Multilevel IRT using dichotomous and polytomous response data

A structural multilevel model is presented where some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal polytomous response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure Markov chain Monte Carlo (MCMC), to estimate all parameters simultaneously is presented. It is shown that certain model checks and model comparisons can be done using the MCMC output. The techniques are illustrated using a simulation study and an application involving students' achievements on a mathematics test and test results regarding management characteristics of teachers and principles.     

Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood

Pairwise maximum likelihood (PML) estimation is a promising method for multilevel models with discrete responses. Multilevel models take into account that units within a cluster tend to be more alike than units from different clusters. The pairwise likelihood is then obtained as the product of bivariate likelihoods for all within-cluster pairs of units and items. In this study, we investigate the PML estimation method with computationally intensive multilevel random intercept and random slope structural equation models (SEM) in discrete data. In pursuing this, we first reconsidered the general ‘wide format’ (WF) approach for SEM models and then extend the WF approach with random slopes. In a small simulation study we the determine accuracy and efficiency of the PML estimation method by varying the sample size (250, 500, 1000, 2000), response scales (two-point, four-point), and data-generating model (mediation model with three random slopes, factor model with one and two random slopes). Overall, results show that the PML estimation method is capable of estimating computationally intensive random intercept and random slopes multilevel models in the SEM framework with discrete data and many (six or more) latent variables with satisfactory accuracy and efficiency. However, the condition with 250 clusters combined with a two-point response scale shows more bias.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data

Multilevel data often cannot be represented by the strict form of hierarchy typically assumed in multilevel modeling. A common example is the case in which subjects change their group membership in longitudinal studies (e.g., students transfer schools; employees transition between different departments). In this study, cross-classified and multiple membership models for multilevel and longitudinal item response data (CCMM-MLIRD) are developed to incorporate such mobility, focusing on students' school change in large-scale longitudinal studies. Furthermore, we investigate the effect of incorrectly modeling school membership in the analysis of multilevel and longitudinal item response data. Two types of school mobility are described, and corresponding models are specified. Results of the simulation studies suggested that appropriate modeling of the two types of school mobility using the CCMM-MLIRD yielded good recovery of the parameters and improvement over models that did not incorporate mobility properly. In addition, the consequences of incorrectly modeling the school effects on the variance estimates of the random effects and the standard errors of the fixed effects depended upon mobility patterns and model specifications. Two sets of large-scale longitudinal data are analyzed to illustrate applications of the CCMM-MLIRD for each type of school mobility.     

Polite Girls and Creative Boys? Students' Gender Moderates Accuracy of Teachers' Ratings of Creativity

The aim of this study was to examine whether, and to what extent, teachers are able to recognize the creativity of their students. The study measured the creative abilities, creative attitude, creative activity, as well as intrinsic motivation, intelligence, and school functioning of 589 Polish high school students, while their teachers (N = 178) rated students' creativity. The structural equation model (SEM) demonstrated that the accuracy of teachers' ratings of students' creativity is generally low—the latent factor of students' creativity reliably, however weakly, predicted teachers' ratings. The accuracy of teachers' ratings was moderated by gender: Only in the case of male students did the latent creativity factor reliably predict teachers' ratings. Students' school functioning emerged as a key factor positively associated with the perception of students as creative.     

Life satisfaction trajectories among junior high school students in China: The role of parent–child communication

A 3-year follow-up test (from grades 7 to 9) was administered to 807 junior high school students from two regions in Hunan Province, China, using multilevel analysis to examine trends in junior high school students' life satisfaction, differences by gender and location of life and the effects of father–child/mother–child communication on the development of life satisfaction. The results showed that (1) Chinese junior high school students' life satisfaction showed a decreasing trend from the seventh grade to the ninth grade, and there was a significant decreasing process in the eighth grade; (2) father–child communication and mother–child communication had a significant positive predictive effect on Chinese junior high school students' life satisfaction and (3) father–child communication and mother–child communication had a significant negative predictive effect on the decreasing trend of life satisfaction, in which the effect of mother–child communication was particularly significant.     

Dancing is belonging! How social networks mediate the effect of a dance intervention on students' sense of belonging to their classroom

What does it take to feel you belong? Using a sample of 606 students in 30 classrooms, with 15 classrooms participating in a school‐based dance intervention, we examined intrapsychic and extrapsychic sources of social belonging using social network analysis. Whereas outdegree (the number of outgoing liking nominations to classmates) served as a proxy variable for students' active acceptance of others, indegree (the number of ingoing liking nominations from other peers) served as a proxy variable for the passive acceptance by others. Both measures should account for changes in students' sense of belonging to their classroom. Multilevel longitudinal mediation analyses supported our predictions—increased belonging related to increasing acceptance by others and of others, which were experienced by students participating in the dance intervention for a year (vs. a non‐treated control group). We discuss our findings within the current debate on the use of distal variables to explain intrapsychic constructs.     

