A unified approach to multiple‐set canonical correlation analysis and principal components analysis

Multiple‐set canonical correlation analysis and principal components analysis are popular data reduction techniques in various fields, including psychology. Both techniques aim to extract a series of weighted composites or components of observed variables for the purpose of data reduction. However, their objectives of performing data reduction are different. Multiple‐set canonical correlation analysis focuses on describing the association among several sets of variables through data reduction, whereas principal components analysis concentrates on explaining the maximum variance of a single set of variables. In this paper, we provide a unified framework that combines these seemingly incompatible techniques. The proposed approach embraces the two techniques as special cases. More importantly, it permits a compromise between the techniques in yielding solutions. For instance, we may obtain components in such a way that they maximize the association among multiple data sets, while also accounting for the variance of each data set. We develop a single optimization function for parameter estimation, which is a weighted sum of two criteria for multiple‐set canonical correlation analysis and principal components analysis. We minimize this function analytically. We conduct simulation studies to investigate the performance of the proposed approach based on synthetic data. We also apply the approach for the analysis of functional neuroimaging data to illustrate its empirical usefulness.     

Compressing movement information via principal components analysis (PCA): Contrasting outcomes from the time and frequency domains

PCA has become an increasingly used analysis technique in the movement domain to reveal patterns in data of various kinds (e.g., kinematics, kinetics, EEG, EMG) and to compress the dimension of the multivariate data set recorded. It appears that virtually all movement related PCA analyses have, however, been conducted in the time domain (PCA_t). This standard approach can be biased when there are lead-lag (phase-related) properties to the multivariate time series data. Here we show through theoretical derivation and analysis of simulated and experimental postural kinematics data sets that PCA_t and, PCA in the frequency domain (PCA_f), can lead to contrasting determinations of the dimension of a data set, with the tendency of PCA_t to overestimate the number of components. PCA_f also provides the possibility of obtaining amplitude and phase-difference spectra for each principal component that are uniquely suitable to reveal control mechanisms of the system. The bias in the PCA_t estimate of the number of components can have significant implications for the veracity of the interpretations drawn in regard to the dynamical degrees of freedom of the perceptual-motor system.     

Improved Insight into and Prediction of Network Dynamics by Combining VAR and Dimension Reduction

To understand within-person psychological processes, one may fit VAR(1) models (or continuous-time variants thereof) to multivariate time series and display the VAR(1) coefficients as a network. This approach has two major problems. First, the contemporaneous correlations between the variables will frequently be substantial, yielding multicollinearity issues. In addition, the shared effects of the variables are not included in the network. Consequently, VAR(1) networks can be hard to interpret. Second, crossvalidation results show that the highly parametrized VAR(1) model is prone to overfitting. In this article, we compare the pros and cons of two potential solutions to both problems. The first is to impose a lasso penalty on the VAR(1) coefficients, setting some of them to zero. The second, which has not yet been pursued in psychological network analysis, uses principal component VAR(1) (termed PC-VAR(1)). In this approach, the variables are first reduced to a few principal components, which are rotated toward simple structure; then VAR(1) analysis (or a continuous-time analog) is applied to the rotated components. Reanalyzing the data of a single participant of the COGITO study, we show that PC-VAR(1) has the better predictive performance and that networks based on PC-VAR(1) clearly represent both the lagged and the contemporaneous variable relations.     

The dynamical structure of handball penalty shots as a function of target location

We used principal components analysis (PCA) to investigate variations in the dynamical structure of handball penalty shots as a factor of target location and phase of shot. Participants completed a total of 10 successful shots to each of four target locations in the handball goal. Three dimensional movement time series data were analyzed. Also, data were analyzed across three temporally distinct time windows in line with the evolving kinematic chain. Statistical analyses were undertaken to determine differences across target locations. There were no significant differences between dynamical structures as a factor of target or phase. Covariance between time evolutions as a factor of target reduced in line with the ranking of the component. When shots were analyzed as three distinct time windows, only the low time evolution covariances suggested differences between targets in any time window. Our findings show that the dynamical structure underpinning the handball penalty shot does not differ greatly across locations. However, the time evolution of principal components suggests there are some variations in dynamics which may differentiate shot direction.     

Validation of a full body 3-D dynamic linked segment model

In studies related to human movement, linked segment models (LSM's) are often used to quantify forces and torques, generated in body joints. Some LSM's represent only a few body segments. Others, for instance used in studies on the control of whole body movements, include all body segments. As a consequence of the complexity of 3-dimensional (3-D) analyses, most LSM's are restricted to one plane of motion. However, in asymmetric movements this may result in a loss of relevant information. The aim of the current study was to develop and validate a 3-D LSM including all body segments. Braces with markers, attached to all body segments, were used to record the body movements. The validation of the model was accomplished by comparing the measured with the estimated ground reaction force and by comparing the torques at the lumbo-sacral joint that resulted from a bottom-up and a top-down mechanical analysis. For both comparisons, reasonable to good agreement was found. Sources of error that could not be analysed this way, were subjected to an additional sensitivity analysis. It was concluded that the internal validity of the current model is quite satisfactory.     

