Stability analysis in K‐means clustering

This paper develops a new procedure, called stability analysis, for K‐means clustering. Instead of ignoring local optima and only considering the best solution found, this procedure takes advantage of additional information from a K‐means cluster analysis. The information from the locally optimal solutions is collected in an object by object co‐occurrence matrix. The co‐occurrence matrix is clustered and subsequently reordered by a steepest ascent quadratic assignment procedure to aid visual interpretation of the multidimensional cluster structure. Subsequently, measures are developed to determine the overall structure of a data set, the number of clusters and the multidimensional relationships between the clusters.     

Model selection for minimum‐diameter partitioning

The minimum‐diameter partitioning problem (MDPP) seeks to produce compact clusters, as measured by an overall goodness‐of‐fit measure known as the partition diameter, which represents the maximum dissimilarity between any two objects placed in the same cluster. Complete‐linkage hierarchical clustering is perhaps the best‐known heuristic method for the MDPP and has an extensive history of applications in psychological research. Unfortunately, this method has several inherent shortcomings that impede the model selection process, such as: (1) sensitivity to the input order of the objects, (2) failure to obtain a globally optimal minimum‐diameter partition when cutting the tree at K clusters, and (3) the propensity for a large number of alternative minimum‐diameter partitions for a given K. We propose that each of these problems can be addressed by applying an algorithm that finds all of the minimum‐diameter partitions for different values of K. Model selection is then facilitated by considering, for each value of K, the reduction in the partition diameter, the number of alternative optima, and the partition agreement among the alternative optima. Using five examples from the empirical literature, we show the practical value of the proposed process for facilitating model selection for the MDPP.     

Improved Fisher z estimators for univariate random‐effects meta‐analysis of correlations

Several authors have studied or used the following estimation strategy for meta‐analysing correlations: obtain a point estimate or confidence interval for the mean Fisher z correlation, and transform this estimate to the Pearson r metric. Using the relationship between Fisher z and Pearson r random variables, I demonstrate the potential discrepancy induced by directly z‐to‐r transforming a mean correlation parameter. Point and interval estimators based on an alternative integral z‐to‐r transformation are proposed. Analytic expressions for the expectation and variance of certain meta‐analytic point estimators are also provided, as are selected moments of correlation parameters; numerical examples are included. In an application of these analytic results, the proposed point estimator outperformed its usual direct z‐to‐r counterpart and compared favourably with an estimator based on Pearson r correlations. Practical implications, extensions of the proposed estimators, and uses for the analytic results are discussed.     

Gaussian model‐based partitioning using iterated local search

The emergence of Gaussian model‐based partitioning as a viable alternative to K‐means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model‐based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple‐restart (multistart) approach commonly used for K‐means partitioning less effective as a heuristic solution strategy. As an alternative, we propose an approach based on iterated local search (ILS), which has proved effective in previous combinatorial data analysis contexts. We compared multistart, ILS and hybrid multistart–ILS procedures for minimizing a very general model‐based criterion that assumes no restrictions on cluster size or within‐group covariance structure. This comparison, which used 23 data sets from the classification literature, revealed that the ILS and hybrid heuristics generally provided better criterion function values than the multistart approach when all three methods were constrained to the same 10‐min time limit. In many instances, these differences in criterion function values reflected profound differences in the partitions obtained.     

Constrained k‐means on cluster proportion and distances among clusters for longitudinal data analysis

Clustering individuals by measures of similarity or dissimilarity at trajectories of changes in longitudinal data enables determination of typical patterns of development and growth. The present research proposes a new constrained k‐means method with lower bound constraints on cluster proportions and distances among clusters at focused variables and time points to fulfill various needs in clustering longitudinal data. The method assumes a large number of clusters at the onset and iteratively deletes and combines clusters according to these constraints. An additional property of the proposed constrained k‐means includes direct estimation of the unknown number of clusters. Simulation results clearly show the usefulness of the method for extracting clusters in plausible, real‐life analysis including non‐normality within clusters, and the proposed algorithm works well and convergence of the estimates is satisfactory. An actual example using Japanese longitudinal data regarding sleep habits and mental health is presented to verify the utility of the proposed constrained k‐means.     

