The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

Using Raw VAR Regression Coefficients to Build Networks can be Misleading

Many questions in the behavioral sciences focus on the causal interplay of a number of variables across time. To reveal the dynamic relations between the variables, their (auto- or cross-) regressive effects across time may be inspected by fitting a lag-one vector autoregressive, or VAR(1), model and visualizing the resulting regression coefficients as the edges of a weighted directed network. Usually, the raw VAR(1) regression coefficients are drawn, but we argue that this may yield misleading network figures and characteristics because of two problems. First, the raw regression coefficients are sensitive to scale and variance differences among the variables and therefore may lack comparability, which is needed if one wants to calculate, for example, centrality measures. Second, they only represent the unique direct effects of the variables, which may give a distorted picture when variables correlate strongly. To deal with these problems, we propose to use other VAR(1)-based measures as edges. Specifically, to solve the comparability issue, the standardized VAR(1) regression coefficients can be displayed. Furthermore, relative importance metrics can be computed to include direct as well as shared and indirect effects into the network.     

Coefficients alpha and reliabilities of unrotated and rotated components

It has been shown by Kaiser that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation. In this paper, Kaiser's result is generalized. First, the invariance property is shown to hold for any set of orthogonal components. Next, a similar invariance property is derived for the reliability of any set of components. Both generalizations are established by considering simultaneously optimal weights for components with maximum alpha and with maximum reliability, respectively. A short-cut formula is offered to evaluate the coefficients alpha for orthogonally rotated principal components from rotation weights and eigenvalues of the correlation matrix. Finally, the greatest lower bound to reliability and a weighted version are discussed.Comments by Henk A.L. Kiers and by anonymous referees are gratefully acknowledged.     

Estimating psychological networks and their accuracy: A tutorial paper

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.     

社会网络视角下的同伴关系与心理健康

近年来, 从社会网络视角考察同伴关系与心理健康的相互作用正成为发展心理学和健康心理学研究的热点。研究者多借助整体网和纵向数据, 通过两种作用机制, 即选择过程(selection process) (强调心理和行为变量对社会网络和同伴关系的影响, 如关系的形成、维持和解除)和影响过程(influence process) (强调社会网络和同伴关系对心理和行为变量的影响), 来分析同伴关系与心理健康协同演进的动态过程。实证研究关注的领域集中在青少年健康风险行为(如吸烟、喝酒、药物滥用)和情绪问题(如抑郁、焦虑、孤独感)。未来研究应该注重拓展社会网络的类型和样本、加强理论建构、增加对积极心理和消极关系的研究, 并有望在互联网领域及社会网络的生物学基础等方面取得进展。     

Dealing with Multiple Solutions in Structural Vector Autoregressive Models

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.     

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

粗糙集和神经网络在心理测量中的应用

探讨当因素分析和多元回归方法的使用条件未得到满足时,是否可采用粗糙集方法进行观察变量的精简,以及是否可采用神经网络方法进行预测效度检验。理论分析了粗糙集和神经网络在心理测量中应用的可能性,并运用粗糙集对于人事干部胜任力评估数据进行分析,比较了7种离散化方法和2种约简算法构成的14种组合,发现当采用Manual方法进行离散化、遗传算法进行约简时,能够很好地对观测变量进行精简;运用概率神经网络能够比等级回归方法更好地进行预测效度检验。研究结果表明对于处理心理测量中的非等距变量,粗糙集和神经网络是非常有用的方法     

A Computationally More Efficient and More Accurate Stepwise Approach for Correcting for Sampling Error and Measurement Error

Over the last decade or two, multilevel structural equation modeling (ML-SEM) has become a prominent modeling approach in the social sciences because it allows researchers to correct for sampling and measurement errors and thus to estimate the effects of Level 2 (L2) constructs without bias. Because the latent variable modeling software Mplus uses maximum likelihood (ML) by default, many researchers in the social sciences have applied ML to obtain estimates of L2 regression coefficients. However, one drawback of ML is that covariance matrices of the predictor variables at L2 tend to be degenerate, and thus, estimates of L2 regression coefficients tend to be rather inaccurate when sample sizes are small. In this article, I show how an approach for stabilizing covariance matrices at L2 can be used to obtain more accurate estimates of L2 regression coefficients. A simulation study is conducted to compare the proposed approach with ML, and I illustrate its application with an example from organizational research.     

Assessment of stress-buffering effects of social networks on psychological symptoms in an inner-city elderly population

Social network researchers have been divided into two camps: those who propose that social networks have a direct effect on subsequent psychological symptoms and those who posit a stress-buffering effect as well. Previous research has been limited by rudimentary measures of social interaction and the absence of longitudinal data as well as by different approaches to the assessment of possible buffering effects. In the present study, using 19 social network variables, the authors followed 133 elderly residents of mid-Manhattan SRO hotels for 1 year. Three different methods of determining buffering effects were examined: Dividing the sample into high- and low-stress groups and contrasting differences in percentage variance accounted for by social networks between the two groups; Examining the group as a whole to assess if any Network Variable X Stress interactional terms are significant; Examining the group as a whole to assess whether there is a reduction in the beta value of stress with respect to psychological symptoms when network variables are added to the analysis. Method 1 indicated a direct network effect, but none of the methods indicated a buffering effect. Of clinical relevance was the nonlinearity of the network effects, that is, depending upon a person's stressor level, different network dimensions must be emphasized and strengthened.     

L’évaluation thérapeutique et collaborative : preuves empiriques

This paper covers the empirical research that addressed utility and effectiveness of therapeutic assessment or of its components (i.e., providing individualize feedback to clients). Studies vary in terms of methods and problems addressed but provide the consistent picture of therapeutic assessment as a brief approach which increases process variables related to subsequent treatment and has direct effects of symptoms reduction for a variety of psychological problems. Future directions of studies in this are finally provided.     