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。     

Stepwise Latent Class Models for Explaining Group-Level Outcomes Using Discrete Individual-Level Predictors

Explaining group-level outcomes from individual-level predictors requires aggregating the individual-level scores to the group level and correcting the group-level estimates for measurement errors in the aggregated scores. However, for discrete variables it is not clear how to perform the aggregation and correction. It is shown how stepwise latent class analysis can be used to do this. First, a latent class model is estimated in which the scores on a discrete individual-level predictor are used to construct group-level latent classes. Second, this latent class model is used to aggregate the individual-level predictor by assigning the groups to the latent classes. Third, a group-level analysis is performed in which the aggregated measures are related to the remaining group-level variables while correcting for the measurement error in the class assignments. This stepwise approach is introduced in a multilevel mediation model with a single individual-level mediator, and compared to existing methods in a simulation study. We also show how a mediation model with multiple group-level latent variables can be used with multiple individual-level mediators and this model is applied to explain team productivity (group level) as a function of job control (individual level), job satisfaction (individual level), and enriched job design (group level).     

Multilevel Measurement of Dimensions of Collaborative Functioning in a Network of Collaboratives that Promote Child and Family Well-Being

Evaluating collaboration between community partners presents a series of methodological challenges (Roussos and Fawcett in Annu Rev Public Health 21:369-402, 2000; Yin and Kaftarian 1997), one of which is selection of the appropriate level of analysis. When data are collected from multiple members of multiple settings, multilevel analysis techniques should be used. Multilevel confirmatory factor analysis (MCFA) is an analytic approach that incorporates the advantages of latent variable measurement modeling and multilevel modeling for nested data. This study utilizes MCFA on data obtained from an evaluation survey of collaborative functioning provided to members of 157 community collaboratives in Georgia. This study presents a well-fitting measurement model that includes five dimensions of collaborative functioning, and a structural component with individual- and collaborative-level covariates. Findings suggest that members' role and meeting attendance significantly predicted their assessment of collaboration at the individual level, and that tenure of collaborative leaders predicted the overall functioning of the collaborative at the collaborative level. Dimensionality of collaborative functioning and implications of potentially substantial measurement biases associated with selection of respondents are addressed.     

School-wide social emotional learning (SEL) and bullying victimization: Moderating role of school climate in elementary,middle, and high schools

Guided by the school-wide social-emotional learning framework and social-ecological model, in this study we examined the associations between students' perceptions of four core social emotional learning (SEL) competencies (i.e., responsible decision-making, social awareness, self-management, and relationship skills) and school climate and their experience with bullying victimization through a multilevel framework. We also examined the multilevel moderating effects of students' perceptions of school climate, gender, and school levels (elementary, middle, and high schools) on the association between SEL competencies and bullying victimization. Participants were 23,532 students (4th to 12th grade) from 90 schools in Delaware. Using hierarchical linear modeling and controlling for demographic factors and school climate at both student and school levels, we found that three of the four core SEL competencies (i.e., social awareness, relationship skills, and self-management) and student-level school climate perceptions had significant associations with students' bullying victimization experiences. Moreover, the positive association between social awareness and bullying victimization and the negative association between self-management and bullying victimization were both mitigated in schools with more positive school climate at the student level. The association between some of the SEL competencies and bullying victimization varied depending on students' gender and grade levels. The findings highlight the unique and differentiated relations among the four core SEL competencies and students' bullying victimization experiences; they also suggest the importance of including school climate assessment and applying gender- and grade-level-specific efforts in bullying prevention programs with an SEL focus.     

A Multilevel Investigation of the Influences of Employees' Resistance to Empowerment

We employed a multilevel research design to examine the effects of employees' resistance to empowerment. Survey responses were obtained from 637 customer service engineers who worked in 121 empowered teams. At the team level of analysis, resistance to empowerment climate related negatively to customer satisfaction as mediated by transition processes. In addition, resistance to empowerment climate evidenced an indirect relation with team performance via team action processes. At the individual level of analysis, employees' resistance to empowerment related negatively to their job satisfaction. Moreover, a cross-level relation was evidenced whereby team-level resistance to empowerment climate related negatively to job satisfaction, beyond that accounted for by the individual-level effects, as partially mediated by team interpersonal processes. Results are discussed in terms of the multilevel manner in which employees' resistance to empowerment can undermine organizational design changes.     

The Recoverability of P-technique Factor Analysis

It seems that just when we are about to lay P–technique factor analysis finally to rest as obsolete because of newer, more sophisticated multivariate time-series models using latent variables—dynamic factor models—it rears its head to inform us that an obituary may be premature. We present the results of some simulations demonstrating that even though it does not explicitly model lagged information, P–technique's ability to recover the parameters of underlying dynamic processes involving lagged relations among the manifest variables is apparently robust and accurate. An empirical example is presented using 103 days of affective mood self-ratings from a young pregnant woman. Implications of the simulation and empirical findings are briefly discussed.     