De‐Centering and Re‐Centering: Rethinking Concepts and Methods in the Sociological Study of Religion

Four conceptual and methodological edges or areas of study are outlined. They are located near what have been the boundaries between the sociology of religion and other subfields, where we believe a potential exists to encourage a wide range of scholars to revisit some central concepts. Paying attention to these edges—as a means to de‐center to re‐center our debates in new ways—not only broadens and deepens our knowledge of the “religious,” it encourages us to reexamine long‐standing conceptual tools, unquestioned assumptions, and accepted methods in the sociology of religion. We illustrate these edges through a review of recent literature and examples drawn from our current empirical projects.     

Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r, to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation (K), our formulation of risk allows us to construct games that vary in risk (as indexed by r) while controlling for cooperativeness (as indexed by K). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.     

Standing in the gap: ref lections on translating the Jung‐Neumann correspondence

This paper considers the experience of translating the correspondence between C.G. Jung and Erich Neumann as part of the Philemon series. The translator explores the similarities between analytical work and the task of translation by means of the concepts of the dialectical third and the interactional field. The history and politics of the translation of analytic writing and their consequences for the lingua franca of analysis are discussed. Key themes within the correspondence are outlined, including Jung and Neumann's pre‐war exploration of Judaism and the unconscious, the post‐war difficulties around the publication of Neumann's Depth Psychology and a New Ethic set against the early years of the C.G. Jung Institute in Zurich, and the development of the correspondents’ relationship over time.     

Influence of Self‐Affirmation on Responses to Gain‐ Versus Loss‐Framed Antismoking Messages

Self‐affirmation has been shown to reduce biased processing of threatening health messages. In this study, the impact of self‐affirmation on college smokers' reactions to gain‐ versus loss‐framed antismoking public service announcements (PSAs) was examined. A consistent pattern of interaction was observed wherein self‐affirmation produced more favorable responses to loss‐framed PSAs and more unfavorable responses to gain‐framed PSAs. Self‐affirmation also reduced smoking intention in the loss frame condition and increased antismoking self‐efficacy across framing conditions. These findings are discussed in light of previous research linking self‐affirmation to increased message scrutiny.     

Getting going and letting go: Religiosity fosters opportunity‐congruent coping with work‐related uncertainties

This study investigated how religiosity relates to goal engagement (i.e., investing time and effort; overcoming obstacles) and goal disengagement (i.e., protecting self‐esteem and motivational resources against failure experiences; distancing from unattainable goals) in coping with perceived work‐related uncertainties (e.g., growing risk of job loss) that arise from current social change. We hypothesised that religiosity not only expands individuals' capacities for both engagement and disengagement but also fosters an opportunity‐congruent pattern of engagement and disengagement, promoting engagement especially under favourable opportunities for goal‐striving in the social ecology and facilitating disengagement especially under unfavourable opportunities. Multilevel analyses in a sample of N = 2089 Polish adults aged 20–46 years partly supported these predictions. Religiosity was associated with higher goal engagement, especially under favourable economic opportunities for goal‐striving in the social ecology (as measured by the regional net migration rate). For disengagement, the results were more mixed; religiosity was related to higher self‐protection independently of the economic opportunity structure and predicted higher goal‐distancing only under the most unfavourable opportunities. These results suggest that religiosity can promote different coping strategies under different conditions, fostering a pattern of opportunity‐congruent engagement and, to some extent, disengagement that is likely to be adaptive.     

Psychological effects of (non)employment: A cross‐national comparison of the United States and Japan

The involuntary loss of employment has been shown to deteriorate subjective well‐being. Adopting a cross‐cultural perspective on Jahoda's ( 1982 ) deprivation model this study examines several latent and manifest benefits of work that were expected to mediate the effects of employment status on well‐being. It was hypothesized that in more collectivistic societies the decline in subjective well‐being would be a consequence of a diminished sense of collective purpose for the non‐employed, whereas in individualistic societies the crucial factors would be a loss of social status and financial benefits. The findings from two representative national surveys conducted in the United States (N = 1,093) and Japan (N = 647) provided partial support for these hypotheses. Cultural differences moderated the effects of employment status on the benefits of work. As a consequence, different processes mediated the decline in well‐being for the non‐employed in the two countries. These results are embedded within the wider discourse on culture and its effect on unemployment.     

