On the perception of a class of bilaterally symmetric forms

Two experiments were performed to determine the manner in which people perceive a class of bilaterally symmetric forms. In the first experiment, paired, comparison dissimilarity judgments and unidimensional single stimulus ratings were collected from the Ss. The second experiment involved the collecting of semantic differential and paired comparison dissimilarity judgments from two groups of Ss. The judgments and ratings from both experiments were compared to each other and to a set of objective measures of the forms by a series of multivariate statistical techniques. It was found that three primary attributes, orientation, convexity-concavity, and curvature, accounted for the perceptual reports, but the manner in which the attributes were used differed for different response procedures and for the same response on different occasions.     

Modeling within-subject dependencies in ordinal paired comparison data

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments. It is argued that a core assumption of latent class choice models, independence of individual decisions, may not be well-suited for the analysis of paired comparison data. Instead, the analysis and interpretation of paired comparison data may be much simplified by allowing for within-person dependencies that result from repeated evaluations of the same options in different pairs. Moreover, by relating dependencies among the individual-level responses to (in)consistencies in the judgmental process, we show that the proposed graded paired comparison models reduce to ranking models under certain conditions. Three applications are presented to illustrate the approach.This research was partially supported by NSF grant SBR-9409531. The authors are grateful to the reviewers, Alan Agresti and Herbert Hoijtink for their helpful comments on this research.     

A model for repeat paired comparison preference tests

A model is proposed that describes subject behavior on repeat paired comparison preference tests. The model extends prior work in this area in that it explicitly allows for abstentions and permits the derivation of individual true scores for discrimination ability as well as conditional estimates of proportionate preference. With these results, the properties of a paired comparison test can be thoroughly explored. An empirical example is presented, and test design issues are considered. In particular, repeat paired comparison preference tests are shown to be inherently less efficient discrimination tests than are pick 1 of 2 tests.     

An investigation of data collection methods for auditory stimuli: Paired comparisons versus a computer sorting task

Two experiments were performed to determine whether a computer sorting task could be used to collect data for auditory stimuli. Within each experiment, subjects were assigned to either a paired comparison task or a computer sorting task. For the first experiment, the stimuli were 18 graph representations constructed to vary on three parameters (shape, frequency, and amplitude). The stimuli for the second experiment were 30 sentences produced by actors portraying five emotions (anger, fear, happiness, sadness, and neutral). Multidimensional scaling solutions were produced and comparisons were made between the paired comparison and computer sorting task in each experiment. The results suggest that the computer sorting task is a viable alternative to the paired comparison task traditionally used for the investigation of the perception of auditory stimuli.     

Hierarchical modeling of paired comparison data

The method of paired comparisons belongs to a small group of techniques that provide explicit information about the consistency of individual and aggregated choices. This article investigates the link between the individual- and group-level judgments by extending R. D. Luce's (1959) model, which was originally developed for individual choice behavior, to a mixed-effects paired comparison model. It is shown that standard multilevel software for binary data can be used to estimate the model. The interpretation of the paired comparison parameters and statistical model tests are discussed in detail. An extensive analysis of an experimental study illustrates the usefulness of a hierarchical approach in modeling multiple pairwise judgments.     

Multivariate thurstonian models

The recent development of probabilistic Thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter- and intra-individual difference, the multidimensional nature of choice objects, and the effects of similarity and comparability among choice objects. A common feature of these models is that they focus on asingle preference judgment. It is customary, however, to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes. This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments.I am grateful to James, Austin, Ingo Böckenholt, and anonymous referees for helpful comments on this research. This paper is based on research presented at the Meeting of the Society for the Multivariate Analysis in the Behavioral Sciences, Groningen, The Netherlands, December 1988.     

