Dynamic GSCA (Generalized Structured Component Analysis) with Applications to the Analysis of Effective Connectivity in Functional Neuroimaging Data

We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also incorporates direct and modulating effects of input variables on specific latent variables and on connections between latent variables, respectively. An alternating least square (ALS) algorithm is developed for parameter estimation. An improved bootstrap method called a modified moving block bootstrap method is used to assess reliability of parameter estimates, which deals with time dependence between consecutive observations effectively. We analyze synthetic and real data to illustrate the feasibility of the proposed method.     

Multilevel Dynamic Generalized Structured Component Analysis for Brain Connectivity Analysis in Functional Neuroimaging Data

We extend dynamic generalized structured component analysis (GSCA) to enhance its data-analytic capability in structural equation modeling of multi-subject time series data. Time series data of multiple subjects are typically hierarchically structured, where time points are nested within subjects who are in turn nested within a group. The proposed approach, named multilevel dynamic GSCA, accommodates the nested structure in time series data. Explicitly taking the nested structure into account, the proposed method allows investigating subject-wise variability of the loadings and path coefficients by looking at the variance estimates of the corresponding random effects, as well as fixed loadings between observed and latent variables and fixed path coefficients between latent variables. We demonstrate the effectiveness of the proposed approach by applying the method to the multi-subject functional neuroimaging data for brain connectivity analysis, where time series data-level measurements are nested within subjects.     

Regularized Generalized Structured Component Analysis

Generalized structured component analysis (GSCA) has been proposed as a component-based approach to structural equation modeling. In practice, GSCA may suffer from multi-collinearity, i.e., high correlations among exogenous variables. GSCA has yet no remedy for this problem. Thus, a regularized extension of GSCA is proposed that integrates a ridge type of regularization into GSCA in a unified framework, thereby enabling to handle multi-collinearity problems effectively. An alternating regularized least squares algorithm is developed for parameter estimation. A Monte Carlo simulation study is conducted to investigate the performance of the proposed method as compared to its non-regularized counterpart. An application is also presented to demonstrate the empirical usefulness of the proposed method.     

Generalized Structured Component Analysis with Latent Interactions

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling. In practice, researchers may often be interested in examining the interaction effects of latent variables. However, GSCA has been geared only for the specification and testing of the main effects of variables. Thus, an extension of GSCA is proposed to effectively deal with various types of interactions among latent variables. In the proposed method, a latent interaction is defined as a product of interacting latent variables. As a result, this method does not require the construction of additional indicators for latent interactions. Moreover, it can easily accommodate both exogenous and endogenous latent interactions. An alternating least-squares algorithm is developed to minimize a single optimization criterion for parameter estimation. A Monte Carlo simulation study is conducted to investigate the parameter recovery capability of the proposed method. An application is also presented to demonstrate the empirical usefulness of the proposed method.     

Bayesian generalized structured component analysis

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modelling, which adopts components of observed variables as proxies for latent variables and examines directional relationships among latent and observed variables. GSCA has been extended to deal with a wider range of data types, including discrete, multilevel or intensive longitudinal data, as well as to accommodate a greater variety of complex analyses such as latent moderation analysis, the capturing of cluster-level heterogeneity, and regularized analysis. To date, however, there has been no attempt to generalize the scope of GSCA into the Bayesian framework. In this paper, a novel extension of GSCA, called BGSCA, is proposed that estimates parameters within the Bayesian framework. BGSCA can be more attractive than the original GSCA for various reasons. For example, it can infer the probability distributions of random parameters, account for error variances in the measurement model, provide additional fit measures for model assessment and comparison from the Bayesian perspectives, and incorporate external information on parameters, which may be obtainable from past research, expert opinions, subjective beliefs or knowledge on the parameters. We utilize a Markov chain Monte Carlo method, the Gibbs sampler, to update the posterior distributions for the parameters of BGSCA. We conduct a simulation study to evaluate the performance of BGSCA. We also apply BGSCA to real data to demonstrate its empirical usefulness.     

Structural Equation Modeling in the Communication Sciences, 1995–2000

Structural equation modeling (SEM) is a viable multivariate tool used by communication researchers for the past quarter century. Building off Cappella (1975) as well as McPhee and Babrow (1987), this study summarizes the use of this technique from 1995–2000 in 37 communication‐based academic journals. We identify and critically assess 3 unique methods for testing structural relationships via SEM in terms of the specification, estimation, and evaluation of their respective structural equation models. We provide general guidelines for the use of SEM and make recommendations concerning latent variable models, sample size, reporting parameter estimates, model fit statistics, cross‐sectional data, univariate normality, cross‐validation, nonrecursive modeling, and the decomposition of effects (direct, indirect, and total).     

