Nonlinear principal components analysis: introduction and application

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.     

First impressions: gait cues drive reliable trait judgements

Personality trait attribution can underpin important social decisions and yet requires little effort; even a brief exposure to a photograph can generate lasting impressions. Body movement is a channel readily available to observers and allows judgements to be made when facial and body appearances are less visible; e.g., from great distances. Across three studies, we assessed the reliability of trait judgements of point-light walkers and identified motion-related visual cues driving observers' judgements. The findings confirm that observers make reliable, albeit inaccurate, trait judgements, and these were linked to a small number of motion components derived from a Principal Component Analysis of the motion data. Parametric manipulation of the motion components linearly affected trait ratings, providing strong evidence that the visual cues captured by these components drive observers' trait judgements. Subsequent analyses suggest that reliability of trait ratings was driven by impressions of emotion, attractiveness and masculinity.     

STATISTICAL AND PSYCHOMETRIC INFERENCE IN PRINCIPAL COMPONENTS ANALYSIS

Statistical inference applied to principal components analysis deals with estimating the parameters of the correlation matrix, R, found in the population, from the characteristics of the sample matrix, R*. On the other hand, psychometric inference refers to estimating the internal consistency of the components themselves, so that the decisions about retaining a component for further analysis can be based upon psychometric criteria. A slightly modified approach to statistical inference, which focuses upon the variance of the Components in the population, has been suggested. This viewpoint can be extended to estimating the true score variance and the reliabilities of the components in the population of subjects. Psychometric tests of significance can then be made statistical in nature.     

Competition among auditory streaming,dichotic fusion,and diotic fusion

When a component of a complex tone is captured into a stream by other events that precede and follow it, it does not fuse with the other components of the complex tone but tends to to be heard as a separate event. The current study examined the ability of elements of a stream to resist becoming fused with other synchronous events, heard either in the same ear or at the opposite ear. The general finding was that events in one ear fuse strongly with elements of an auditory stream in the other ear only when they are spectrally very similar. In this case, the fusion of simultaneous components at opposite ears is stronger than of simultaneous components heard in the same ear. However, when the spectra of the synchronous events are mismatched even slightly, components in the same ear fuse more strongly than components at opposite ears. These results are accounted for by a theory that assumes that decisions that perceptually integrate sequential events, synchronous events, and events at opposite ears are interdependent.     

Statistical analyses of the resilience function

The extent to which distracting information influences decisions can be informative about the nature of the underlying cognitive and perceptual processes. In a recent paper, a response time-based measure for quantifying the degree of interference (or facilitation) from distracting information termed resilience was introduced. Despite using a statistical measure, the analysis was limited to qualitative comparisons between different model predictions. In this paper, we demonstrate how statistical procedures from workload capacity analysis can be applied to the new resilience functions. In particular, we present an approach to null-hypothesis testing of resilience functions and a method based on functional principal components analysis for analyzing differences in the functional form of the resilience functions across participants and conditions.     

TOWARDS AN UNDERSTANDING OF INTEGRITY TEST SIMILARITIES AND DIFFERENCES: AN ITEM-LEVEL ANALYSIS OF SEVEN TESTS

A judgmental sort of 798 items from 7 paper-and-pencil integrity tests produced 23 thematic composites. Patterns of correlations between these composites and the 7 integrity measures and 2 Big Five measures shed light on similarities and differences between different integrity tests. Principal components analysis of 23 composites indicated 4 principal components that further illuminate the content domain of integrity tests. The relationships between 4 integrity principal components and integrity test scores as well as measures of the Big Five dimensions of personality are reported. The findings suggest that integrity tests can differ in their emphasis on various thematic composites, and, yet, be very similar in terms of their standing on the 4 integrity principal components. Different integrity tests can be quite different in terms of surface content, and, yet, assess the same underlying constructs.     

Decision making, risk taking and psychological time: Review of empirical findings and psychological theory

Three domains of research (1) involvement in past and future events, (2) knowledge of the past and the future, and (3) value as a function of time (discounting) were used to elucidate man's limitations when he makes decisions based on earlier experience with consequences in the close and distant future. Evidence from all three areas illustrate that man is captured in a narrow time-space sphere around "here and now".—One consequence of this limitation is that risk-willingness increases the longer ahead the outcome of a decision is likely to occur. To specify, the less we are involved in, the less we know of and the less the consequences are evaluated the larger is our willingness to make decisions with future risks. Learning from experience seems to play a minor role in improving decision making. Ill-defined problems and non-distinct outcomes make "economic man" fairly useless as a norm for decision making in decisions with longranging effects and of a non-repititive character.—The paper ends with a discussion of strategies that can compensate for the limitations of distal cognition.     