Effects of Covariance Heterogeneity on Three Procedures for Analyzing Multivariate Repeated Measures Designs

Empirical Type I error and power rates were estimated for (a) the doubly multivariate model, (b) the Welch-James multivariate solution developed by Keselman, Carriere and Lix (1993) using Johansen's results (1980), and for (c) the multivariate version of the modified Brown-Forsythe (1974) procedure. The performance of these procedures was investigated by testing within- blocks sources of variation in a multivariate split-plot design containing unequal covariance matrices. The results indicate that the doubly multivariate model did not provide effective Type I error control while the Welch-James procedure provided robust and powerful tests of the within-subjects main effect, however, this approach provided liberal tests of the interaction effect. The results also indicate that the modified Brown-Forsythe procedure provided robust tests of within-subjects main and interaction effects, especially when the design was balanced or when group sizes and covariance matrices were positively paired.     

Modelling intransitive preferences: A random-effects approach

Current models for individual-level paired comparison data are based on the three assumptions that (1) pairwise judgments are independent, (2) the utility of an item remains invariant across trials, and (3) pair-specific variability can account for intransitive choice behaviour. All three assumptions seem strong and likely to be violated in empirical applications. This paper introduces a new framework for the analysis of paired comparison data which relaxes these three assumptions and considers the utilities associated with the same item across trials to be neither independent nor identical, but related. The proposed approach provides new insights about the reliability and consistency of paired comparison judgments and can account for systematic violations of transitivity. An application, based on a replication of Tversky's [(1969). Intransitivity of preference. Psychological Review, 76, 31-48] gamble study, illustrates the usefulness of the new approach in modelling both transitive and intransitive preferences.     

Assessing vocational interests in the Basque Country using paired comparison design

This article proposes the Thurstonian paired comparison model to assess vocational preferences and uses this approach to evaluate the Realistic, Investigative, Artistic, Social, Enterprise, and Conventional (RIASEC) model in the Basque Country (Spain). First, one unrestricted model is estimated in the Structural Equation Modelling framework using one paired comparison design. Secondly, the RIASEC circumplex structure is evaluated upon the estimated latent preferences correlation matrix. The results show good fit between the Thurstonian model and the data, but do not confirm the RIASEC structure in the Basque population.     

On the importance of distinguishing between within- and between-subject effects in intransitive intertemporal choice

Most probabilistic paired comparison models treat inconsistent choices as caused by independent and random errors in the pairwise judgments. In this paper, we argue that this assumption is too restrictive for the analysis of paired comparison data obtained from multiple judges when transitivity violations are systematic. We present a new framework that contains the random error assumption as a special case but also allows for systematic changes in an option's utility assessments over the pairwise comparisons. Accounting for both between- and within-judge sources of variability, we demonstrate in an application on intertemporal choice that the proposed framework can capture systematic transitivity violations as well as individual taste differences.     

Paired comparison,triple comparison,and ranking experiments as generalized linear models,and their implementation on GLIM

A wide variety of paired comparison, triple comparison, and ranking experiments may be viewed as generalized linear models. These include paired comparison models based on both the Bradley-Terry and Thurstone-Mosteller approaches, as well as extensions of these models that allow for ties, order of presentation effects, and the presence of covariates. Moreover, the triple comparison model of Pendergrass and Bradley, as well as models for complete rankings of more than three items, can also be represented as generalized linear models. All such models can be easily fit by maximum likelihood, using the widely available GLIM computer package. Additionally, GLIM enables the computation of likelihood ratio statistics for testing many hypotheses of interest. Examples are presented that cover a variety of cases, along with their implementation on GLIM.     

Preference for tones as a function of frequency (hertz) and intensity (decibels)

An extension of the Wundt hypothesis concerning stimulus intensity and hedonic tone leads to the prediction that Ss prefer tones of intermediate frequency (hertz) and of intermediate intensity (decibels). In Experiment 1, tones varying from 60 to 5000 Hz were presented in a paired comparison procedure, and, as predicted, Ss′ preference was an inverted-U-shaped function of frequency, with the most preferred tones in the range of 400–750 Hz. In Experiment 2, tones varying in intensity from 40 to 90 dB were also presented in a paired comparison procedure, and again the predicted inverted-U-shaped preference function was found, with 50 dB as the preferred intensity. Related research and some unexpected findings are discussed.     

