Multiple Group Analysis in Multilevel Structural Equation Model Across Level 1 Groups

This article introduces and evaluates a procedure for conducting multiple group analysis in multilevel structural equation model across Level 1 groups (MG1-MSEM; Ryu, 2014). When group membership is at Level 1, multiple group analysis raises two issues that cannot be solved by a simple extension of the standard multiple group analysis in single-level structural equation model. First, the Level 2 data are not independent between Level 1 groups. Second, the standard procedure fails to take into account the dependency between members of different Level 1 groups within the same cluster. The MG1-MSEM approach provides solutions to these problems. In MG1-MSEM, the Level 1 mean structure is necessary to represent the differences between Level 1 groups within clusters. The Level 2 model is the same regardless of Level 1 group membership. A simulation study examined the performance of MUML (Muthén's maximum likelihood) estimation in MG1-MSEM. The MG1-MSEM approach is illustrated for both a multilevel path model and a multilevel factor model using empirical data sets.     

Equivalency for Father and Mother Ratings of the ADHD Symptoms

The study used multiple-group confirmatory factor analysis (CFA) and multiple indicators multiple causes (MIMIC) procedures to examine the measurement and construct equivalencies for father and mother ratings of ADHD symptoms, recoded as binary scores. Fathers (N = 387) and mothers (N = 411) rated their primary school-aged children on the Disruptive Behavior Rating Scale (Barkley & Murphy, 1998). For the multiple-group CFA analyses, the results involving differences in practical fit indices supported full measurement and construct equivalencies, whereas the chi-square difference test showed lack of equivalency in five symptoms for factor loadings, four symptoms for error variance, and the variance and mean scores for the hyperactivity-impulsivity factor. For the MIMIC analyses, six symptoms lacked equivalency for thresholds. These findings extend existing data in this area. The theoretical, psychometric and clinical implications of the findings are discussed.     

Single and Multiple Ability Estimation in the SEM Framework: A Noninformative Bayesian Estimation Approach

Latent variable models with many categorical items and multiple latent constructs result in many dimensions of numerical integration, and the traditional frequentist estimation approach, such as maximum likelihood (ML), tends to fail due to model complexity. In such cases, Bayesian estimation with diffuse priors can be used as a viable alternative to ML estimation. This study compares the performance of Bayesian estimation with ML estimation in estimating single or multiple ability factors across 2 types of measurement models in the structural equation modeling framework: a multidimensional item response theory (MIRT) model and a multiple-indicator multiple-cause (MIMIC) model. A Monte Carlo simulation study demonstrates that Bayesian estimation with diffuse priors, under various conditions, produces results quite comparable with ML estimation in the single- and multilevel MIRT and MIMIC models. Additionally, an empirical example utilizing the Multistate Bar Examination is provided to compare the practical utility of the MIRT and MIMIC models. Structural relationships among the ability factors, covariates, and a binary outcome variable are investigated through the single- and multilevel measurement models. The article concludes with a summary of the relative advantages of Bayesian estimation over ML estimation in MIRT and MIMIC models and suggests strategies for implementing these methods.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

Children's Depression Inventory: invariance across children and adolescents with and without depressive disorders

In the study, the authors examined the measurement (configural, factor loadings, thresholds, and error variances) and structural (factor variances, covariances, and mean scores) invariance of the Children's Depression Inventory (CDI; Kovacs, 1992) across ratings provided by clinic-referred children and adolescents with (N = 383) and without (N = 412) depressive disorders. Multiple-group confirmatory factor analysis of the Craighead, Smucker, Craighead, and Ilardi (1998) CDI model supported full measurement invariance and invariance for structural variances and covariances. Invariance for thresholds was also supported by multiple indicators multiple causes (MIMIC) procedures that controlled for the effects of age; sex; and the presence or absence of anxiety disorders, attention-deficit/hyperactivity disorder, and oppositional defiant/conduct disorders. The MIMIC analyses showed that for latent mean scores, the group with depressive disorders had higher scores, with at least medium effect sizes, for Self-Deprecation and Biological Dysregulation. The theoretical, psychometric, and clinical implications of the findings are discussed.     

Latent variable modeling in heterogeneous populations

Common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values. This article describes the problem and gives an overview of methodology that can address heterogeneity. Artificial examples of mixtures are given, where if the mixture is not recognized, strongly distorted results occur. MIMIC structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple-group analysis. Other useful methods instead take a random effects approach, describing heterogeneity in terms of random parameter variation across groups. These random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data. Examples are drawn from educational achievement testing, psychopathology, and sociology of education. Estimation is carried out by the LISCOMP program.Presidential address delivered at the Psychometric Society meetings in Los Angeles, USA and Leuven, Belgium, July 1989. The research was supported by Grant No. SES-8821668 from the National Science Foundation and by Grant No. OERI-G-86-003 from the Office for Educational Research and Improvement, Department of Education. I thank Leigh Burstein, Mike Hollis, Linda Muthén, and Albert Satorra for helpful discussions and Tammy Tam, Jin-Wen Yang, Suk-Woo Kim, and Lynn Short for computational assistance. Designs were created by Arlette Collier, Rita Ling and Jennifer Edic-Bryant.     

