Probabilistic Disjoint Principal Component Analysis

One of the most relevant problems in principal component analysis and factor analysis is the interpretation of the components/factors. In this paper, disjoint principal component analysis model is extended in a maximum-likelihood framework to allow for inference on the model parameters. A coordinate ascent algorithm is proposed to estimate the model parameters. The performance of the methodology is evaluated on simulated and real data sets.     

非正态分布下概化理论方差分量变异量估计

方差分量估计是概化理论的必用技术,但受限于抽样,需要对其变异量进行探讨。采用Monte Carlo数据模拟技术,探讨非正态数据分布对四种方法估计概化理论方差分量变异量的影响。结果表明：（1）不同非正态数据分布下,各种估计方法的“性能”表现出差异性;（2）数据分布对方差分量变异量估计有影响,适合于非正态分布数据的方差分量变异量估计方法不一定适合于正态分布数据。     

Component analyses differentiate between exploratory behaviour of spontaneously hypertensive rats and Wistar Kyoto rats in a two-compartment free-exploration open field

The present study investigated behaviour in a two-compartment free-exploration open field by means of a component analysis. Seven spontaneously hypertensive rats (SHR) and six normotensive Wistar Kyoto control rats (WKY) were tested repeatedly on eight behaviour parameters in this apparatus. A two-compartment free-exploration open field evokes less fear than the standard one-compartment forced-exploration open field, because it permits the rat to enter the field from its home cage. The data were subjected to principal component analysis and multivariate analysis of variance. The results showed that the recorded behaviour grouped into two independent components, encompassing behaviour in the cage and in the field, respectively. These components are interpreted as reflecting different kinds of exploration: (i) distant exploration when the rat explores from its home cage, and (ii) close exploration when the rat explores by entering the novel field. The SHR scored highest on both, although they mostly used close exploration. In the WKY rats, which mainly stayed in their cages, distant exploration was predominant. The present free-exploration open-field procedure discriminates between two different exploration strategies employed by SHR and WKY rats.     

Structural aspects of face recognition and the other-race effect

The other-race effect was examined in a series of experiments and simulations that looked at the relationships among observer ratings of typicality, familiarity, attractiveness, memorability, and the performance variables ofd’ and criterion. Experiment 1 replicated the other-race effect with our Caucasian and Japanese stimuli for both Caucasian and Asian observers. In Experiment 2, we collected ratings from Caucasian observers on the faces used in the recognition task. A Varimax-rotated principal components analysis on the rating and performance data for the Caucasian faces replicated Vokey and Read’s (1992) finding that typicality is composed of two orthogonal components, dissociable via their independent relationships to: (1) attractiveness and familiarity ratings and (2) memorahility ratings. For Japanese faces, however, we fond that typicality was related only to memorahility. Where performance measures were concerned, two additional principal components dominated by criterion and byd’ emerged for Caucasian faces. For the Japanese faces, however, the performance measures ofd’ and criterion merged into a single component that represented a second component of typicality, one orthogonal to thememorability-dominated component. A measure offace representation quality extracted from an autoassociative neural network trained with a majority of Caucasian faces and a minority of Japanese faces was incorporated into the principal components analysis. For both Caucasian and Japanese faces, the neural network measure related both to memorability ratings and to human accuracy measures. Combined, the human data and simulation results indicate that the memorahility component of typicality may be related to small, local, distinctive features, whereas the attractiveness/familiarity component may be more related to the global, shape-based properties of the face.     

Comparison of Response Formats for Mulitdimensional Health Locus of Control Scales: Six Levels Versus Two Levels

Two formats of the Multidimensional Health Locus of Control (MHLC) Scales were administered to 54 college students. Each subject completed the MHLC Scales in the standard 6-level response format (ranging from strongly disagree to strongly agree) and in a revised 2-level format (ranging from disagree to agree). Comparisons of internal consistency measures, principal components, and classification of subjects into groups indicate that the 2-level response format yields comparable data to those obtained with the 6-level format, particularly when classification of subjects is the goal.     

Comparison of response formats for Multidimensional Health Locus of Control Scales: six levels versus two levels

Two formats of the Multidimensional Health Locus of Control (MHLC) Scales were administered to 54 college students. Each subject completed the MHLC Scales in the standard 6-level response format (ranging from strongly disagree to strongly agree) and in a revised 2-level format (ranging from disagree to agree). Comparisons of internal consistency measures, principal components, and classification of subjects into groups indicate that the 2-level response format yields comparable data to those obtained with the 6-level format, particularly when classification of subjects is the goal.     