Multiple Views on Family Data: The Sample Case of Adolescent,Maternal, and Paternal Perspectives on Family Differentiation Levels

The major objective of this article is to demonstrate a data analysis technique — confirmatory factor analysis with structural equation modeling — that can be used when the researcher has multiple perspectives on the same variables. The present data set was constructed from two samples that contained information collected on adolescents', mothers', and fathers' perspectives on family differentiation levels as measured by the Differentiation in the Family System Scale (DIFS; 4 ). Results of the combined sample confirmatory factor analysis procedures indicated that the family members’ perspectives converged and could be used as a single latent variable. The methodological implications of these findings are discussed.     

多水平项目反应理论模型在测验发展中的应用

作者简要介绍了多水平项目反应模型,对多水平项目反应理论与通常项目反应理论之间的关系进行了探讨,得到了多水平项目反应模型参数与通常项目反应模型参数之间的关系,并讨论了多水平项目反应模型的推广模型。通过一个实际例子,用多水平项目反应模型对测验中项目的特征进行分析;检验个体水平和组水平预测变量对能力参数的影响;对项目功能差异进行分析。最后文章就多水平项目反应理论模型的优势与不足进行了讨论     

On the use of multilevel modeling as an alternative to items analysis in psycholinguistic research

The use of multilevel modeling is presented as an alternative to separate item and subject ANOVAs (F1 x F2) in psycholinguistic research. Multilevel modeling is commonly utilized to model variability arising from the nesting of lower level observations within higher level units (e.g., students within schools, repeated measures within individuals). However, multilevel models can also be used when two random factors are crossed at the same level, rather than nested. The current work illustrates the use of the multilevel model for crossed random effects within the context of a psycholinguistic experimental study, in which both subjects and items are modeled as random effects within the same analysis, thus avoiding some of the problems plaguing current approaches.     

Reconsidering the Factor Structure of the Beavers Interactional Scales: Do External Ratings Mirror Self-Reports?

Factor analytic studies indicate that family relationships assessed by self-reports may be most clearly and parsimoniously differentiated along three dimensions, namely, Affective Expression, Behavioral Control, and Shared Activity. The present study explored the question of whether this were true of family ratings by outside parties. Confirmatory factor analysis was used with three data sets (n = 97, 91, and 95; N = 283) employing the Beavers Interactional Scales of family functioning. Multicollinearity of the observed variables was a pervasive problem. When the redundancy of the observed variables was pared down so that there were two observed variables for each latent factor, these three factors in oblique relationship provided a good fit to the observed data.     

The relationship of engagement and job satisfaction in working samples

The present study explored the factor structure of engagement and its relationship with job satisfaction. The authors hypothesize that work engagement comprises 3 constructs: vigor, dedication, and absorption. Using structural equation modeling, the authors analyze data from 3 archival data sets to determine the factor structure of engagement. In addition, they examine the hypothesis that engagement and job satisfaction are separate but related constructs, using structural equation modeling and hierarchical regression. The authors test models in which engagement and job satisfaction items loaded onto a single latent variable and 1 in which they loaded onto 2 separate variables. Results from the confirmatory factor analysis indicate engagement has 3 factors. In addition, confirmatory factor analysis and hierarchical regressions indicate engagement and job satisfaction are separate constructs. Last, hierarchical regressions demonstrated the constructs have different relationships with the areas of work-life scale. Implications for theory and research are discussed.     

The Core of Darkness: Uncovering the Heart of the Dark Triad

The Dark Triad consists of three overlapping but distinct personality variables: narcissism, Machiavellianism and psychopathy. To date, however, no research has empirically identified what leads these three variables to overlap or whether other variables share the same core. The present research addresses why and how dark personalities overlap. Drawing from classic work in psychopathy, Hare's Factor 1 or manipulation and callousness were found to be the common antagonistic core. A series of latent variable procedures, including Multisample Structural Equation Models, revealed that for both samples, manipulation and callousness, completely accounted for the associations among the facet scores of the psychopathy, narcissism and Machiavellianism scales. Sample 2 also included Social Dominance Orientation, and results further confirmed that Social Dominance Orientation has the same common core as the Dark Triad. In sum, Hare's Factor 1—manipulation–callousness—emerged as common dark core that accounts for the overlap among antagonistic traits. Copyright © 2012 European Association of Personality Psychology     

Gender Inequality in Europe and the Life Satisfaction of Working and Non-working Women

Empirical analysis of data drawn from the European Social Survey reveals that—after individual characteristics are controlled for—women engaging in market work and housework have similar life satisfaction levels. Complementing the micro-level data from the survey with country-level variables, namely GDP per capita and gender inequality (measured by the World Economic Forum’s Global Gender Gap Index, GGGI), we estimate a multilevel regression model to shed light on the contextual factors of the life satisfaction of women in Europe. We find that working women’s well-being relative to housewives is greater in countries where the GGGI indicates a smaller gender gap, i.e. where women are in a better position in terms of equality with men in the public domains. We interpret this finding to mean that the so-called ‘paradox of declining female happiness’ is in part due to persistent gender roles which appear to have a larger impact on the well-being of working women.