The Factor Structure and Measurement Invariance of the Daily Spiritual Experiences Scale

The current study has two main goals: (a) to identify a factor structure of the Daily Spiritual Experiences Scale (DSES) on a large archival data, collected from 1,325 adults in the United States (709 women, 616 men) by the U.S. General Social Survey in 2004 and (b) to examine the measurement invariance of the 16 DSES items between women and men in the same data to see whether any of the items are favoring or biased toward either women or men. The one-factor confirmatory factor analysis (CFA) model fit our data better than the two-factor CFA models because of high correlations between the two factors (r > .90). The fit of the one-factor CFA to our sample data was improved when we specified seven correlated residuals suggested by overlapping item content and large modification indices. The ensuing measurement invariance testing of the one-factor CFA model with seven correlated residuals supported full measurement invariance of factor loadings, thresholds, and residual variances, as well as factor variances between the women and the men. Yet the factor mean for the women was .841 units (Cohen’s d = .496) higher than it was for the men, indicating that higher levels of daily spiritual experiences for women reported in gender comparison studies in the United States are not likely to be an artifact of bias in the questionnaire.     

Generalized full-information item bifactor analysis

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single-group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than 1 group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker's (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood requires only 2-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy.     

Confirmatory Measurement Model Comparisons Using Latent Means

Confirmatory factor analysis (CFA) is often used to verify measurement models derived from classical test theory: the parallel, tau-equivalent, and congeneric test models. In this application, CFA is traditionally applied to the observed covariance or correlation matrix, ignoring the observed mean structure. But CFA is easily extended to allow nonzero observed and latent means. The use of CFA with nonzero latent means in testing six measurement models derived from classical test theory is discussed. Three of these models have not been addressed previously in the context of CFA. The implications of the six models for observed mean and covariance structures are fully described. Three examples of the use of CFA in testing these models are presented. Some advantages and limitations in using CFA with nonzero latent means to verify classical measurement models are discussed.     

基于多层验证性因素分析的各种信度系数方法

近年来,心理学研究的复现性受到广泛关注,许多实证研究难以重复验证,信度较低。大量研究使用多层技术,但只报告整体信度,导致研究可重复危机。基于各种信度系数和验证性因素分析的理论,以二层模型为例,总结多层信度计算方法,通过文献综述检索应用情况,并用MPLUS进行实例演示,最后讨论单层信度估计存在的偏差及分层估计的好处。总之,对多层数据进行分层信度估计是很有必要的,可消除因测量工具缺乏信度而导致的研究不可重复。     

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。     

Multilevel Mixture Factor Models

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs) have in common that—as in multilevel regression analysis—variation at the higher level is modeled using continuous random effects. In this article, we present an alternative multilevel extension of factor analysis which we call the Multilevel Mixture Factor Model (MMFM). It is based on the assumption that higher level units belong to latent classes that differ in terms of the parameters of the factor model specified for the lower level units. We demonstrate the added value of MMFM compared with MFM, both from a theoretical and applied perspective, and we illustrate the complementarity of the two approaches with an empirical application on students' satisfaction with the University of Florence. The multilevel aspect of this application is that students are nested within study programs, which makes it possible to cluster these programs based on their differences in students' satisfaction.     

Multilevel analysis of matching behavior

Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within‐subject and between‐subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.     

Cool and Hot Aspects of Executive Function in Childhood Obsessive-Compulsive Disorder

Aspects of executive functioning (EF) have been put forward as endophenotypes in obsessive- compulsive disorder (OCD) and meta-analyses support EF underperformance in adult samples. Childhood-onset OCD has been suggested to constitute a separate neurodevelopmental subtype of the disorder but studies on neuropsychological functioning in childhood OCD are limited. The aim of the present study was to investigate performance-based EF in pediatric OCD using observed and latent variable analyses. A case-control design was applied including 50 unmedicated children and adolescents with OCD aged 7–17 years of which 70% were female, 50 pairwise age and gender matched non-psychiatric controls (NP) and 38 children and adolescents with mixed anxiety disorders (MA). Participants underwent structured diagnostic interviews and assessment with a battery encompassing cool EF tasks of working memory, set shifting, inhibition, and planning, and hot EF tasks of decision making and dot probe paradigm affective interference. First, groups were compared on observed variables with multilevel mixed-effects linear regression and analysis of variance. Then the latent structure of cool EF was tested with confirmatory factor analysis (CFA) and groups were compared on the CFA scores. No significant differences between groups appeared on individual cool EF tasks. On the hot EF tasks the OCD group displayed significant interference effects on the dot probe paradigm OCD-specific stimuli relative to NP, but not compared to MA and no group differences emerged for decision making. In the CFA a one-factor solution showed best fit, but the groups did not differ significantly on the resulting latent variable. The present study does not support cool or hot EF impairments in childhood OCD.     