Constrained Candecomp/Parafac via the Lasso

The Candecomp/Parafac (CP) model is a well-known tool for summarizing a three-way array by extracting a limited number of components. Unfortunately, in some cases, the model suffers from the so-called degeneracy, that is a solution with diverging and uninterpretable components. To avoid degeneracy, orthogonality constraints are usually applied to one of the component matrices. This solves the problem only from a technical point of view because the existence of orthogonal components underlying the data is not guaranteed. For this purpose, we consider some variants of the CP model where the orthogonality constraints are relaxed either by constraining only a pair, or a subset, of components or by stimulating the CP solution to be possibly orthogonal. We theoretically clarify that only the latter approach, based on the least absolute shrinkage and selection operator and named the CP-Lasso, is helpful in solving the degeneracy problem. The results of the application of CP-Lasso on simulated and real life data show its effectiveness.     

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.     

Information processing components of substitution test performance

Although substitution tests have been included in tests of intelligence for years, the underlying abilities they measure have still not been clearly determined. This study used componential analysis to investigate the information-processing components underlying substitution test performance. The bases of sex and age differences were also of interest. One hundred subjects from each of three age groups (9–11, 18–25, and 60–89 years) were tested.The componential analysis found that substitution tests measure perceptual speed and, to a lesser extent, memory ability and writing speed. The component “Stimulus Orientation, Response Initiation, and Execution” was related to substitution test performance in the sample of children and the sample of older adults but not in the sample of younger adults. Verbal ability was not significantly related to substitution test performance in the two younger samples but was strongly related to substitution performance in the oldest sample. Although females outperformed males on the Symbol Digit Test, males did as well as females on the computerized tasks. Apparently, sex differences in substitution test performance cannot be explained by the components of the test measured here.     

Differential effects of adding and removing components of a context on the generalization of conditional freezing

Rats were conditioned across 2 consecutive days where a single unsignaled footshock was presented in the presence of specific contextual cues. Rats were tested with contexts that had additional stimulus components either added or subtracted. Using freezing as a measure of conditioning, removal but not addition of a cue from the training context produced significant generalization decrement. The results are discussed in relation to the R. A. Rescorla and A. R. Wagner (1972), J. M. Pearce (1994), and A. R. Wagner and S. E. Brandon (2001) accounts of generalization. Although the present data are most consistent with elemental models such as Rescorla and Wagner, a slight modification of the Wagner-Brandon replaced-elements model that can account for differences in the pattern of generalization obtained with contexts and discrete conditional stimuli is proposed.     

Comparison of the Matthews Youth Test for Health and the Hunter-Wolf A-B Rating Scale: measures of type A behavior in children

This study evaluated the extent to which two youth measures of Type A behavior--the Matthews Youth Test for Health (MYTH) and the Hunter-Wolf A-B Rating Scale--similarly assess the Type A construct. Data from 25 elementary teachers and from 300 of their students revealed that these scales are weakly correlated and that the concordance of their Type A-Type B classifications was only slightly above that expected by chance. Weak agreement was found even when teachers and students rated the same Type A behaviors, which suggests that variability in content was not the principal reason for the lack of agreement between these measures. The major implication of this study is that the MYTH and the Hunter-Wolf scale should not be considered interchangeable measures of Type A behavior. The study reveals that investigators' choice of a Type A measure may strongly affect the nature of their research findings and may inhibit the integration of their data with data from other investigators who employ different measures of the Type A construct. It is recommended that, if multiple measures cannot be used in a study, the investigator employ the MYTH.     

Artifactual power curves in forgetting

Recent studies of the mathematical relationship between time and forgetting suggest that it is a power function rather than an exponential function, a finding that has important theoretical consequences. Through computational analysis and reanalyses of published data, we demonstrate that arithmetic averaging of exponential curves can produce an artifactual power curve, particularly when there are large and systematic differences among the slopes of the component curves. A series of simulations showed that the amount of power artifact is small when the slopes of the component curves are normally or rectangularly distributed and when the performance measure is noise free. However, the simulations also showed that the artifact can be quite large, depending on the shape of the noise distribution and restrictions in the performance range. We conclude that claims concerning the form of memory functions should consider whether the data are likely to contain artifact caused by averaging or by the presence of range-restricted noise.     

Principal Cluster Axes: A Projection Pursuit Index for the Preservation of Cluster Structures in the Presence of Data Reduction

A measure of “clusterability” serves as the basis of a new methodology designed to preserve cluster structure in a reduced dimensional space. Similar to principal component analysis, which finds the direction of maximal variance in multivariate space, principal cluster axes find the direction of maximum clusterability in multivariate space. Furthermore, the principal clustering approach falls into the class of projection pursuit techniques. Comparisons are made with existing methodologies both in a simulation study and analysis of real-world data sets. Furthermore, a demonstration of how to interpret the results of the principal cluster axes is provided on the analysis of Supreme Court voting data and similarities between the interpretation of competing procedures (e.g., factor analysis and principal component analysis) are provided. In addition to the Supreme Court analysis, we analyze several data sets often used to test cluster analysis procedures, including Fisher's Iris data, Agresti's Crab data, and a data set on glass fragments. Finally, discussion is provided to help determine when the proposed procedure will be the most beneficial to the researcher.     

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.     

