Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.     

Assessing the stability of principal components using regression

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.The authors would like to thank the four anonymous reviewers and the two editors for their valuable comments. Atanu R. Sinha gratefully acknowledges the research support received from the Marketing Studies Center, AGSM, UCLA. Send requests for reprints to Atanu R. Sinha, B418 Gold Hall, 110 Westwood Plaza, Los Angeles, CA 90095.     

多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。     

Dimensional analyses of taxonic data

Principal component analysis (PCA) and common factor analysis are often used to model latent data structures. Typically, such analyses assume a single population whose correlation or covariance matrix is modelled. However, data may sometimes be unwittingly sampled from mixed populations containing a taxon (nonarbitrary subpopulation) and its complement class. One derives relations between values of PCA parameters within subpopulations and their values in the mixed population. These results are then extended to factor analysis in mixed populations. As relationships between subpopulation and mixed-population principal components and factors sensitively depend on within-subpopulation structures and between-subpopulation differences, naive interpretation of PCA or factor analytic findings can potentially mislead. Several analyses, better suited to the dimensional analysis of admixture data structures, are presented and compared.     

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).     

An auditory evoked potential study of consonant perception in different vowel environments

Auditory evoked responses (AER) to series of consonant—vowel syllables were recorded from temporal and parietal scalp locations from 20 right-handed female college students. Averaged AERs were submitted to principal components analysis and analysis of variance. Seven components of the group's AERs were found to reflect various aspects of the stimulus parameters. One component reflected changes over only the left hemisphere to different consonants independent of the following vowel sound. A second component changed systematically over both hemispheres in response to only consonant changes. A third component systematically changed for the different consonants depending on the following vowel.     

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.     

Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach

The specifications of state space model for some principal component-related models are described, including the independent-group common principal component (CPC) model, the dependent-group CPC model, and principal component-based multivariate analysis of variance. Some derivations are provided to show the equivalence of the state space approach and the existing Wishart-likelihood approach. For each model, a numeric example is used to illustrate the state space approach. In addition, a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions. In order to cope with the nonnormality conditions, the robust standard errors are also computed. Finally, other possible applications of the state space approach are discussed at the end.     

Left hemisphere sensitivity to consonant sounds not displayed by the right hemisphere: electrophysiological correlates

Auditory evoked responses (AER) to a series of consonant-vowel syllables were recorded from frontal, temporal, and parietal scalp locations from 14 right-handed college students. Averaged AERs were submitted to principal components analysis and analysis of variance. Six components of the group's AERs were found to reflect various aspects of the stimulus parameters. One component reflected changes over only the left hemisphere to different consonants. A second component changed systematically over both hemispheres but did not discriminate between all consonants.     

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.     

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.     

Quantitative analysis of human movement synergies: constructive pattern analysis for gait

To record three-dimensional coordinates of the joints from normal human subjects during locomotion, we used a digital motion analysis system (ELITE). Recordings were obtained under several different conditions, which included normal walking and stepping over obstacles. Principal component analysis was used to analyze coordinate data after conversion of the data to segmental angles. This technique gave a stable summary of the redundancy in gait kinematic data in the form of reduced variables (principal components). By modeling the shapes of the phase plots of reduced variables (distortion analysis) and using a limited number of model parameters, good resolution was obtained between subtly different conditions. Hence, it was possible to accurately resolve small distributed changes in gait patterns within subjects. These methods seem particularly suited to longitudinal studies in which relevant movement features are not known a priori. Assumptions and neurophysiological applications are discussed.     

Generalized structured component analysis

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We wish to thank Richard Bagozzi for permitting us to use his organizational identification data and Wynne Chin for providing PLS-Graph 3.0.     

Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

企业员工自我职业生涯管理的结构及关系

在文献研究的基础上 ,通过访谈、开放式问卷等方法 ,确立了企业员工自我职业生涯管理的结构。根据该结构 ,结合问卷及访谈所搜集的自我职业生涯管理活动 ,编制了自我职业生涯管理问卷 (简称ICMQ)。该问卷在177名被试中进行了初步调查 ,结果发现 :尽管该结构主体结构得到了证实 ,但有些方面如职业生涯发展策略比较混乱。在此基础上 ,修订问卷 ,重新选取 13家企业的中低层管理者及技术人员、文职人员进行了测试 ,获得了 4 4 9份有效问卷 ,对问卷的探索性因素分析结果表明 :该问卷是个五因素的结构 ,这 5个因素是职业探索、职业目标和策略确立、继续学习、自我展示和注重关系。为了进一步验证自我职业生涯管理问卷的结构效度 ,并获得问卷的信度和效度指标 ,研究选取了 11家企业进行了调查 ,获得了 399份有效问卷。验证性因素分析结果表明 :自我职业生涯管理是个并列的 5因素结构     

A general latent trait model for response processes

The purpose of the current paper is to propose a general multicomponent latent trait model (GLTM) for response processes. The proposed model combines the linear logistic latent trait (LLTM) with the multicomponent latent trait model (MLTM). As with both LLTM and MLTM, the general multicomponent latent trait model can be used to (1) test hypotheses about the theoretical variables that underlie response difficulty and (2) estimate parameters that describe test items by basic substantive properties. However, GLTM contains both component outcomes and complexity factors in a single model and may be applied to data that neither LLTM nor MLTM can handle. Joint maximum likelihood estimators are presented for the parameters of GLTM and an application to cognitive test items is described.This research was partially supported by the National Institute of Education grant number NIE-6-7-0156 to Susan Embretson (Whitely), principal investigator. However the optinions expressed herein do not necessarily reflect the position or policy of the National Institute of Education, and no official endorsement by the National Institute of Education should be inferred.     

互联网的使用对中老年人生活幸福感的影响

采用2018年中国健康与养老追踪调查数据(CHARLS),运用主成分回归和结构方程模型,探究互联网的使用对中国中老年人生活幸福感的影响。主成分回归的结果显示中老年人互联网使用程度、家庭情况以及其身体状况都会对其生活幸福感产生积极的影响,结构方程模型的结果显示中老年人家庭情况会直接或通过影响其互联网使用程度间接的对其身体状况产生积极的影响,进而提升其生活幸福感。     

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.     

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.     

Principal component analysis with external information on both subjects and variables

A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.The work reported in this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first author. Thanks are due to Jim Ramsay, Haruo Yanai, Henk Kiers, and Shizuhiko Nishisato for their insightful comments on earlier versions of this paper. Jim Ramsay, in particular, suggested the use of the QR decomposition, which simplified the presentation of the paper considerably.