Psychometric properties of the Trauma Stages of Recovery

Of the trauma theories available, Herman's has captured the essential features common to most traumatic etiologies. Continued development of this theory has included dimensions within stages of recovery. The Trauma States of Recovery is presented here as a way of assessing stages of recovery and inherent components. Three samples of about 500 college students each and a clinical sample (n=34) were recruited. Independent principal components analyses, employing a scree plot, gave a five-component solution accounting for 40.2% of the total variance. The component solution employed Promax rotation for the correlated components. The five components were named Emotional Awareness and Control, Symptom Mastery, Coping, Memory, and Relationships. Internal consistencies, test-retest reliability, and split-half reliability were acceptable. Response bias was low. Convergent validity (with various subscales from the Beck Depression Inventory, the Self-esteem Scale, the Spielberger Anger-Expression Scale, and the Dissociative Experiences Scale) and discriminant validity (with various subscales of the AIDS Knowledge and Attitudes Survey and Jackson's Personality Research Form Dominance Scale) were promising. The Trauma Stages of Recovery also significantly discriminated between clinical and nonclinical samples on three of the five components, Symptom Mastery, Coping, and Memory.     

Common functional principal components analysis: a new approach to analyzing human movement data

In many human movement studies angle-time series data on several groups of individuals are measured. Current methods to compare groups include comparisons of the mean value in each group or use multivariate techniques such as principal components analysis and perform tests on the principal component scores. Such methods have been useful, though discard a large amount of information. Functional data analysis (FDA) is an emerging statistical analysis technique in human movement research which treats the angle-time series data as a function rather than a series of discrete measurements. This approach retains all of the information in the data. Functional principal components analysis (FPCA) is an extension of multivariate principal components analysis which examines the variability of a sample of curves and has been used to examine differences in movement patterns of several groups of individuals. Currently the functional principal components (FPCs) for each group are either determined separately (yielding components that are group-specific), or by combining the data for all groups and determining the FPCs of the combined data (yielding components that summarize the entire data set). The group-specific FPCs contain both within and between group variation and issues arise when comparing FPCs across groups when the order of the FPCs alter in each group. The FPCs of the combined data may not adequately describe all groups of individuals and comparisons between groups typically use t-tests of the mean FPC scores in each group. When these differences are statistically non-significant it can be difficult to determine how a particular intervention is affecting movement patterns or how injured subjects differ from controls. In this paper we aim to perform FPCA in a manner allowing sensible comparisons between groups of curves. A statistical technique called common functional principal components analysis (CFPCA) is implemented. CFPCA identifies the common sources of variation evident across groups but allows the order of each component to change for a particular group. This allows for the direct comparison of components across groups. We use our method to analyze a biomechanical data set examining the mechanisms of chronic Achilles tendon injury and the functional effects of orthoses.     

Loss aversion,diminishing sensitivity,and the effect of experience on repeated decisions

Three experiments are presented that explore the assertion that loss aversion and diminishing sensitivity drive the effect of experience on choice behavior. The experiments are focused on repeated choice tasks where decision makers choose repeatedly between alternatives and get feedback after each choice. Experiments 1a and 1b show that behavioral tendencies that were previously interpreted as indications of loss aversion in decisions from experience are better described as products of diminishing sensitivity to absolute payoffs. Experiment 2 highlights a nominal magnitude effect: A decrease in the magnitude of the nominal payoffs eliminates the evidence for diminishing sensitivity. These and related previous results can be captured with a model that assumes reliance on small samples of subjective experiences, and an increase in diminishing sensitivity with payoff variability. Copyright © 2008 John Wiley & Sons, Ltd.     

How the brain separates sounds

In everyday life we often listen to one sound, such as someone's voice, in a background of competing sounds. To do this, we must assign simultaneously occurring frequency components to the correct source, and organize sounds appropriately over time. The physical cues that we exploit to do so are well-established; more recent research has focussed on the underlying neural bases, where most progress has been made in the study of a form of sequential organization known as "auditory streaming". Listeners' sensitivity to streaming cues can be captured in the responses of neurons in the primary auditory cortex, and in EEG wave components with a short latency (< 200ms). However, streaming can be strongly affected by attention, suggesting that this early processing either receives input from non-auditory areas, or feeds into processes that do.     

Consensus effects in categorization decisions

A previous study (Gilat et al., J. Exp. Psychol. Appl. 3 (1997) 83) has shown that the incentive to reach consensus can raise the tendency to rely on base rates in signal detection decisions and can reduce the probability that less likely events will be accurately classified. This phenomenon was named the “consensus effect”. The current study assesses the conditions under which this effect develops and in particular the effects of information about the game and of the incentive structure on the learning process. The results of three experiments show that the learning process slows when participants have information about the actual state of nature. This finding is captured by a reinforcement learning model with the assumption that information narrows the distribution of the initial propensities for choosing among cutoffs. The results are further evidence for the utility of the combination of learning models and analyses of cognitive processes for the prediction of decision making in situations involving multiple players.     

