Comparison of two models of similarity judgment

The conventional multidimensional distance model of similarity judgment was compared with a new model in which component differences are weighted and then averaged. To evaluate the models, qualitative and quantitative predictions were derived from Romney and D'Andrade's (1964) componential analysis of American kinship terms, and these predictions were tested by having subjects rate the similarity (in experiment 1) and the difference (in experiment 2) between all possible pairs of 12 kinship terms. In both experiments, violations of qualitative predictions for both a simple distance model and a simple averaging model revealed that the componential analysis was not sufficient to account for the data. However the averaging model was able to account for the data when the dichotomous dimension of lineality used by Romney and D'Andrade was replaced by a continuous dimension of immediacy or closeness of kin. In contrast, no comparable elaboration under the distance model was successful. These results were discussed in terms of the likely psychological processes underlying similarity judgment.     

The relative sensitivities of same-different and identification judgment models to perceptual dependence

Probabilistic models of same-different and identification judgments are compared (within each paradigm) with regard to their sensitivity to perceptual dependence or the degree to which the underlying psychological dimensions are correlated. Three same-different judgment models are compared. One is a step function or decision bound model and the other two are probabilistic variants of a similarity model proposed by Shepard. Three types of identification models are compared: decision bound models, a probabilistic multidimensional scaling model, and probabilistic models based on the Shepard-Luce choice rule. The decision bound models were found to be most sensitive to perceptual dependence, especially when there is considerable distributional overlap. The same-different model based on the city-block metric and an exponential decay similarity function, and the corresponding identification model were found to be particularly insensitive to perceptual dependence. These results suggest that if a Shepard-type similarity function accurately describes behavior, then under typical experimental conditions it should be difficult to see the effects of perceptual dependence. This result provides strong support for a perceptualindependence assumption when using these models. These theoretical results may also play an important role in studying different decision rules employed at different stages of identification training.We thank Robert Melara, Jerome Busemeyer and three anonymous reviewers for comments on an earlier draft of this paper.     

Processes of similarity judgment

Similarity underlies fundamental cognitive capabilities such as memory, categorization, decision making, problem solving, and reasoning. Although recent approaches to similarity appreciate the structure of mental representations, they differ in the processes posited to operate over these representations. We present an experiment that differentiates among extant structural accounts of similarity in their ability to account for patterns of similarity ratings. These data pose a challenge for transformation-based models and all but one mapping-based model, the Similarity as Interactive Activation and Mapping (SIAM) model of similarity.     

Visual judgment of similarity across shape transformations: evidence for a compositional model of articulated objects

A single biological object, such as a hand, can assume multiple, very different shapes, due to the articulation of its parts. Yet we are able to recognize all of these shapes as examples of the same object. How is this invariance to pose achieved? Here, we present evidence that the visual system maintains a model of object transformation that is based on rigid, convex parts articulating at extrema of negative curvature, i.e., part boundaries. We compared similarity judgments in a task in which subjects had to decide which of the two transformed versions of a 'base' shape-one a 'biologically valid' articulation and one a geometrically similar but 'biologically invalid' articulation-was more similar to the base shape. Two types of comparisons were made: in the figure/ground-reversal, the invalid articulation consisted of exactly the same contour transformation as the valid one with reversed figural polarity. In the axis-of-rotation reversal, the valid articulation consisted of a part rotated around its concave part boundaries, while the invalid articulation consisted of the same part rotated around the endpoints on the opposite side of the part. In two separate 2AFC similarity experiments-one in which the base and transformed shapes were presented simultaneously and one in which they were presented sequentially-subjects were more likely to match the base shape to a transform when it corresponded to a legitimate articulation. These results suggest that the visual system maintains expectations about the way objects will transform, based on their static geometry.     

