Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis

The selection of a subset of variables from a pool of candidates is an important problem in several areas of multivariate statistics. Within the context of principal component analysis (PCA), a number of authors have argued that subset selection is crucial for identifying those variables that are required for correct interpretation of the components. In this paper, we adapt the variable neighborhood search (VNS) paradigm to develop two heuristics for variable selection in PCA. The performances of these heuristics were compared to those obtained by a branch-and-bound algorithm, as well as forward stepwise, backward stepwise, and tabu search heuristics. In the first experiment, which considered candidate pools of 18 to 30 variables, the VNS heuristics matched the optimal subset obtained by the branch-and-bound algorithm more frequently than their competitors. In the second experiment, which considered candidate pools of 54 to 90 variables, the VNS heuristics provided better solutions than their competitors for a large percentage of the test problems. An application to a real-world data set is provided to demonstrate the importance of variable selection in the context of PCA.     

Modeling Differences in the Dimensionality of Multiblock Data by Means of Clusterwise Simultaneous Component Analysis

Given multivariate multiblock data (e.g., subjects nested in groups are measured on multiple variables), one may be interested in the nature and number of dimensions that underlie the variables, and in differences in dimensional structure across data blocks. To this end, clusterwise simultaneous component analysis (SCA) was proposed which simultaneously clusters blocks with a similar structure and performs an SCA per cluster. However, the number of components was restricted to be the same across clusters, which is often unrealistic. In this paper, this restriction is removed. The resulting challenges with respect to model estimation and selection are resolved.     

The generation and resemblance heuristics in face recognition: cooperation and competition

Like all probabilistic decisions, recognition memory judgments are based on inferences about the strength and quality of stimulus familiarity. In recent articles, B. W. A. Whittlesea and J. Leboe (2000; J. Leboe & B. W. A. Whittlesea, 2002) proposed that such memory decisions entail various heuristics, similar to well-known heuristics in overt decision making. Using verbal stimulus materials, Whittlesea and Leboe illustrated 3 separate memory heuristics: fluency, generation, and resemblance. In the present investigation, the authors examined the generation and resemblance heuristics in face recognition. In 12 experiments, people memorized faces and later performed exclusion (source memory) tasks. Every experiment contained natural groups of facial photographs (e.g., Caucasian vs. Asian faces), but such groups were not always valid source-memory predictors. Instead, across experiments, the potential utility of generation and resemblance strategies was systematically varied. People were quite sensitive to such variations, changing from one heuristic to another as needed. However, they also combined heuristics, both improving and damaging performance across conditions. The relevance of recognition decision heuristics to eyewitness memory is considered.     

A process model for water jug problems

We develop and evaluate a model for the water jug task in which a subject is required to find a sequence of moves (pouring operations) which produce a specified amount of water in each jug. Experiment 1 was designed to evaluate the meansends, move selection heuristics that are assumed by the model. Experiment 2 tested the model's predictions concerning those aspects of the water jug task that determine problem difficulty.A three stage process model incorporating GPS-like, means-ends heuristics and assumptions concerning the utilization of short- and long-term memory was able to account for differences across problems as well as details of the performance of subjects solving a given problem. We conclude that a GPS-like model that only selects one move at a time (no forward planning of move sequences or setting up of subgoals) can provide a good account of solution behavior in the water jug task.     

Environments That Make Us Smart: Ecological Rationality

ABSTRACT— Traditional views of rationality posit general-purpose decision mechanisms based on logic or optimization. The study of ecological rationality focuses on uncovering the "adaptive toolbox" of domain-specific simple heuristics that real, computationally bounded minds employ, and explaining how these heuristics produce accurate decisions by exploiting the structures of information in the environments in which they are applied. Knowing when and how people use particular heuristics can facilitate the shaping of environments to engender better decisions.     

CPCA: A program for principal component analysis with external information on subjects and variables

A program is described for principal component analysis with external information on subjects and variables. This method is calledconstrained principal component analysis (CPCA), in which regression analysis and principal component analysis are combined into a unified framework that allows a full exploration of data structures both within and outside known information on subjects and variables. Many existing methods are special cases of CPCA, and the program can be used for multivariate multiple regression, redundancy analysis, double redundancy analysis, dual scaling with external criteria, vector preference models, and GMANOVA (growth curve models).     

Mechanism Discovery and Design Explanation: Where Role Function Meets Biological Advantage Function

In the recent literature on explanation in biology, increasing attention is being paid to the connection between design explanation and mechanistic explanation, viz. the role of design principles and heuristics for mechanism discovery and mechanistic explanation. In this paper we extend the connection between design explanation and mechanism discovery by prizing apart two different types of design explanation and by elaborating novel heuristics that one specific type offers for mechanism discovery across species. We illustrate our claims in terms of two lines of biological research on the biological advantages of organismal traits, one on the eye-size of giant squid, the other on foraging habits of specific bat species. We argue that this research illustrates useful heuristics for mechanism discovery across species, viz. reasoning strategies to infer likely mechanisms for a certain biological role based on assessments of the environmental conditions in which the role is performed efficiently (i.e., offers a biological advantage) and less or in-efficiently. We bring out the novel features of our analysis in terms of a comparison with mechanistic approaches to mechanism discovery, amongst which graph-theoretical ones, and by comparing the different types of design explanation and the discovery heuristics they support.     