Formulas for component scores

General formulas for obtaining scores for individuals on components (factors derived from correlation matrices with unit communality estimates) are given. They are specialized to give Hotelling's formula for principal component scores. Formulas for scores on components rotated from principal components are developed.The final version of this paper was prepared while the author was a U. S. Public Health Service Fellow at the Center for Advanced Study in the Behavioral Sciences.     

Better to Decide Together: Shared Consumer Decision Making,Perceived Power,and Relationship Satisfaction

Shared consumer decisions, particularly those made with a relationship partner, can be very different from decisions that are made alone. Across multiple studies, we investigate how shared consumer decision making affects perceptions of power and relationship satisfaction. We integrate two streams of research to create a novel theory about consumer decision making and perceived power. Specifically, we suggest that shared consumer decision making combines two necessary components of power—an individual's influence over and a partner's engagement in the decision—and that these combined components drive power perceptions. In other words, individuals who relinquish some control and make a decision with their partner, ironically, perceive having greater power than if they had made the decision alone. We further find that shared decision making and greater perceived power lead to greater satisfaction with the relationship in which the decisions are made. By focusing on consumer decision making within relationships, the current research contributes to the literatures on decision making, social influences in consumer behavior, close relationships, consumer well-being, and power.     

Components of reliability

As an alternative to the analysis of variance approach to reliability a multiple-factor analysis approach is illustrated. The one-factor and the multiple-factor models for reliability are compared. Tests on the latent roots associated with the principal components of intercorrelation matrices are used to determine the number of components to be retained. Conditions under which one or more of the principal components should be utilized are discussed.This investigation was completed at the Oregon Research Institute and supported by NIMH grant MH-0892-01 and NSF grant GB-257. Computations were performed at the Western Data Processing Center and the Health Sciences Computing Facility, University of California at Los Angeles.     

Access to identity-specific semantic codes from familiar faces

Information codes that can specify the surface form of a face are contrasted with semantic codes describing the properties of the person to whom the face belongs. Identity-specific semantic codes that specify characteristics of familiar people based on personal knowledge are in turn contrasted with the visually derived semantic codes and expression codes that can be derived even from unfamiliar faces. The idea that familiarity decisions (i.e., categorizing faces as belonging to known or unknown people) can be based on surface form, whereas certain types of semantic decision demand additional access to identity-specific semantic codes was investigated in four experiments. Experiments 1 and 3 showed that decisions based on identity-specific semantic codes (semantic decisions) usually take longer than decisions that do not demand access to an identity-specific semantic code (familiarity decisions). Experiment 2 showed that the use of familiar faces drawn from consistent or mixed categories affected reaction times for semantic decisions but not for familiarity decisions. Experiment 4 showed that semantic decisions to faces are taken more quickly (primed) when the faces have been recently seen, whereas there is no differential effect on semantic decisions to faces from previous semantic decisions involving the same people's names. These findings are consistent with the view that identity-specific semantic codes are accessed via face recognition units, and that outputs from face recognition units (which respond to the face's surface form) can be used as the basis for familiarity decisions.     

Distinctiveness,typicality, and recollective experience in face recognition: A principal components analysis

In this study, participants rated previously unseen faces on six dimensions: familiarity, distinctiveness, attractiveness, memorability, typicality, and resemblance to a familiar person. The faces were then presented again in a recognition test in which participants assigned their positive recognition decisions to either remember (R), know (K), or guess categories. On all dimensions except typicality, faces that were categorized as R responses were associated with significantly higher ratings than were faces categorized as K responses. Study ratings for R and K responses were then subjected to a principal components analysis. The factor loadings suggested that R responses were influenced primarily by the distinctiveness of faces, but K responses were influenced by moderate ratings on all six dimensions. These findings indicate that the structural features of a face influence the subjective experience of recognition.     

A developmental dissociation between category and function judgments about novel artifacts

Two studies investigated the relative importance of information about intended design and current use on judgments about the function (Experiment 1) or category (Experiment 2) of novel artifacts in preschool children and adults. Adults assigned function and name on the basis of information about design across all conditions, while children’s decisions about function dissociated from decisions about category. Function judgments (in both 4 and 6-year-olds) were neutral between design and current use, both when the current use was idiosyncratic (e.g. performed by just one agent) and conventional (performed by many people; Experiment 1). By contrast, where category judgments were required for the very same objects (Experiment 2), children named according to design intentions - but only if the alternate function was idiosyncratic. Judging function and assigning category are thus cognitive tasks that draw on different information across development, a fact that should be captured by theories of developing artifact concept structure.