The relative merit of empirical priors in non-identifiable and sloppy models: Applications to models of learning and decision-making

Formal modeling approaches to cognition provide a principled characterization of observed responses in terms of a set of postulated processes, specifically in terms of parameters that modulate the latter. These model-based characterizations are useful to the extent that there is a clear, one-to-one mapping between parameters and model expectations (identifiability) and that parameters can be recovered from reasonably sized data using a typical experimental design (recoverability). These properties are sometimes not met for certain combinations of model classes and data. One suggestion to improve parameter identifiability and recoverability involves the use of “empirical priors”, which constrain parameters according to a previously observed distribution of values. We assessed the efficacy of this proposal using a combination of real and artificial data. Our results showed that a point-estimate variant of the empirical-prior method could not improve parameter recovery systematically. We identified the source of poor parameter recovery in the low information content of the data. As a follow-up step, we developed a fully Bayesian variant of the empirical-prior method and assessed its performance. We find that even such a method that takes the covariance structure of the parameter distributions into account cannot reliably improve parameter recovery. We conclude that researchers should invest additional efforts in improving the informativeness of their experimental designs, as many of the problems associated to impoverished designs cannot be alleviated by modern statistical methods alone.     

A theory of relative judgment

This paper is concerned with the scaling method of “ratio estimation.” The simple theory that equates reported ratio judgments to ratios of psychological magnitudes is first considered, then two close relatives of this theory are formulated, each of which places weaker constraints on the structure of the data. Structural conditions are stated that express the relations that must hold among observed ratio judgments for each of the models. The models proposed are “cumulative” in the sense that the second is a weakened version of the first, and the third a weakened version of the second. A special feature of the models is that they may be tested entirely in terms of observables, avoiding the necessity of scale construction prior to testing. Tests were carried out on data from 9 published studies. The strongest model, typically used in scale construction using ratio estimation data, was generally inadequate, showing large systematic errors. However, the weakest version generally passed the tests of internal consistency, and the model equation provided a basis for constructing ratio scales utilizing bias parameters.     

A semantic memory sentence verification model based on relative judgment theory

A subjective referent model of sentence verification in semantic memory tasks based on the relative judgment theory of Link and Heath (1975), together with the derivation of a discriminability index, are presented in this paper. An attractive feature of the model is its consideration of both error rates and response times (RTs) in the calculation of the discriminability index. The model is also able to account for the frequent finding in semantic memory tasks that error RTs are longer than correct RTs. A partial replication of Experiment 2 of McCloskey and Glucksberg's (1979) sentence verification context effect studies, in which we employed 44 subjects and 28 categories, and controlled for item familiarity, revealed that error RTs were consistently longer than correct RTs--a finding inconsistent with the McCloskey and Glucksberg property comparison model, but in accord with the subjective referent model. An important fortuitous result was the detection of a context effect by the discriminability measure, an effect not detected by the RT data alone. The discriminability measures yielded a near perfect correlation with estimates of the mean step size of the random walk obtained by application of the parameter estimation program FITTRW (Heath, 1983).     

Asymptotic judgment of cause in a relative validity paradigm

We report three experiments in which we tested asymptotic and dynamic predictions of the Rescorla-Wagner (R-W) model and the asymptotic predictions of Cheng's probabilistic contrast model (PCM) concerning judgments of causality when there are two possible causal candidates. We used a paradigm in which the presence of a causal candidate that is highly correlated with an effect influences judgments of a second, moderately correlated or uncorrelated cause. In Experiment 1, which involved a moderate outcome density, judgments of a moderately positive cause were attenuated when it was paired with either a perfect positive or perfect negative cause. This attenuation was robust over a large set of trials but was greater when the strong predictor was positive. In Experiment 2, in which there was a low overall density of outcomes, judgments of a moderately correlated positive cause were elevated when this cause was paired with a perfect negative causal candidate. This elevation was also quite robust over a large set of trials. In Experiment 3, estimates of the strength of a causal candidate that was uncorrelated with the outcome were reduced when it was paired with a perfect cause. The predictions of three theoretical models of causal judgments are considered. Both the R-W model and Cheng's PCM accounted for some but not all aspects of the data. Pearce's model of stimulus generalization accounts for a greater proportion of the data.     

Content and distance similarity models: a correction to Sjöberg

Corrections are made to a statement by Sjöberg (1977) concerning the compatibility of results obtained by him and by Gregson (1976).     

