Eye-movement data: Cumulative fixation time and cluster analysis

This paper describes procedures for the visual presentation and cluster analysis of eye-movement data. Methods for two- and three-dimensional representation of cumulative fixation time (CFT) and ways of enhancing the peaks in CFT distributions are outlined and illustrated by reference to examples from eye-movement studies of cognitive processes. CFT distributions may also be partitioned using thek means clustering technique (MacQueen, 1967), and applications of variants of this technique to eye-movement data are discussed. Cluster analyses such ask means require the user to make initial estimates of the number and value of the means. One classification procedure (Wallace & Boulton, 1968a, 1968b), based on information theory, avoids these initial assumptions. This procedure is applied to a CFT distribution and has its solution compared with that ofk means for the same distribution. Finally, programs that implement these procedures on Macintosh computers are listed and offered on floppy disk.     

Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

The equivalence of three statistical packages for performing hierarchical cluster analysis

Three different software programs which contain hierarchical agglomerative cluster analysis procedures were shown to generate different solutions on the same data set using apparently the same options. The basis for the differences in the solutions was the formulae used to calculate Euclidean distance. Users of statistical software were warned of terminological confusion concerning cluster analysis.This research was supported by a National Science Foundation grant (DCR#74-20007) entitled A Consumer Report on Cluster Analysis Software. I wish to thank the authors of the three programs for their helpful comments on the paper.     

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.     

On the importance of avoiding shortcuts in applying cognitive models to hierarchical data

Psychological experiments often yield data that are hierarchically structured. A number of popular shortcut strategies in cognitive modeling do not properly accommodate this structure and can result in biased conclusions. To gauge the severity of these biases, we conducted a simulation study for a two-group experiment. We first considered a modeling strategy that ignores the hierarchical data structure. In line with theoretical results, our simulations showed that Bayesian and frequentist methods that rely on this strategy are biased towards the null hypothesis. Secondly, we considered a modeling strategy that takes a two-step approach by first obtaining participant-level estimates from a hierarchical cognitive model and subsequently using these estimates in a follow-up statistical test. Methods that rely on this strategy are biased towards the alternative hypothesis. Only hierarchical models of the multilevel data lead to correct conclusions. Our results are particularly relevant for the use of hierarchical Bayesian parameter estimates in cognitive modeling.     

The hierarchical order of processes underlying the direction illusion and the direction aftereffect

Motion perception involves the processing of velocity signals through several hierarchical stages of the visual cortex. To better understand this process, a number of studies have sought to localise the neural substrates of two misperceptions of motion direction, the direction illusion (DI) and the direction aftereffect (DAE). These studies have produced contradictory evidence as to the hierarchical order of the processing stages from which the respective phenomena arise. We have used a simple stimulus configuration to further investigate the sequential order of processes giving rise to the DI and DAE. To this end, we measured the two phenomena invoked in combination, and also manually parsed this combined effect into its two constituents by measuring the two phenomena individually in both possible sequential orders. Comparing the predictions made from each order to the outcome from the combined effect allowed us to test the tenability of two models: the DAE-first model and the DI-first model. Our results indicate that DAE-invoking activity does not occur earlier in the motion processing hierarchy than DI-invoking activity. Although the DI-first model is not inconsistent with our data, the possible involvement of non-sequential processing may be better able to reconcile these results with those of previous studies.     

Problematic effects of aggregation in z ROC analysis and a hierarchical modeling solution

The confidence-rating recognition memory paradigm has been used extensively for testing theories of memory. Current methods for analyzing confidence-rating data require that data be aggregated over participants, items, or both. We show that this aggregation threatens claims of curvature in zROCs and distorts estimates of signal-distribution variance—the very findings that are used to make fine-grained distinctions between competing models. We develop a hierarchical signal detection model that accounts for variability from the sampling of participants and items in addition to variability from the underlying psychological processes. The model provides for accurate signal detection parameter estimates. With accurate estimates, the validity of benchmark findings in recognition memory may be assessed.     