Should reason be fragmented?

Cognitive relativists‐pragmatists (Stich, Churchland) claim that human cognitive strategies, lacking a common goal, are in addition divergent to the point of incommensurability. They appeal to the study of reasoning heuristics for evidence on cognitive diversity and incorrigibility. It is here argued that no such evidence is offered by the research, which, on the contrary (1) presents heuristics as uniform across great variations; (2) offers advice for correcting and improving human reasoning; and (3) very often postulates a uniformity of core logical strategies, built into reasoning competence. Cognitive research thus supports a moderate rationalism rather than relativism‐pragmatism.     

Integrating Fast and Frugal Heuristics with a Model of Memory‐based Cue Generation

Although the fast and frugal heuristics have been studied extensively, relatively little attention has been paid to how cues are generated to be used within the heuristics. The goal of this paper is to propose and test a memory‐based model of how cues are generated and used in cue‐based inferences. The current study advances theory by integrating the fast and frugal heuristics with HyGene, a memory‐based model of how decision makers generate and evaluate hypotheses. Using archival data in which memory retrieval variables were not directly manipulated, we demonstrate that participants' cue selection behavior is consistent with memory‐based retrieval. Further, by directly manipulating memory retrieval within a cue‐based stock‐forecasting task, we demonstrate that memory processes underlie cue use. Participants' cue use varied depending on the relationship between cue validity and the frequency with which the cues were seen during learning. The HyGene model provided the best account of the empirical data, providing further evidence for the critical role of memory in judgment and decision making. Copyright © 2018 John Wiley & Sons, Ltd.     

Eye movements and processing stages in reading: relative contribution of visual,lexical, and contextual factors

The independent and the combined influence of word length, word frequency, and contextual predictability on eye movements in reading was examined across processing stages under two priming-context conditions. Length, frequency, and predictability were used as predictors in multiple regression analyses, with parafoveal, early, late, and spillover eye movement measures as the dependent variables. There were specific effects of: (a) length, both on where to look (how likely a word was fixated and in which location) and how long to fixate, across all processing stages; (b) frequency, on how long to fixate a word, but not on where to look, at an early processing stage; and (c) predictability, both on how likely a word was fixated and for how long, in late processing stages. The source of influence for predictability was related to global rather than to local contextual priming. The contribution of word length was independent of contextual source. These results are relevant to determine both the time course of the influence of visual, lexical, and contextual factors on eye movements in reading, and which main component of eye movements, that is, location or duration, is affected.     

Organizational Decision-making in the Appropriation of Technological Innovation: Cognitive and Political Dimensions

Abstract

Outcomes of innovation may depend upon the user's decision processes in its appropriation. The context for the user's decision-making comprises three interdependent elements: (1) the innovation pool; (2) the user; and (3) the supplier of the innovation. User decisions are seen as a series of four interlocking decision episodes. During the first two episodes (agenda formation and selection) the problem is defined and a solution chosen. In the latter two episodes (implementation and usage) the innovation is adopted and used. Appropriation may depend on dual modification of the innovation and organizational practices until the innovation meets the unique requirements of the user. Cognitive and political variables relevant to technological innovation are suggested and explored by drawing upon qualitative comparisons across seven cases of technological innovation in British manufacturing firms. Particular problems occur when users have inadequate knowledge bases, overuse heuristics and analogies, and have conflicting beliefs about the chosen innovation. The extent to which cognitive variables impose on success with the innovation may be mediated by political processes, and may also interact with national culture. Focus is on the processes during the early episodes of agenda formation and selection on the grounds that problems engendered here carry over to implementation.     

Contributions of invariants, heuristics, and exemplars to the visual perception of relative mass

Some potential contributions of invariants, heuristics, and exemplars to the perception of dynamic properties in the colliding balls task were explored. On each trial, an observer is asked to determine the heavier of 2 colliding balls. The invariant approach assumes that people can learn to detect complex visual patterns that reliably specify which ball is heavier. The heuristic approach assumes that observers only have access to simple motion cues. The exemplar-based approach assumes that people store particular exemplars of collisions in memory, which are later retrieved to perform the task. Mathematical models of these theories are contrasted in 2 experiments. Observers may use more than 1 strategy to determine relative mass. Although observers can learn to detect and use invariants, they may rely on either heuristics before the invariant has been learned or exemplars when memory demands and similarity relations allow.     

Acquisition of strategies depending on the opponents' competence level

The development of problem-solving skills from novices to advanced subjects in dependence of the competence level of the opponent is examined in a two-person zero-sum game (Othello). In a repeated-measurement design 18 Ss. (6 Ss in 3 groups) played 10 games against one of three opponent-strategies (implemented on a computer): one "expertlike" strategy, which uses domain specific knowledge and local heuristics (minimax-algorithm with alpha-beta pruning); one "novicelike" strategy, in which global, domain independent problem solving strategies (means-ends analysis, goal-reduction) are implemented; and one strategy, which contradicts the supposed heuristics of the novices, but which results in a "weak" performance (minimization in move-selection). Contrary to our assumptions no significant effects of experience could be verified (win versus loss during single runs). An experience dependent differentiation of global problem solving strategies could not be shown for any of the groups. Neither could a general improving effect of the model for acquiring local, task specific heuristics be proved.     

