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。     

一种新的统计方法和研究思路——结构方程建模述评

结构方程建模(SEM)是一种新的统计方法和研究思路,近年来在心理学和社会科学领域的应用日益增多。本文在非数学化的基础上,结合心理学研究实例介绍了SEM的渊源、发展、基本概念、分析过程以及相应的计算机统计软件LI-SREL。本文认为SEM有四大优点:①引进潜变量使研究更为深入,②遵循一般线性模式进行验证型分析,使研究更有意义,③妥善处理多变量间的复杂关系,④模型具有参数不变性。SEM应该引起国内心理学界的重视。     

回归混合模型：方法进展与软件实现

近来以个体为分析对象的方法日益受到研究者的重视, 其中潜类别和潜剖面模型最为流行。研究者在潜类别和潜剖面模型建模时往往需要进一步探讨协变量与潜分组之间的关系(即带有协变量的潜类别模型)。例如, 哪些变量预测个体类别归属, 以及个体的类别归属对结果变量的预测。本文对近年来研究者提出的各种方法进行了回顾和比较。包括当结果变量是分类变量的LTB法; 当结果变量是连续变量时的BCH和稳健三步法。在此基础上, 文章为应用研究者提供了Mplus软件示例, 并在最后对当前研究存在的问题和未来研究趋势进行了简要评价。     

如何描述发展趋势的差异：潜变量混合增长模型

在追踪研究中,研究者不仅关心某一特质随时间的发展趋势,而且关注个体之间发展趋势的差异及其存在差异的原因。在总体发展同质的情形下,多层线性模型和潜变量增长曲线模型为解决这一问题提供了切实有效的方法。但是如果所研究的总体本身不同质,就需要一种能够描述总体中不同质子总体的不同发展特点的方法。该文简要介绍了一种能够描述不同群体不同发展趋势特征的统计模型——潜变量混合增长模型,并通过一个实际例子介绍了这一方法的应用过程,同时说明了潜变量混合增长模型与多层线性模型和潜变量增长曲线模型之间的关系     

潜变量交互效应分析方法

简要回顾了分析显变量交互效应的常用方法。详细讨论了目前分析潜变量交互效应的主要方法,包括用潜变量的因子得分做回归分析、分组线性结构方程模型分析、加入乘积项的结构方程模型分析和两步最小二乘回归分析,并比较和评价了这些方法的优缺点。最后归纳了潜变量交互效应分析方法的研究趋势,并介绍了新近进展(包括LMS方法和GAPI方法)。     

新世纪20年国内测验信度研究

随着验证性因子分析模型的应用, 信度研究进入了崭新的发展阶段。新世纪前20年国内有关测验信度的研究有三条发展主线。一是基于验证性因子模型的信度发展, 包括同质性系数、合成信度、最大信度等; 二是数据类型的拓展, 包括两水平和追踪数据的信度; 三是信度用途的拓展, 如评分者信度、编码者信度等。对于通常的测验(题目之间的测量误差不相关), 如果α系数够高, 信度就够高; 否则使用合成信度。如果一个统计模型中所有变量的合成信度都很高(超过0.95), 使用显变量建模与使用潜变量建模的结果差别不大; 否则, 使用潜变量建模较好。     

心理研究中引入贝叶斯统计推断的必要性、应用思路与领域

本文从科学范式演变和概率统计推断特征分析出发,就贝叶斯统计推断引入心理学的必要性、怎么应用、在哪些领域应用集中进行了论述。首先在分析科学范式演进各阶段统计推断任务需要、经典的频率概率统计推断不足基础上,得出科学范式处于危机和革命阶段时需要对相关理论做可信度检验。然后,在介绍贝叶斯定理及其统计推断的基础上,进一步分析了贝叶斯推断能解决理论可信度的多种假设检验情景。最后本文还就贝叶斯统计推断在心理学理论争鸣与建构、心理技术产品开发与评估具体领域应用做了分析。     

潜变量交互效应建模: 告别均值结构

潜变量交互效应建模研究近年来有了长足的发展, 但模型中被认为不可缺少的均值结构往往让实际应用工作者却步。本文首先分析了潜变量交互效应模型中均值结构产生的根源; 然后讨论了指标变换与均值结构的关系; 接着提出了一个均值为零的潜变量交互结构, 所建立的模型不需要均值结构, 却不会改变主效应和交互效应等参数; 最后用模拟例子对无均值结构和有均值结构的两种模型的参数估计进行了比较, 结果符合理论预期, 困扰人们多年的均值结构问题从此可以终结。     