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely‐held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single‐premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker‐than‐classical K₃ logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to—whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non‐classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.     

Relative Persuasiveness of Gain‐ Versus Loss‐Framed Human Papillomavirus Vaccination Messages for the Present‐ and Future‐Minded

This research examines how young adults' attitudes toward human papillomavirus (HPV) vaccination and their intentions to get the vaccine are influenced by the framing of health messages (gain vs. loss) and time orientation (i.e., the extent to which people value immediate vs. distant consequences of their decisions). Results of an experiment showed an overall persuasive advantage for loss‐framed messages. Attitudes and behavioral intentions toward HPV vaccination were found to be more favorable among future‐minded individuals. Moreover, an interaction between framing and time orientation was found to predict persuasive outcomes. Present‐minded participants responded more favorably to the loss‐framed message, whereas future‐minded participants were equally persuaded by both frames. Implications of the findings for vaccine risk communication are discussed.     

a‐Stratified CAT design with content blocking

Content balancing is often required in the development and implementation of computerized adaptive tests (CATs). In the current study, we propose a modified a‐stratified method, the a‐stratified method with content blocking. As a further refinement of a‐stratified CAT designs, the new method incorporates content specifications into item pool stratification. Simulation studies were conducted to compare the new method with three previous item selection methods: the a‐stratified method; the a‐stratified with b‐blocking method; and the maximum Fisher information method with Sympson‐Hetter exposure control. The results indicated that the refined a‐stratified design performed well in reducing item overexposure rates, balancing item usage within the pool, and maintaining measurement precision, in a situation where all four procedures were forced to balance content.     

Speech‐perception‐in‐noise deficits in dyslexia

Speech perception deficits in developmental dyslexia were investigated in quiet and various noise conditions. Dyslexics exhibited clear speech perception deficits in noise but not in silence. Place‐of‐articulation was more affected than voicing or manner‐of‐articulation. Speech‐perception‐in‐noise deficits persisted when performance of dyslexics was compared to that of much younger children matched on reading age, underscoring the fundamental nature of speech‐perception‐in‐noise deficits. The deficits were not due to poor spectral or temporal resolution because dyslexics exhibited normal ‘masking release’ effects (i.e. better performance in fluctuating than in stationary noise). Moreover, speech‐perception‐in‐noise predicted significant unique variance in reading even after controlling for low‐level auditory, attentional, speech output, short‐term memory and phonological awareness processes. Finally, the presence of external noise did not seem to be a necessary condition for speech perception deficits to occur because similar deficits were obtained when speech was degraded by eliminating temporal fine‐structure cues without using external noise. In conclusion, the core deficit of dyslexics seems to be a lack of speech robustness in the presence of external or internal noise.     

Distinct pathways to persuasion: The role of affect in message‐framing effects

Health‐promoting messages can be framed in terms of the gains that are associated with healthy behaviour (gain frame) or the losses that are associated with unhealthy behaviour (loss frame). In the present research, we examined the role of positive and negative affect in the persuasive effects of gain‐ and loss‐framed health‐promoting information. Experiment 1 (N = 98) showed that gain‐framed information resulted in higher levels of information acceptance than loss‐framed information and that this effect was mediated by positive affect. The results of Experiment 2 (N = 129) showed that gain‐framed information resulted in higher levels of information acceptance and attitude, an effect that was again mediated by positive affect. In addition, loss‐framed information resulted in more negative affect than gain‐framed information and negative affect increased participants' intention to engage in the healthy behaviour. These results suggest that affect may be of great importance in the persuasion process and may be particularly helpful to explain the underlying mechanisms of message framing effects. The findings also suggest that gain‐ and loss‐framed messages offer distinct pathways to persuasion. Copyright © 2009 John Wiley & Sons, Ltd.     

Connection‐based and object‐based grouping in multiple‐object tracking: A developmental study

Developmental research on Gestalt laws has previously revealed that, even as young as infancy, we are bound to group visual elements into unitary structures in accordance with a variety of organizational principles. Here, we focus on the developmental trajectory of both connection‐based and object‐based grouping, and investigate their impact on object formation in participants, aged 9–21 years old (N = 113), using a multiple‐object tracking paradigm. Results reveal a main effect of both age and grouping type, indicating that 9‐ to 21‐year‐olds are sensitive to both connection‐based and object‐based grouping interference, and tracking ability increases with age. In addition to its importance for typical development, these results provide an informative baseline to understand clinical aberrations in this regard.