Properties of judgment models in a financial setting

The purpose of this study is to extend judgment research by investigating properties of information processing models utilized in a financial judgment situation. Forty-seven graduate business school students estimated percentage changes in the prices of 50 securities. An important element of the research design is the availability of an objective, readily determinable “environmental” processing model. Dimensions of cognitive processing considered here include the accuracy and reliability of judgments, linear versus nonlinear processing, interjudge agreement, and self-insight into weighting and combining of information cues. The results are compared with evidence from other areas of applied psychology. Individual and aggregated (“nominal group”) judgment models were generated. Aggregation models depict processing representative of the set of subjects, and diversification out of individual biases and errors is possible. Statistically significant levels of judgment accuracy are reported here. Moderate agreement among the subjects was noted, and a linear model did not explain a large percentage of the variance in judgments. A significant degree of self-insight into the relative weighting of cues by subjects is indicated. The aggregation models outperformed the “average” individual within the respective groups of subjects.     

An application of a dynamic model of judgment to magnitude production

A dynamic model of judgment, together with a model of stimulus context effects, is applied to magnitude production (MP) and magnitude estimation (ME) experiments. Participants' responses in MP were correlated across trials, as is typically found for ME. The magnitudeof the autocorrelation, however, was small, which suggests that participants in MP tend to rely more heavily on a long-term frame of reference. Second, a stimulus context effect found for ME did not appear for MP, most likely because of the different nature of the task (i.e., intermediate values of the stimulus were heard while the participant produced a response). A fit of an earlier regression model, on the other hand, suggests that the number presented on the previous trial in MP has a large contrastive effect on the current response.The present model offers a different view of this result, in that it shows that a negative coefficient for the earlier model is consistent with a positive judgmental effect. The regression effect noted by Stevens and Greenbaum (1966), which is a value of the estimated ME exponent that is smaller than the inverse of the estimated MP exponent, was also found; it i s shown that the effect did not arise from bias in estimation.     

Experimental evidence for serial models of lexical access: a judgment task

The hypothesis that the lemma and lexeme levels of lexical access are in a feed-forward serial relation is supported. Subjects judge the degree of semantic relatedness of pairs of words. Stimuli are all functionally synonymous; they are pairs of words implicated in natural word blends. Half the stimuli are phonologically related and the other half are not. In one experiment the pairs are presented in a sentential context and in the other no context is provided. In both the experiments the phonologically unrelated pairs are judged closer in meaning than the phonologically related pairs. This is interpreted as support for serial models of lexical access.     

On the discrepant results in synchrony judgment and temporal-order judgment tasks: a quantitative model

Research on the perception of temporal order uses either temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks, in both of which two stimuli are presented with some temporal delay and observers must judge the order of presentation. Results generally differ across tasks, raising concerns about whether they measure the same processes. We present a model including sensory and decisional parameters that places these tasks in a common framework that allows studying their implications on observed performance. TOJ tasks imply specific decisional components that explain the discrepancy of results obtained with TOJ and SJ tasks. The model is also tested against published data on audiovisual temporal-order judgments, and the fit is satisfactory, although model parameters are more accurately estimated with SJ tasks. Measures of latent point of subjective simultaneity and latent sensitivity are defined that are invariant across tasks by isolating the sensory parameters governing observed performance, whereas decisional parameters vary across tasks and account for observed differences across them. Our analyses concur with other evidence advising against the use of TOJ tasks in research on perception of temporal order.     

Self-other similarity judgment asymmetries reverse for people to whom you want to be similar

People typically judge themselves to be less similar to others than others are to themselves. The selective accessibility model [Mussweiler, T. (2003). Comparison process in social judgement: mechanical consequences. Psychological Review, 110, 472-489.] suggests that the direction of this self-other similarity asymmetry could reverse for comparison others to whom people want to be more similar. Motivation to be more similar is thought to prompt a focal hypothesis of similarity as opposed to dissimilarity, which influences the amount and kind of information accessed when making the judgment. A study found a typical asymmetry for comparison others to whom participants did not wish to be more similar, and a reversed asymmetry for comparison others to whom participants did wish to be more similar. The direction of the asymmetry was not dependent on whether participants knew a lot or a little about the comparison other.