心理研究引入贝叶斯统计推断的必要性、应用思路与领域

本文从科学范式演变和概率统计推断特征分析出发,就贝叶斯统计推断引入心理学的必要性、怎么应用、在哪些领域应用进行了论述。首先在分析科学范式演进各阶段统计推断任务需要、经典的频率概率统计推断不足基础上,得出科学范式处于危机和革命阶段时需要对相关理论做可信度检验。然后,在介绍贝叶斯定理及其统计推断的基础上,进一步分析了贝叶斯推断能解决理论可信度的多种假设检验情景。最后本文还就贝叶斯统计推断在心理学理论争鸣与建构、心理技术产品开发与评估具体领域应用做了分析。     

第二类有中介的调节模型

心理学研究常用有中介的调节模型揭示调节作用通过中介变量间接实现的现象。介绍了第二类有中介的调节模型(meMO-II)的概念及优势; 将meMO-II与其它中介调节混合模型进行了辨析; 给出了meMO-II的建模方法和分析流程, 并用一个实例演示; 介绍了基于潜变量的meMO-II的分析方法、meMO-II建模方法的新进展以及meMO-II的变式。研究有助于推动调节机制研究的发展。     

Information-theoretic latent distribution modeling: distinguishing discrete and continuous latent variable models

Distinguishing between discrete and continuous latent variable distributions has become increasingly important in numerous domains of behavioral science. Here, the authors explore an information-theoretic approach to latent distribution modeling, in which the ability of latent distribution models to represent statistical information in observed data is emphasized. The authors conclude that loss of statistical information with a decrease in the number of latent values provides an attractive basis for comparing discrete and continuous latent variable models. Theoretical considerations as well as the results of 2 Monte Carlo simulations indicate that information theory provides a sound basis for modeling latent distributions and distinguishing between discrete and continuous latent variable models in particular.     

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

Bayesian Semiparametric Structural Equation Models with Latent Variables

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.     

The design and analysis of state-trace experiments

State-trace analysis (Bamber, 1979) addresses a question of interest in many areas of psychological research: Does 1 or more than 1 latent (i.e., not directly observed) variable mediate an interaction between 2 experimental manipulations? There is little guidance available on how to design an experiment suited to state-trace analysis, despite its increasing use, and existing statistical methods for state-trace analysis are problematic. We provide a framework for designing and refining a state-trace experiment and statistical procedures for the analysis of accuracy data using Klugkist, Kato, and Hoijtink's (2005) method of estimating Bayes factors. The statistical procedures provide estimates of the evidence favoring 1 versus more than 1 latent variable, as well as evidence that can be used to refine experimental methodology.     

Models with discrete latent variables for analysis of categorical data: A framework and a MATLAB MDLV toolbox

Studies in the social and behavioral sciences often involve categorical data, such as ratings, and define latent constructs underlying the research issues as being discrete. In this article, models with discrete latent variables (MDLV) for the analysis of categorical data are grouped into four families, defined in terms of two dimensions (time and sampling) of the data structure. A MATLAB toolbox (referred to as the “MDLV toolbox”) was developed for applying these models in practical studies. For each family of models, model representations and the statistical assumptions underlying the models are discussed. The functions of the toolbox are demonstrated by fitting these models to empirical data from the European Values Study. The purpose of this article is to offer a framework of discrete latent variable models for data analysis, and to develop the MDLV toolbox for use in estimating each model under this framework. With this accessible tool, the application of data modeling with discrete latent variables becomes feasible for a broad range of empirical studies.     

有调节的多层中介效应分析

多层中介和多层调节效应分析在社科领域已常有应用,但如果将多层中介和调节整合在一起,可以产生2（多层中介类型）×2（调节变量的层次）×3（调节的中介路径）共12种有调节的多层中介模型。面对有调节的多层中介效应分析,研究者往往束手无策。详述了基于多层线性模型的12种有调节的多层中介的分析方法和基于多层结构方程模型的4类有调节的多层中介分析方法,包括正交分割法,随机系数预测法,潜调节结构方程法和贝叶斯合理值法。这四类方法的核心议题在于如何处理潜调节项。当样本量足够大时,建议选择潜调节结构方程法;当样本量不足时,建议选择贝叶斯合理值法。随后用一个实际例子演示如何进行有调节的多层中介效应分析并有相应的Mplus程序。最后展望了有调节的多层中介效应分析研究的拓展方向。     

A comparison of methods for estimating quadratic effects in nonlinear structural equation models

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data.     

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.