Functional Generalized Structured Component Analysis

An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.     

How to perform multiblock component analysis in practice

To explore structural differences and similarities in multivariate multiblock data (e.g., a number of variables have been measured for different groups of subjects, where the data for each group constitute a different data block), researchers have a variety of multiblock component analysis and factor analysis strategies at their disposal. In this article, we focus on three types of multiblock component methods—namely, principal component analysis on each data block separately, simultaneous component analysis, and the recently proposed clusterwise simultaneous component analysis, which is a generic and flexible approach that has no counterpart in the factor analysis tradition. We describe the steps to take when applying those methods in practice. Whereas plenty of software is available for fitting factor analysis solutions, up to now no easy-to-use software has existed for fitting these multiblock component analysis methods. Therefore, this article presents the MultiBlock Component Analysis program, which also includes procedures for missing data imputation and model selection.     

Algorithms for detecting concealed knowledge among groups when the critical information is unavailable

We examined whether the Concealed Information Test (CIT) may be used when the critical details are unavailable to investigators (the Searching CIT [SCIT]). This use may have important applications in criminal investigations (e.g., finding the location of a murder weapon) and in security-related threats (e.g., detecting individuals and groups suspected in planning a terror attack). Two classes of algorithms designed to detect the critical items and classify individuals in the SCIT were examined. The 1st class was based on averaging responses across subjects to identify critical items and on averaging responses across the identified critical items to identify knowledgeable subjects. The 2nd class used clustering methods based on the correlations between the response profiles of all subject pairs. We applied a principal component analysis to decompose the correlation matrix into its principal components and defined the detection score as the coefficient of each subject on the component that explained the largest portion of the variance. Reanalysis of 3 data sets from previous CIT studies demonstrated that in most cases the efficiency of differentiation between knowledgeable and unknowledgeable subjects in the SCIT (indexed by the area under the receiver operating characteristic curve) approached that of the standard CIT for both algorithms. We also examined the robustness of our results to variations in the number of knowledgeable and unknowledgeable subjects in the sample. This analysis demonstrated that the performance of our algorithms is relatively robust to changes in the number of individuals examined in each group, provided that at least 2 (but desirably 5 or more) knowledgeable examinees are included. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Some mathematical notes on three-mode factor analysis

The model for three-mode factor analysis is discussed in terms of newer applications of mathematical processes including a type of matrix process termed the Kronecker product and the definition of combination variables. Three methods of analysis to a type of extension of principal components analysis are discussed. Methods II and III are applicable to analysis of data collected for a large sample of individuals. An extension of the model is described in which allowance is made for unique variance for each combination variable when the data are collected for a large sample of individuals.     

Racial Bias and the MCMI

We studied the scores obtained on the Millon Clinical Multiaxial Inventory (MCMI) by Black and White male psychiatric inpatients to determine the presence or absence of racial bias. In predicting psychopathology for the two races, comparisons of MCMI performance indicated significant differences for all diagnoses except the personality disorders. The subjects were then matched into two groups of 209 patients each, according to DSM-111 psychiatric diagnoses. The data were analyzed at the item, scale, and structural levels. At the item level, application of the Mantel-Haenszel Procedure revealed that 45 of the 175 items of the inventory were answered significantly different by the two racial groups. Because this number was higher than what could be expected by chance, the finding suggested possible deficiencies in terms of the culture-fairness of the items used in the test. At the scale level, an analysis of variance (ANOVA) demonstrated that the scores obtained by the Black and White groups were significantly different in 9 of the 20 scales (Histrionic, Narcissistic, Antisocial, Paraphrenia, Hypomania, Dysthyrnia, Alcohol Abuse, Drug Abuse, and Psychotic Delusion). With the exception of the Dysthymic scale, all of the differences were in the direction of the Blacks obtaining a higher score than the Whites. At the structural level, however, a principal components factor analysis performed on each group resulted in factor structures that looked identical.     