Predicting the decision to pursue mediation in civil disputes: a hierarchical classes analysis

Clients (N = 185) involved in civil court cases completed the CPR Institute's Mediation Screen, which is designed to assist in making a decision about pursuing mediation. The authors modeled data using hierarchical classes analysis (HICLAS), a clustering algorithm that places clients into 1 set of classes and CPRMS items into another set of classes. HICLAS then links the sets of classes so that any class of clients can be identified in terms of the classes of items they endorsed. HICLAS-derived item classes reflected 2 underlying themes: (a) suitability of the dispute for a problem-solving process and (b) potential benefits of mediation. All clients who perceived that mediation would be beneficial also believed that the context of their conflict was favorable to mediation; however, not all clients who saw a favorable context believed they would benefit from mediation. The majority of clients who agreed to pursue mediation endorsed items reflecting both contextual suitability and perceived benefits of mediation.     

Relativism due to underdetermination of theory by data

Three different versions of the underdetermination thesis are identified in the later writings of the Edinburgh School by which its relativism is maintained. These I call the Stratagems UT, the Floating‐feather UT, and the Oxygen UT. It is argued the marshalling of historiographical evidence to support the Floating‐feather UT involves a version of the Liar's paradox; that a variant of the Stratagems UT with the evidence provided by the Edinburgh School is internally inconsistent; that the Edinburgh School has failed to show the adequacy and the conformity of the historical evidence offered to support the Oxygen UT; that the Oxygen UT thoroughly neutralizes empirical evidence of any efficacy, and, thus, of any role, first, in the truth/falsity evaluation of the theory at the physical level, and second, in the explanation of theory‐evaluation at the explanatory metaphysical or socio‐historical level. I also show that Larry Laudan is quite mistaken in concurring with the Edinburgh School's thesis of symmetrical explanation of theories insofar as their epistemic status is concerned.     

Contributions of automatic and controlled processes to the analysis of hierarchical structure

Three experiments provide evidence that 2 mechanisms, 1 automatic and 1 controlled, produce variations in the efficiency with which local and global forms are processed. Targets are identified faster if they appear at the same level (global or local) as the target on the previous trial. M. R. Lamb, B. London, H. M. Pond, and K. A. Whitt (1998) provided evidence that the beneficial effect of level repetition is due to an automatic process that is outside voluntary control. In the present experiments, pretrial cues informed participants as to the level of the upcoming target. Valid cues benefited performance, whereas invalid cues harmed performance relative to noninformative neutral cues. This was so even when the relation between the cue and the level it signaled was arbitrary, indicating that the cues initiated voluntary shifts of attention. The benefit associated with level repetition, however, was unaffected by the cues. These data suggest that the benefit of level repetition results from a process that is not subject to voluntary control.     

A comparison of the classification capabilities of the 1-dimensional kohonen neural network with two pratitioning and three hierarchical cluster analysis algorithms

Neural Network models are commonly used for cluster analysis in engineering, computational neuroscience, and the biological sciences, although they are rarely used in the social sciences. In this study we compare the classification capabilities of the 1-dimensional Kohonen neural network with two partitioning (Hartigan and Späthk-means) and three hierarchical (Ward's, complete linkage, and average linkage) cluster methods in 2,580 data sets with known cluster structure. Overall, the performance of the Kohonen networks was similar to, or better than, the performance of the other methods.     

Myopic perception of having a deadline in negotiations: An anchoring effect due to question order

In negotiations, people tend to perceive a deadline as more detrimental to themselves than to their opponents. This phenomenon is termed myopic perception. The present research proposes that myopic perception can be understood as a result of an anchoring effect due to the question order used in probing the perception of a deadline. When people estimate deal prices before rating the influence of a deadline, their judgements are anchored on their negotiation outcomes, making their perception egocentric, which leads to myopic perception. As a result, myopic perception was hypothesized to be reduced by reversing the above question order to change the respondents' judgement anchor from negotiation outcomes to negotiation procedures. In Study 1, myopic perception disappeared when participants rated the general influence of a deadline before estimating deal price in a negotiation scenario. In Study 2, pairs of participants negotiated under a tight deadline. Myopic perception of a deadline was manipulated before the negotiation. Dyads without myopic perception had a smaller discrepancy in reservation price. However, myopic perception had no effect on impasse rates or final deal prices. The results are discussed with respect to behavioural forecasting and practical implications of myopic perception.