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.     

无均值结构的潜变量交互效应模型的标准化估计

潜变量交互效应建模研究近年来有两项重要进展, 一是提出了潜变量交互效应模型的标准化估计及其计算公式; 二是发现无均值结构模型可以取代传统的有均值结构模型, 建模大为简化。但标准化估计是在传统的有均值结构模型中建立的, 在简化的模型中同样适用吗？本文在无均值结构模型的框架内, 给出了潜变量交互效应模型的标准化形式、计算公式和建模步骤, 并通过模拟研究比较了极大似然和广义最小二乘两种估计方法、配对乘积指标和全部乘积指标两种指标类型, 结果表明, 在计算交互效应的标准化估计时, 应当使用配对乘积指标建模, 并且首选极大似然估计。     

A comparative evaluation of factor- and component-based structural equation modelling approaches under (in)correct construct representations

Structural equation modelling (SEM) has evolved into two domains, factor-based and component-based, dependent on whether constructs are statistically represented as common factors or components. The two SEM domains are conceptually distinct, each assuming their own population models with either of the statistical construct proxies, and statistical SEM approaches should be used for estimating models whose construct representations correspond to what they assume. However, SEM approaches have often been evaluated and compared only under population factor models, providing misleading conclusions about their relative performance. This is partly because population component models and their relationships have not been clearly formulated. Also, it is of fundamental importance to examine how robust SEM approaches can be to potential misrepresentation of constructs because researchers may often lack clear theories to determine whether a factor or component is more representative of a given construct. Addressing these issues, this study begins by clarifying several population component models and their relationships and then provides a comprehensive evaluation of four SEM approaches – the maximum likelihood approach and factor score regression for factor-based SEM as well as generalized structured component analysis (GSCA) and partial least squares path modelling (PLSPM) for component-based SEM – under various experimental conditions. We confirm that the factor-based SEM approaches should be preferred for estimating factor models, whereas the component-based SEM approaches should be chosen for component models. Importantly, the component-based approaches are generally more robust to construct misrepresentation than the factor-based ones. Of the component-based approaches, GSCA should be chosen over PLSPM, regardless of whether or not constructs are misrepresented.     

结构方程模型统计检验力分析：原理与方法

结构方程模型是心理学、管理学、社会学等学科中重要的统计工具之一。然而, 大量使用结构方程模型的研究忽视了对该方法的统计检验力进行必要的分析和报告, 在一定程度上降低了这些研究的结果的证明效力。结构方程模型的统计检验力分析方法主要有Satorra-Saris法、MacCallum法与Monte Carlo法三类。其中Satorra-Saris法适用于备择模型清晰、检验对象相对简单、检验方法基于χ²分布的情形; MacCallum法适用于基于χ²分布的模型拟合检验且备择模型不明的情形; Monte Carlo法适用于检验对象相对复杂、采用模拟或重抽样方法进行检验的情形。在实际应用中, 研究者应当首先判断检验的目的、方法以及是否有明确的备择模型, 并根据这些信息选择具体的分析方法。     

结构方程模型拟合评鉴：整体拟合、内部拟合与复核效度检验

该文主要介绍了评价和鉴定结构方程中构建的模型与数据拟合程度的三个方面：整体拟合、内部拟合及复核效度检验.整体拟合评鉴主要是结合拟合指数,当拟合指数处于临界值时,应同时参照其他检验结果并根据模型构建的理论依据进行综合判断;内部拟合从项目质量检验、测验信度、平均变异萃取量和效度四个角度进行检验;复核效度检验在多样本分析中可分为宽松复核、温和复核和严格复核,但如果为研究样本所限,可以通过ECVI来实现.     

潜变量交互效应模型标准化估计中的检验问题

讨论了潜变量交互效应模型是否能直接用统计软件输出的原始估计的t值对模型的标准化估计进行检验的问题,详细介绍了标准化估计的t值计算及其难点,用Bootstrap方法算出标准化估计的标准误和相应的t值（记为t_bs）,并将其与原始估计的t值比较.结果发现,当原始估计t值超过3时,无论用t值还是用t_ bs检验,结果都是显著,即可以使用t值进行检验.而当t值不超过3时,与t_bs很接近,也可以用t值检验,但t值在临界值附近（例如1.5 ～2.5）时,最好还是使用Bootstrap法计算t_bs进行检验.     