Racial bias and the MCMI

We studied the scores obtained on the Millon Clinical Multiaxial Inventory (MCMI) by Black and White male psychiatric inpatients to determine the presence or absence of racial bias. In predicting psychopathology for the two races, comparisons of MCMI performance indicated significant differences for all diagnoses except the personality disorders. The subjects were then matched into two groups of 209 patients each, according to DSM-III psychiatric diagnoses. The data were analyzed at the item, scale, and structural levels. At the item level, application of the Mantel-Haenszel Procedure revealed that 45 of the 175 items of the inventory were answered significantly different by the two racial groups. Because this number was higher than what could be expected by chance, the finding suggested possible deficiencies in terms of the culture-fairness of the items used in the test. At the scale level, an analysis of variance (ANOVA) demonstrated that the scores obtained by the Black and White groups were significantly different in 9 of the 20 scales (Histrionic, Narcissistic, Antisocial, Paraphrenia, Hypomania, Dysthymia, Alcohol Abuse, Drug Abuse, and Psychotic Delusion). With the exception of the Dysthymic scale, all of the differences were in the direction of the Blacks obtaining a higher score than the Whites. At the structural level, however, a principal components factor analysis performed on each group resulted in factor structures that looked identical.     

Coordination modes in sensorimotor synchronization of whole-body movement: a study of street dancers and non-dancers

This study investigated whole-body sensorimotor synchronization (SMS) in street dancers and non-dancers. Two kinds of knee bending movement in a standing position to a metronome beat were explored in terms of stability under different movement frequencies: down-movement condition (knee flexion on the beat) and up-movement condition (knee extension on the beat). Analyses of phase relation between movement and beat revealed several distinct differences between the down- and up-movement conditions, and between dancers and non-dancers. In both groups under the up-movement condition, deviation from intended phase relation at higher beat rates, and enhanced fluctuations were observed. The deviation from intended phase relation under up-movement condition, and movement fluctuations were greater in non-dancers than in dancers. Moreover, subjective difficulty rating revealed that both groups felt that the up-movement condition was more difficult at higher beat rates. These findings suggest that down and up movements are two distinguishable coordination modes in whole-body coordination, and that street dancers have superior whole-body SMS ability.     

EXPLORATORY ANALYSIS OF A DEVELOPMENTAL MODEL FOR TASK-ORIENTED SMALL GROUPS

The purpose of this study was to describe and perform an exploratory analysis of a conceptual model for task-oriented small group development. The four phases of the model were defined as: latency, adaptation, integration, and goal-attainment. To test assumptions of phasic development, data from minute-byminute observations made on 30 groups of undergraduate women were collapsed into quarters and submitted to a one-way multivariate analysis of variance for the purpose of making a priori nonorthogonal comparisons. Results from the initial a priori comparisons and subsequent data-snooping techniques did not confirm the existence of four sequential phases in group development. Results did disclose a pattern of development that began with an extended adaptation phase covering most of the first half of group interaction. Groups characteristically shifted into a partially defined integration phase where affectivity and neutrality themes appeared to follow each other. Goal-attainment themes were most prominent during the final quarter of interaction.     

Occupational classification in terms of interest patterns

This study was designed to identify the important clusters of occupational groups identifiable from an analysis of the dimensions accounting for similarity in profile shapes among a set of 28 new vocational interest measures. A total of over 47,000 individuals belonging to 189 particular occupational groups have completed the Strong Vocational Interest Blank and had their data summarized in the form of group profiles. The matrix of 189 occupational group profiles of the 22 SVIB Basic Scales was analyzed by a series of multivariate procedures designed to predict group profiles on the Jackson Vocational Interest Survey (JVIS). Predicted JVIS profiles were obtained using an intercorrelation matrix of 548 males who had completed both the SVIB and the JVIS. Predicted JVIS profiles were subjected to a form of transpose factor analysis to obtain clusters of similar occupations. A total of 23 distinct occupational clusters were obtained, ranging from military officers to salesmen, and were interpreted as representing the major groupings of occupations defined by similar patterns of vocational interest.     

Postural and focal inhibition of voluntary movements prepared under various temporal constraints

Large disturbances arising from the moving segments (focal movement) are commonly counteracted by anticipatory postural adjustments (APAs). The aim of this study was to investigate how APAs – focal movement coordination changes under temporal constraint. Ten subjects were instructed to perform an arm raising movement in the reactive (simple reaction time) and predictive (anticipation–coincidence) tasks. A stop paradigm was applied to reveal the coordination. On some unexpected trials, a stop signal indicated to inhibit the movement; it occurred randomly at different delays (SOA) relative to the go signal in the reactive task, and at different delays prior to the focal response initiation in the predictive task. Focal movement was measured using contact switch, accelerometer and EMG from the anterior deltoid. APAs were quantified using centre of pressure displacement and EMG from three postural muscles. The inhibition rates as a function of the SOA produce psychometric functions where the bi-serial points allow the moment of the motor "command release" to be estimated. Repeated measures ANOVAs showed that APAs and focal movement were closely timed in the reactive task but distinct in a predictive task. Data were discussed according to two different models of coordination: (1) hierarchical model where APAs and focal movement are the results of a single motor command; (2) parallel model implying two independent motor commands. The data clearly favor the parallel model when the temporal constraint is low. The stop paradigm appears as a promising technique to explore APAs – focal movement coordination.     