Statement of contribution

What is already known on this subject?

• The origin of the Gestalt principles is still an ongoing debate: Are they innate, learned over time, or both?
• Developmental research has revealed how each Gestalt principle has its own trajectory and unique relationship to visual experience.
• Both connectedness and object‐based grouping play an important role in object formation during childhood.

What does this study add?

• The study identifies how sensitivity to connectedness and object‐based grouping evolves in individuals, aged 9–21 years old.
• Using multiple‐object tracking, results reveal that the ability to track multiple objects increases with age.
• These results provide an informative baseline to understand clinical aberrations in different types of grouping.

     

Reactions to social and non‐social novelties in 2‐year‐olds

The purpose of this study is to investigate the internal structure of behavioural inhibition [cf. Goldsmith, H.H. and Campos, J.J. (1990). Child Development, 61 , 1944–1964]. Observations of 45 2‐year‐olds’ approaching/positive reactions, inhibited/negative reactions, and latencies, when encountering strangers as well as unfamiliar objects, are made in a laboratory setting. The intercorrelations between the six different measures, obtained from the observations, are analysed by means of a multitrait–multimethod matrix. It is concluded, from inspection of the matrix, that aggregations of data into indexes covering different reactions (approaching/positive reactions, inhibited/negative reactions, and latency) and settings (stranger and objects), respectively, are appropriate. To further validate the different indexes, assessments of concurrent variables (separation reactions, reactions to physical intrusion, reactions in a new setting, and maternal ratings of reactions to strangers) are used. The results indicate that all reactions to both social and non‐social novelties can be assigned to one construct, which is in line with the assumption made by Kagan and his co‐workers about behavioural inhibition. Copyright © 1999 John Wiley & Sons, Ltd.     

Extending SME to Handle Large‐Scale Cognitive Modeling

Analogy and similarity are central phenomena in human cognition, involved in processes ranging from visual perception to conceptual change. To capture this centrality requires that a model of comparison must be able to integrate with other processes and handle the size and complexity of the representations required by the tasks being modeled. This paper describes extensions to Structure‐Mapping Engine (SME) since its inception in 1986 that have increased its scope of operation. We first review the basic SME algorithm, describe psychological evidence for SME as a process model, and summarize its role in simulating similarity‐based retrieval and generalization. Then we describe five techniques now incorporated into the SME that have enabled it to tackle large‐scale modeling tasks: (a) Greedy merging rapidly constructs one or more best interpretations of a match in polynomial time: O(n²log(n)); (b) Incremental operation enables mappings to be extended as new information is retrieved or derived about the base or target, to model situations where information in a task is updated over time; (c) Ubiquitous predicates model the varying degrees to which items may suggest alignment; (d) Structural evaluation of analogical inferences models aspects of plausibility judgments; (e) Match filters enable large‐scale task models to communicate constraints to SME to influence the mapping process. We illustrate via examples from published studies how these enable it to capture a broader range of psychological phenomena than before.     

K ⊈ E

In a series of very influential works, Tim Williamson has advanced and defended a much discussed theory of evidence containing, among other claims, the thesis that, if one knows P, P is part of one's evidence (K ? E). I argue that K ? E is false, and indeed that it is so for a reason that Williamson himself essentially provides in arguing against the thesis that, if one has a justified true belief in P, P is part of one's evidence: together with a very plausible principle governing the acquisition of knowledge by non‐deductive inference based on evidence, K ? E leads, in a sorites‐like fashion, to what would seem a series of unacceptably bootstrapping expansions of one's evidence. I then develop some considerations about the functions of and conditions for evidence which are suggested by the argument against K ? E. I close by discussing the relationship of the argument with anti‐closure arguments of the style exemplified by the preface paradox: I contend that, if closure is assumed, it is extremely plausible to expect that the diagnosis of what goes wrong in the preface‐paradox‐style argument cannot be used to block my own argument.