CROSS-VALIDATIONAL EVIDENCE ON THE DIMENSIONS OF PROBLEM BEHAVIOR IN THE EARLY GRADES

One hundred forty-seven children in the first through the third grades were rated by their teachers on a behavior problem inventory employed in previous studies. The data were subjected to a principal axis factor analysis and rotated to an oblique position. Congruence coefficients were computed among the twelve factors resulting from the current analysis, and the eight factors extracted in an earlier study. Six of the factor matches were significant at or beyond the .O1 level. Five of these matches had a sufficient number of salient variables common to the two studies. The five dimensions meeting the consideration of significance of congruence across samples and sufficient common salients were termed, in an earlier study, Hyperactivity, Sluggishness, Paranoid Tendencies, Social Withdrawal, and Acting Out. The evidence of the predictive validity of these was briefly discussed.     

Reliability and motor memory

The generalizability framework was employed to estimate variance components and reliability of performance in a positioning task. The subjects (n =70) performed 16 trials at each of three target lengths of 25 cm, 45 cm, and 65 cm. The data were analyzed using a subjects x targets x trials repeated measures ANOVA. Two reliability coefficients were estimated. The first (R) provided an estimate of performance reliability generalized over targets and trials. The second (R') treated targets as a source of true-score variance and hence was generalized over trials alone. Both reliability coefficients were higher for algebraic error than for absolute error, and R1 provided higher reliability estimates than R for both dependent variables. Increasing the number of positioning trials from 2 to 16 at each target length did not appreciably alter either reliability coefficient. The overall low reliability of R appears to compound the dependent variables and statistical power problems associated with short-term motor-memory studies.     

Critical Hopefulness: A Person-Centered Analysis of the Intersection of Cognitive and Emotional Empowerment

Leaders in struggles for social justice agree on the importance and the difficulty of maintaining hopefulness while developing critical awareness of social issues. Research has indicated that the analogous components of psychological empowerment (emotional and cognitive) often do not co-vary across populations. This study used a person-centered analytic approach, latent class analysis, to identify subpopulations of participants (n = 1,322) according to the cognitive and emotional components of psychological empowerment. Four distinct sub-groups emerged: those who were relatively (1) critical but alienated, (2) uncritical but hopeful, (3) uncritical and alienated, or (4) critical and hopeful. These clusters were then examined for demographic differences and relationships with a set of conceptually relevant variables including social capital, psychological sense of community, openness, organizational participation and mental wellbeing. Results shed light on the complexity of empowerment processes and yield implications for ongoing community research and action.     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。     

Accounting for Missing Correlation Coefficients in Fixed-Effects MASEM

Meta-analytic structural equation modeling (MASEM) is increasingly applied to advance theories by synthesizing existing findings. MASEM essentially consists of two stages. In Stage 1, a pooled correlation matrix is estimated based on the reported correlation coefficients in the individual studies. In Stage 2, a structural model (such as a path model) is fitted to explain the pooled correlations. Frequently, the individual studies do not provide all the correlation coefficients between the research variables. In this study, we modify the currently optimal MASEM-method to deal with missing correlation coefficients, and compare its performance with existing methods. This study is the first to evaluate the performance of fixed-effects MASEM methods under different levels of missing correlation coefficients. We found that the often used univariate methods performed very poorly, while the multivariate methods performed well overall.     

Using Principal Components as Auxiliary Variables in Missing Data Estimation

To deal with missing data that arise due to participant nonresponse or attrition, methodologists have recommended an “inclusive” strategy where a large set of auxiliary variables are used to inform the missing data process. In practice, the set of possible auxiliary variables is often too large. We propose using principal components analysis (PCA) to reduce the number of possible auxiliary variables to a manageable number. A series of Monte Carlo simulations compared the performance of the inclusive strategy with eight auxiliary variables (inclusive approach) to the PCA strategy using just one principal component derived from the eight original variables (PCA approach). We examined the influence of four independent variables: magnitude of correlations, rate of missing data, missing data mechanism, and sample size on parameter bias, root mean squared error, and confidence interval coverage. Results indicate that the PCA approach results in unbiased parameter estimates and potentially more accuracy than the inclusive approach. We conclude that using the PCA strategy to reduce the number of auxiliary variables is an effective and practical way to reap the benefits of the inclusive strategy in the presence of many possible auxiliary variables.     

Factorially defined verbal and performance IQs derived from the WISC-R: Patterns of cognitive ability in normal and learning disabled children

The axes of the first two dimensions of a principal components analysis of the normative data of the WISC-R were rotated through 45°. This resulted in two orthogonal continua which were interpreted as describing verbal and nonverbal intelligence respectively. Factor score coefficients were used to calculate Verbal Factorial IQs (VFIQs) and Performance Factorial IQs (PFIQs). In normal children, girls (N=1100) prove to be reliably superior to boys (N=1099) in VFIQ, whereas the reverse is the case for PFIQ. In a large group (N=1050) of learning disabled (LD) children, VFIQ is reliably lower than in normal children, and there is also a reliable decline with age over the years 6–16. The LD boys (N=744) are no different from the LD girls (N=306) in VFIQ. In these LD groups the PFIQ is reliably lower than in the normal group at age 6, but rises to a normal level by age 8. The LD boys, overall, return higher PFIQ scores than the LD girls. These results can be used to evaluate the rival hypotheses of ‘deficit’ vs ‘developmental lag’ as a cause of learning disability.