 1939, we end on a ‘critical’ note: however considerable the impact of this work may have been on subsequent developments in metamathematics, there can be no doubt that in it the ideals of Hilbert's original finitism have fallen victim to sheer proof-theoretic pragmatism.