A wavelet packet model of evoked potentials

The standard methods for decomposition and analysis of evoked potentials are bandpass filtering, identification of peak amplitudes and latencies, and principal component analysis (PCA). We discuss the limitations of these and other approaches and introduce wavelet packet analysis. Then we propose the "single-channel wavelet packet model," a new approach in which a unique decomposition is achieved using prior time-frequency information and differences in the responses of the components to changes in experimental conditions. Orthogonal sets of wavelet packets allow a parsimonious time-frequency representation of the components. The method allows energy in some wavelet packets to be shared among two or more components, so the components are not necessarily orthogonal. The single-channel wavelet packet model and PCA both require constraints to achieve a unique decomposition. In PCA, however, the constraints are defined by mathematical convenience and may be unrealistic. In the single-channel wavelet packet model, the constraints are based on prior scientific knowledge. We give an application of the method to auditory evoked potentials recorded from cats. The good frequency resolution of wavelet packets allows us to separate superimposed components in these data. Our present approach yields estimates of component waveforms and the effects of experiment conditions on the amplitude of the components. We discuss future extensions that will provide confidence intervals and p values, allow for latency changes, and represent multichannel data.     

Physical activity,motor competence and movement and gait quality: A principal component analysis

ObjectiveWhile novel analytical methods have been used to examine movement behaviours, to date, no studies have examined whether a frequency-based measure, such a spectral purity, is useful in explaining key facets of human movement. The aim of this study was to investigate movement and gait quality, physical activity and motor competence using principal component analysis.MethodsSixty-five children (38 boys, 4.3 ± 0.7y, 1.04 ± 0.05 m, 17.8 ± 3.2 kg, BMI; 16.2 ± 1.9 kg∙m²) took part in this study. Measures included accelerometer-derived physical activity and movement quality (spectral purity), motor competence (Movement Assessment Battery for Children 2nd edition; MABC2), height, weight and waist circumference. All data were subjected to a principal component analysis, and the internal consistency of resultant components were assessed using Cronbach's alpha.ResultsTwo principal components, with excellent internal consistency (Cronbach α >0.9) were found; the 1st principal component, termed “movement component”, contained spectral purity, traffic light MABC2 score, fine motor% and gross motor% (α = 0.93); the 2nd principal component, termed “anthropometric component”, contained weight, BMI, BMI% and body fat% (α = 0.91).ConclusionThe results of the present study demonstrate that accelerometric analyses can be used to assess motor competence in an automated manner, and that spectral purity is a meaningful, indicative, metric related to children's movement quality.     

Recall initiation strategies must be controlled in training studies that use immediate free recall tasks to measure the components of working memory capacity across time

There has been great interest in using working memory (WM) training regimens as an alternative treatment for ADHD, but it has recently been concluded that existing training regimens may not be optimally designed because they target the primary memory component but not the secondary component of WM capacity. This conclusion requires the ability to accurately measure changes in primary and secondary memory abilities over time. The immediate free recall task has been used in previous studies to measure these changes; however, one concern with these tasks is that the recall order required on training exercises may influence the recall strategy used during free recall, which may in turn influence the relative number of items recalled from primary and secondary memory. To address this issue, previous training studies have explicitly controlled recall strategy before and after training. However, the necessity of controlling for recall strategies has not been explicitly tested. The present study investigated the effects of forward-serial-order training on free recall performance under conditions in which recall strategy was not controlled using a sample of adolescents with ADHD. Unlike when recall order was controlled, the main findings showed selective improvement of the secondary memory component (as opposed to the primary memory component) when recall order was uncontrolled. This finding advances our understanding of WM training by highlighting the importance of controlling for recall strategies when free recall tasks are used to measure changes in the primary and secondary components of WM across time.     

Research about the university teaching performance evaluation under the data envelopment method

How to take active and effective measures to evaluate the university scientifically and rationally has been an eternal topic that the educational circles are constantly exploring. Based on the principle of index construction, the current educational performance evaluation index system is improved and a more reasonable evaluation index system is formed. On this basis, taking the sample data in 2017 as an example, the principal component analysis method is used to reduce the dimension of input and output indicators and eliminate the correlation between indicators, and three principal components of input and three principal components of output are obtained. Secondly, data envelopment analysis model is established, and the data processed are analyzed with the help of MATLAB and DEAP2.1 operation software. The efficiency of these 24 colleges and universities is compared to understand the efficiency and differences of each college. Moreover, projection analysis of non-DEA effective DMU is completed and the direction of improvement and the specific adjustment value are pointed out.     

Pavlovian compound conditioning in the rabbit

Two experiments are reported on eyelid conditioning in the rabbit involving compounds of isolable CSs. In Experiment 1 it was demonstrated that subjects could be trained to respond discriminatively on the basis of specific configurations when no other reliable component cues were available. In Experiment II, a novel test procedure failed to provide further evidence that subjects utilized specific configurational cues when reliable isolable components were available. The findings were discussed in terms of the assumption that any stimulus compound involves both isolable and configurational components with the former being more “salient” than the latter.