Rehearsal of associations stored in long-term memory

Memory & Cognition - A 2 by 2 by 2 design in Experiment I allowed comparison of rehearsers and controls assigned to one of four types of paired associate lists differing in imagery. After...     

The role of part—whole information in reasoning about relative size

Models of comparative judgment have assumed that relative magnitude is computed from knowledge about absolute magnitude rather than retrieved directly. In Experiment 1, participants verified the relative size of part-whole pairs (e.g., tree-leaf) and unrelated controls (e.g., tree-penny). The symbolic distance effect was much smaller for part-whole pairs than for unrelated controls. In two subsequent experiments, participants determined either which of two objects was closer in size to a third object or which of two pairs had a greater difference in the size of its constituents. In contrast to the paired comparison task in Experiment 1, judgments of part-whole items were more sensitive to the influence of symbolic distance than were unrelated controls. The fact that the part-whole relation attenuates the effects of symbolic distance in a paired comparison task but not in tasks that require an explicit comparison of size differences suggests that the part-whole relation provides a source of information about relative magnitude that does not depend on knowledge about absolute magnitude.     

Hormonal sensitivity of preterm versus full-term infants to the effects of maternal depression

Comparisons were made of differences in the hormonal sensitivity of preterm versus full-term infants to maternal depression, as reflected in children's cortisol levels. In Study 1 (N=25), a comparison was made between preterm versus healthy full-term children. In Study 2 (N=80), a comparison was made between preterm infants and full-term infants with mild or moderate medical problems. Preterm infants were found to be highly reactive to maternal depression (as measured by the Beck Depression Inventory). That is, they demonstrated higher cortisol levels when paired with depressed mothers and lower cortisol levels when paired with non-depressed mothers. No equivalent effects were found for children who were full-term, even when they had experienced other medical problems at birth. It was concluded that premature infants are exceptionally sensitive to the "emotional climate" in their home environment. As a result, they may manifest very different hormonal outcomes--with implications for their later development.     

Perceptual accentuation in minimal groups

Differences between paired paintings in a minimal group context were accentuated when assigned preferences served as the categorization basis. Failure to replicate resource allocation bias in control groups was attributed to the procedural emphasis on paintings, which may have precluded the use of the random categorization as a meaningful comparison dimension.     

A thurstonian pairwise choice model with univariate and multivariate spline transformations

A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An EM algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. The authors are indebted to Ulf Böckenholt and Yoshio Takane for useful comments on an earlier draft of this paper.     

A Robust Bayesian Approach for Structural Equation Models with Missing Data

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear structural equation model with fixed covariates, robust Bayesian methods are developed for estimation and model comparison. Results from simulation studies are reported to reveal the characteristics of estimation. The methods are illustrated by using a real data set obtained from diabetes patients.     

Key pecking in pigeons produced by pairing keylight with inaccessible grain

In Experiment I, keylight was paired with inaccessible grain delivery (under two conditions of keylight intensity) to determine if autoshaping would occur in the absence of primary reinforcement. In Experiment II, the procedure was repeated with accessible grain, for comparison. In Experiment III, the procedures were repeated with explicitly unpaired presentations of keylight and either inaccessible or accessible grain. The results indicated that key pecking occurred as quickly in the presence of keylight pairings with inaccessible grain as with accessible grain, though (except for one bird) key pecking was not maintained with inaccessible grain. Furthermore, compared to the dim keylight, the bright keylight greatly suppressed key pecking when paired with inaccessible grain, and reduced the rate of key pecking when paired with accessible grain. Little key pecking occurred in groups exposed to explicitly unpaired presentations of keylight (whether bright or dim) and grain (whether accessible or inaccessible). When the birds in Experiment III were retested with explicitly paired presentations of keylight and grain, little key pecking was observed, suggesting suppressive effects of prior explicitly unpaired presentations. It is suggested that the effects of key-brightness manipulation were produced by the association of grain with cues other than the response key, or by distraction produced by partial illumination of the grain hopper.