Principal postural acceleration and myoelectric activity: Interrelationship and relevance for characterizing neuromuscular function in postural control

One approach to investigating sensorimotor control is to assess the accelerations that produce changes in the kinematic state of the system. When assessing complex whole-body movements, structuring the multi-segmental accelerations is important. A useful structuring can be achieved through a principal component analysis (PCA) performed on segment positions followed by double-differentiation to obtain “principal accelerations” (PAs). In past research PAs have proven sensitive to altered motor control strategies, however, the interrelationship between PAs and muscle activation (surface electromyography, sEMG) have never been determined. The purpose of the current study was therefore to assess the relationship between PAs and sEMG signals recorded from muscles controlling the ankle joint during one-leg standing trials. It was hypothesized that medium correlation should be observed when accounting for neurophysiologic latencies (electro-mechanical delay). Unipedal balancing on a level-rigid ground was performed by 25 volunteers. sEMG activities were recorded from the tibialis anterior, peroneus longus, gastrocnemius medialis, and soleus muscles of the stance leg. The first eight PA-time series were determined from kinematic marker data. Then, a cross-correlation analysis was performed between sEMG and PA time series. We found that peak correlation coefficients for many participants aligned at time delays between 0.116 and 0.362 s and were typically in the range small to medium (|r| = 0.1 to 0.6). Thus, the current study confirmed a direct association between many principal accelerations PA(t) and muscle activation signals recorded from four muscles crossing the ankle joint complex. The combined analysis of PA and sEMG signals allowed exploring the neuromuscular function of each muscle in different postural movement components.     

Recovery of subsampled dimensions and configurations derived from napping data by MFA and MDS

Napping is a multivariate sensory method in which participants physically place stimuli on a large sheet of paper and orient them so that the distance between pairs represents a measure of dissimilarity. The two-dimensional nature of the task may be a limitation to the ability of this and similar methodologies to recover information about complex stimuli. In the first investigation, eight simulated three-dimensional stimuli were created with two different levels for each attribute. Simulated napping experiments had groups of participants attend to two of the dimensions with different probabilities. Multiple factor analysis (an analytical multivariate statistical procedure that can be thought of as a principle components analysis on the individuals) and MDS-INDSCAL (a variation on multidimensional scaling that finds a common configuration through reducing a stress measure associated with lack of fit) recovered full dimensionality from these data, although MFA had trouble when attention was the most unbalanced. In the second experiment, a human napping experiment was designed using custom three-dimensional stimuli: shapes with two levels each of size, color, and shape attributes. This experiment confirmed the results of Experiment 1, as both MDS-INDSCAL and MFA analyses again recovered the full dimensionality of the stimuli.     

Implicit and explicit adjustments to extrinsic visuo-motor transformations and their age-related changes

Humans have unique abilities in using tools. The skilled and goal-directed use of a tool implies that processes of motor control can be adjusted to the transformation of the movement of a part of the body into the movement of the effective part of the tool. A common example is the transformation of a hand movement in the motion of a cursor on a computer monitor. In part the adjustments to such transformations are implicit, that is, without conscious awareness of the novel transformation and the appropriate change of one’s own movements. However, the adjustments can also be explicit and intentional. We review a series of experiments which show that implicit and explicit adjustments to a novel visuo-motor gain are additive. This finding suggests that the processes which generate different types of adjustment are functionally independent. In a second series of experiments it turned out that at older adult age explicit adjustments to novel visuo-motor transformations are impaired, whereas implicit adjustments remain unaffected across working age.     

Interlimb coordination: Learning and transfer under different feedback conditions

The role of intrinsic and extrinsic information feedback in learning a new bimanual coordination pattern was investigated. The pattern required continuous flexion-extension movements of the upper limbs with a 90 ° phase offset. Separate groups practiced the task under one of the following visual feedback conditions: (a) blindfolded (reduced FB group), (b) with normal vision (normal FB group), or (c) with concurrent relative motion information (enhanced FB group). All groups were subjected to three different transfer test conditions at regular intervals during practice. These tests included reduced, normal vision, and enhanced vision conditions. Experiment 1 showed that the group receiving augmented information feedback about its relative motions in real-time produced the required coordination pattern more successfully than the remaining two groups, irrespective of the transfer conditions under which performance was evaluated. Experiment 2 replicated and extended the superiority of the enhanced feedback group during acquisition and retention. Experiment 3 demonstrated that successful transfer to various transfer test conditions was not a result of test-trial effects. Overall, the data suggest that the conditions that optimized performance of the coordination pattern during acquisition also optimized transfer performance.