Structural equation modeling of paired-comparison and ranking data

L. L. Thurstone's (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone's model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently.     

A Matlab function to estimate choice model parameters from paired-comparison data

Tversky (1972) has proposed a family of models for paired-comparison data that generalize the Bradley—Terry—Luce (BTL) model and can, therefore, apply to a diversity of situations in which the BTL model is doomed to fail. In this article, we present a Matlab function that makes it easy to specify any of these general models (EBA, Pretree, or BTL) and to estimate their parameters. The program eliminates the time-consuming task of constructing the likelihood function by hand for every single model. The usage of the program is illustratedby several examples. Features of the algorithm are outlined. The purpose of this article is to facilitate the use of probabilistic choice models in the analysis of data resulting from paired comparisons.     

A Matlab function to estimate choice model parameters from paired-comparison data.

Tversky (1972) has proposed a family of models for paired-comparison data that generalize the Bradley-Terry-Luce (BTL) model and can, therefore, apply to a diversity of situations in which the BTL model is doomed to fail. In this article, we present a Matlab function that makes it easy to specify any of these general models (EBA, Pretree, or BTL) and to estimate their parameters. The program eliminates the time-consuming task of constructing the likelihood function by hand for every single model. The usage of the program is illustrated by several examples. Features of the algorithm are outlined. The purpose of this article is to facilitate the use of probabilistic choice models in the analysis of data resulting from paired comparisons.     

Evaluation of unconstrained sorting data

Two statistics are offered for evaluating unconstrained sorting performance in a specific task when categories are E-defined. One statistic is based upon empirically estimated sampling distributions and can be used for determining sorting performance significantly deviant from chance for any number of S-defined categories; the second statistic can be used to evaluate consistencies between S- and E-defined categories, regardless of the number of categories used by S. The present procedure provides a statistical basis for evaluation of performance where no adequate evaluation procedures are now available.     

Multidimensional scaling of hierarchical sorting data applied to facial expressions

A new algorithm for multidimensional scaling analysis of sorting data and hierarchical-sorting data is tested by applying it to facial expressions of emotion. We construct maps in “facial expression space” for two sets of still photographs: the I-FEEL series (expressions displayed spontaneously by infants and young children), and a subset of the Lightfoot series (posed expressions, all from one actress). The analysis avoids potential artefacts by fitting a map directly to the subject's judgments, rather than transforming the data into a matrix of estimated dissimilarities as an intermediate step. The results for both stimulus sets display an improvement in the extent to which they agree with existing maps. Some points emerge about the limitations of sorting data and the need for caution when interpreting MDS configurations derived from them.     

Using HyperCard and Apple events in a network environment: Collecting data from simultaneous experimental sessions

HyperCard is a useful tool available to teachers and researchers who have access to Macintosh computers. Version 2.1 of HyperCard, in conjunction with the Macintosh Operating System 7, includes some significant new capabilities for users with multiple computers in a network, as is common in many teaching laboratories. This paper describes a HyperCard stack that allows users who wish to run HyperCard-based experiments on several computers simultaneously to conveniently retrieve experimental data from those remote computers onto one program, and to perform several other useful tasks in a computer network.     

Free sorting with stimuli clustered in a multidlmensional attribute space

An experiment was conducted to determine whether Ss leam, without knowledge of results or prior familiarization with the prototypes, to sort histoform stimuli generated by three probablistic rules into categories consistent with these mies. Seven Ss were asked to sort 30 stimuli (10 from each schema population) on each trial. No constraints were placed on the number of categories to be used. A statistic was developed to measure consistency between schema-defined categories and subjeet-defined categories. Four of the seven Ss met the leaming criterion, and demonstrated increasing consistency with the schema-defined categories across trials. In general, more categories than necessary were used to classify the stimuli correctly. The results raise several questions about classification strategies used by Ss in perceptual learning tasks with stimuli generated by probabilistic rules, and indicate the need for further research conceming the variables that influence perceptual category formation.     

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.     

Bio-inspired task-rule retrieval model with auditory sorting test

Cognitive architectures (CAs) are currently used to bring the behavior of computer systems closer to human behavior. One of the main capacities of humans is the ability to plan and make decisions. Thus, part of the human behavior is based on rules associated with the relevant environmental stimuli. Rule management can be divided into six needed processes: rule learning, rule retrieving, rule coding, rule updating, rule reinforcement, and rule changing. A key aspect of rule processing is retrieval, which involves the use of information extracted from memory. This work deals with how rules are stored in coded form in the brain, retrieved and used as the need arises. The proposed model takes inspiration mainly from the processes in the VLPFC and MTL brain areas to extract rules from memory and create a rule-set that is sent to the DLPFC. The DLPFC and VLPFC prefrontal area operations are also described, and a process is proposed to select the appropriate rule and give a response. The experimentation of the implementation of our proposal with different configuration parameters gives rise to different approaches to human behavior in rule retrieval. Our conclusion is that after a virtual entity is endowed with this proposal, it computes in a way similar to human behavior.     

Bubble sorting in a foam under forced drainage

A highly polydisperse foam is subjected to a constant liquid flow from above. For sufficiently high flow rates, large-scale bubble motion is observed, in the course of which large bubbles rise to the top of the foam until a steady state is reached at which the average bubble size increases smoothly with height.     

An efficient algorithm for TUCKALS3 on data with large numbers of observation units

A modification of the TUCKALS3 algorithm is proposed that handles three-way arrays of order I × J × K for any I. When I is much larger than JK, the modified algorithm needs less work space to store the data during the iterative part of the algorithm than does the original algorithm. Because of this and the additional feature that execution speed is higher, the modified algorithm is highly suitable for use on personal computers. This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author.