Bootstrap scree tests: A Monte Carlo simulation and applications to published data

A non‐parametric procedure for Cattell's scree test is proposed, using the bootstrap method. Bentler and Yuan developed parametric tests for the linear trend of scree eigenvalues in principal component analysis. The proposed method is for cases where parametric assumptions are not realistic. We define the break in the scree trend in several ways, based on linear slopes defined with two or three consecutive eigenvalues, or all eigenvalues after the k largest. The resulting scree test statistics are evaluated under various data conditions, among which Gorsuch and Nelson's bootstrap CNG performs best and is reasonably consistent and efficient under leptokurtic and skewed conditions. We also examine the bias‐corrected and accelerated bootstrap method for these statistics, and the bias correction is found to be too unstable to be useful. Using seven published data sets which Bentler and Yuan analysed, we compare the bootstrap approach to the scree test with the parametric linear trend test.     

Assessing program effects in the presence of treatment-baseline interactions: a latent curve approach

Methods for assessing treatment effects of longitudinal randomized intervention are considered. The focus is on modeling the nonlinear relationship between treatment effects and baseline often observed in prevention programs designed for at-risk populations. Piecewise linear growth modeling was used to study treatment effects during the different periods of development. A multistep multiple-group analysis procedure is proposed for assessing treatment effects in the presence of nonlinear treatment-baseline interactions. Standard errors of the estimates from this multistep procedure were obtained using a bootstrap approach. The methods are illustrated using data from the Johns Hopkins Prevention Research Center involving an intervention aimed at improving classroom behavior.     

Structural Equation Modeling of Social Networks: Specification,Estimation, and Application

Psychologists are interested in whether friends and couples share similar personalities or not. However, no statistical models are readily available to test the association between personalities and social relations in the literature. In this study, we develop a statistical model for analyzing social network data with the latent personality traits as covariates. Because the model contains a measurement model for the latent traits and a structural model for the relationship between the network and latent traits, we discuss it under the general framework of structural equation modeling (SEM). In our model, the structural relation between the latent variable(s) and the outcome variable is no longer linear or generalized linear. To obtain model parameter estimates, we propose to use a two-stage maximum likelihood (ML) procedure. This modeling framework is evaluated through a simulation study under representative conditions that would be found in social network data. Its usefulness is then demonstrated through an empirical application to a college friendship network.     

Distance stability analysis in multidimensional scaling using the jackknife method

Stability or sensitivity analysis is an important topic in data analysis that has received little attention in the application of multidimensional scaling (MDS), for which the only available approaches are given in terms of a coordinate‐based analytical jackknife methodology. Although in MDS the prime interest is in assessing the stability of the points in the configuration, this methodology may be influenced by imprecisions resulting from the inherently necessary Procrustes method. This paper proposes an analytical distance‐based jackknife procedure to study stability and cross‐validation in MDS in terms of the jackknife distances, which is not influenced by the Procrustes method. For each object, the corresponding jackknife estimated points are considered as naturally clustered points, and stability and cross‐validation are analysed in terms of the MDS distances arising from the jackknife procedure, on the basis of a weighted cluster‐MDS algorithm. A jackknife‐relevant configuration is also proposed for cross‐validation in terms of coordinates, in a cluster‐MDS framework.     

Comparing standardized coefficients in structural equation modeling: a model reparameterization approach

We propose a two-stage method for comparing standardized coefficients in structural equation modeling (SEM). At stage 1, we transform the original model of interest into the standardized model by model reparameterization, so that the model parameters appearing in the standardized model are equivalent to the standardized parameters of the original model. At stage 2, we impose appropriate linear equality constraints on the standardized model and use a likelihood ratio test to make statistical inferences about the equality of standardized coefficients. Unlike other existing methods for comparing standardized coefficients, the proposed method does not require specific modeling features (e.g., specification of nonlinear constraints), which are available only in certain SEM software programs. Moreover, this method allows researchers to compare two or more standardized coefficients simultaneously in a standard and convenient way. Three real examples are given to illustrate the proposed method, using EQS, a popular SEM software program. Results show that the proposed method performs satisfactorily for testing the equality of standardized coefficients.     

Testing Process Factor Analysis Models Using the Parametric Bootstrap

Process factor analysis (PFA) is a latent variable model for intensive longitudinal data. It combines P-technique factor analysis and time series analysis. The goodness-of-fit test in PFA is currently unavailable. In the paper, we propose a parametric bootstrap method for assessing model fit in PFA. We illustrate the test with an empirical data set in which 22 participants rated their effects everyday over a period of 90 days. We also explore Type I error and power of the parametric bootstrap test with simulated data.