Stability/Instability of Cognitive Strategies Across Tasks Determine Whether Stress Will Affect Judgmental Processes'

Previous research indicates that individuals employ various cognitive heuristics and decision modes in making decisions and judgmental tasks that do not follow an expected value model. It further indicates that several cognitive faculties are affected by stress. The purpose of this study was twofold: first, to examine whether individual differences exist in the use of cognitive heuristics and risk-assessment decision modes; second, to examine whether stress would affect the use of these cognitive strategies. Three versions of a questionnaire measuring the representativeness and availability heuristics, and risk-seeking and risk-aversion decision modes were administered to three different groups of subjects. Consistent individual differences were only observed in the subscales measuring risk-seeking and risk-aversion modes, but not in the use of the heuristics. In a different group of subjects, exposure to noise and task overload stress increased the use of the representativeness heuristic, but did not alter the use of risk-seeking and risk-aversion decision modes. These results indicate that the existence of individual differences in cognitive strategies may determine, in part, whether stress will modify judgmental processes.     

Outlying Observation Diagnostics in Growth Curve Modeling

Growth curve models are widely used for investigating growth and change phenomena. Many studies in social and behavioral sciences have demonstrated that data without any outlying observation are rather an exception, especially for data collected longitudinally. Ignoring the existence of outlying observations may lead to inaccurate or even incorrect statistical inferences. Therefore, it is crucial to identify outlying observations in growth curve modeling. This study comparatively evaluates six methods in outlying observation diagnostics through a Monte Carlo simulation study on a linear growth curve model, by varying factors of sample size, number of measurement occasions, as well as proportion, geometry, and type of outlying observations. It is suggested that the greatest chance of success in detecting outlying observations comes from use of multiple methods, comparing their results and making a decision based on research purposes. A real data analysis example is also provided to illustrate the application of the six outlying observation diagnostic methods.     

Underlying Cognitions in Gambling Behavior Among University Students1

Differences in underlying cognitions across gambling tasks were examined. The South Oaks Gambling Screen, a measure of pathological gambling, was completed by 60 undergraduate students. They also played computer‐simulated games of roulette, slots, and blackjack in a laboratory setting. The “think‐aloud” procedure was used to reveal subjects' cognitions, which were subsequently categorized into cognitive heuristics. Individuals were classified as social gamblers with and without problems and probable pathological gamblers. Results reveal that certain heuristics, including references to an explanation of their losses, hindsight bias, personification of the dealer/machine, chasing behavior, and past experiences were most frequently endorsed by probable pathological gamblers. Empirical evidence supports that probable pathological gamblers are qualitatively different from social gamblers in their emitted verbalized cognitive heuristics.     

Beliefs about the "hot hand" in basketball across the adult life span

Many people believe in streaks. In basketball, belief in the "hot hand" occurs when people think a player is more likely to make a shot if they have made previous shots. However, research has shown that players' successive shots are independent events. To determine how age would impact belief in the hot hand, we examined this effect across the adult life span. Older adults were more likely to believe in the hot hand, relative to younger and middle-aged adults, suggesting that older adults use heuristics and potentially adaptive processing based on highly accessible information to predict future events. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Fertility and intergroup bias in racial and minimal-group contexts: evidence for shared architecture

Recent research has shown that White women's bias against Black men increases with elevated fertility across the menstrual cycle. We demonstrate that the association between fertility and intergroup bias is not limited to groups defined by race, but extends to group categories that are minimally defined, and may depend on the extent to which women associate out-group men with physical formidability. In Study 1, Black and White women with strong associations between the racial out-group and physical formidability displayed greater bias against out-group men as conception risk increased. Study 2 replicated these results in a minimal-group paradigm. These findings are consistent with the notion that women may be endowed with a psychological system that generates intergroup bias via mechanisms that rely on categorization heuristics and perceptions of the physical formidability of out-group men, particularly when the costs of sexual coercion are high.     

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.     

Differential predictability of preferences and choices

A combined multi-attribute utility and expectancy-value model has repeatedly been found to yield a worse fit to choices than to preference ratings. The present study investigated two possible explanations for this finding. First, people's belief-value structures may change in the choice task as they try to find the best alternative. Second, a difficult choice task may cause the decision maker to use simplifying heuristics. In the first of two experiments, subjective belief-value structures were measured on two occasions separated by about one week. Immediately before the second measurement, different groups of subjects performed a choice task, gave preference ratings, or performed a control task. The results did not support an interpretation of the greater difficulty of predicting choices in terms of changes in belief-value structures. However, the notion of simplifying heuristics received support by the finding that adopting simpler versions of the original model improved the predictions of the choices. In the second experiment, beliefs were measured immediately before or after each of a series of choices or preference ratings. The results indicated that although temporary changes in beliefs may occur, they can hardly provide a full account of the differential predictability of preferences and choices.