贝叶斯多组比较——渐近测量不变性

在行为科学研究领域中,检验测量工具的测量不变性是进行群体差异比较的前提。目前,多组验证性因子分析(多组CFA)方法被广泛用于检验测量不变性,但是它对跨组等值的限制过于严格,在实际应用中常常存在大量局限。贝叶斯渐近测量不变性方法基于贝叶斯思想的优良特性,放宽了传统多组CFA方法对跨组差异的严格限制,避免了传统方法的问题,具有较高的应用价值。文章详细介绍了贝叶斯渐近测量不变性方法的原理及优势,同时通过实例展示了渐近测量不变性方法在Mplus软件中的具体分析过程。     

Introduction

A dynamic model of affect suggests that positive and negative affect (PA and NA) are normally relatively independent of one another, whereas the heightened apprehensiveness and narrowed cognitive attention in persons with anxiety may contribute to a more unidimensional affect structure. This possibility was examined in a sample of 230 patients seeking treatment for anxiety and depressive disorders in the Netherlands. Two methods, a multiple-group confirmatory factor analysis (CFA) and Fisher's z test of correlations, were used to test these predicted relationships within a sample of persons diagnosed with either a depressive or an anxiety disorder. Both methods supported these predictions, with the depressed group exhibiting relatively independent PA and NA while the anxious group's affects were more strongly inversely correlated.     

A Multilevel Contextual Model of Family Conflict and Deviance

This paper presents a multiple-group multivariate hierarchical specification of family problem behaviors across ethnicities using structural equation modeling techniques which explicitly model the individual-level and family-level covariance matrices in familial problem behavior. Analyses were conducted across White and African American ethnic groups. The sample (N = 1,168; 647 White and 521 African Americans) comprised children and their parents from 392 families. In addition to relations between family conflict and deviant behaviors, covariates were included at each level of analysis: neighborhood desirability at the family (between) level, and age and gender at the individual (within) level. At the between level, neighborhood desirability influenced family conflict and family conflict influenced family levels of deviance. At the within level, conflict was significantly related to individual levels of deviance. Discussion focuses on the substantive results as well as the application of multilevel analyses to contextual influences of family problem behavior.     

Measuring QoL with SF-36 in Older Americans with TBI

This study demonstrated reliability and factor structure of the Medical Outcomes Study Short-Form Health Survey (SF-36) among older Americans with Traumatic brain injury (TBI), and evaluated effects of injury severity and race on SF-36's items and latent domains. A representative sample of 654 older, racially diverse patients with TBI was selected from the South Carolina Traumatic Brain Injury Follow-up Registry. Reliability and factor structure of SF-36 were evaluated using Cronbach’s alpha and confirmatory factor analysis (CFA). Multiple-indicator multiple-causes (MIMIC) models were used to study effects of injury severity and race on items (differential item functioning, DIF) and latent domains (population heterogeneity) of SF-36. SF-36 was reliable and its current eightfactor structure was confirmed. While TBI severity did not impact latent domain scores of SF-36, race did. Blacks had higher vitality and lower role-emotional scores than whites. The measurement model was invariant to injury severity and race (free of DIF), and DIF did not contribute to the differences of vitality and role-emotional between black and white older TBI patients. SF-36 was valid to measure quality of life (OoL) after TBI in racially diverse elderly population. Blacks tend to assert to strong coping behaviors in the presence of physical stress while admitting low performance due to emotional stress. In QoL research where the primary outcomes are usually composite scores from instruments, MIMIC models have advantages over conventional multivariable regression models in testing the validity of the instruments and assessing covariate effects on latent traits of instruments while controlling for DIF effects.     

The Assessment of Dimensionality for Use in Item Response Theory

The application of item response theory (IRT) models requires the identification of the data's dimensionality. A popular method for determining the number of latent dimensions is the factor analysis of a correlation matrix. Unlike factor analysis, which is based on a linear model, IRT assumes a nonlinear relationship between item performance and ability. Because multidimensional scaling (MDS) assumes a monotonic relationship this method may be useful for the assessment of a data set's dimensionality for use with IRT models. This study compared MDS, exploratory and confirmatory factor analysis (EFA and CFA, respectively) in the assessment of the dimensionality of data sets which had been generated to be either one- or two-dimensional. In addition, the data sets differed in the degree of interdimensional correlation and in the number of items defining a dimension. Results showed that MDS and CFA were able to correctly identify the number of latent dimensions for all data sets. In general, EFA was able to correctly identify the data's dimensionality, except for data whose interdimensional correlation was high.     

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.