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.     

Bayesian analysis of longitudinal multitrait–multimethod data with ordinal response variables

A new multilevel latent state graded response model for longitudinal multitrait–multimethod (MTMM) measurement designs combining structurally different and interchangeable methods is proposed. The model allows researchers to examine construct validity over time and to study the change and stability of constructs and method effects based on ordinal response variables. We show how Bayesian estimation techniques can address a number of important issues that typically arise in longitudinal multilevel MTMM studies and facilitates the estimation of the model presented. Estimation accuracy and the impact of between‐ and within‐level sample sizes as well as different prior specifications on parameter recovery were investigated in a Monte Carlo simulation study. Findings indicate that the parameters of the model presented can be accurately estimated with Bayesian estimation methods in the case of low convergent validity with as few as 250 clusters and more than two observations within each cluster. The model was applied to well‐being data from a longitudinal MTMM study, assessing the change and stability of life satisfaction and subjective happiness in young adults after high‐school graduation. Guidelines for empirical applications are provided and advantages and limitations of a Bayesian approach to estimating longitudinal multilevel MTMM models are discussed.     

Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model

Psychological theories often produce hypotheses that pertain to individual differences in within-person variability. To empirically test the predictions entailed by such hypotheses with longitudinal data, researchers often use multilevel approaches that allow them to model between-person differences in the mean level of a certain variable and the residual within-person variance. Currently, these approaches can be applied only when the data stem from a single variable. However, it is common practice in psychology to assess not just a single measure but rather several measures of a construct. In this paper we describe a model in which we combine the single-indicator model with confirmatory factor analysis. The new model allows individual differences in latent mean-level factors and latent within-person variability factors to be estimated. Furthermore, we show how the model's parameters can be estimated with a maximum likelihood estimator, and we illustrate the approach using an example that involves intensive longitudinal data.     

Using Multilevel Logistic Regression to Evaluate Person-Fit in IRT Models

I describe how multilevel logistic regression can be used to assess the consistency of an individual's response pattern with an item response theory measurement model. Specifically, by treating item responses as being nested within individuals, multilevel logistic regression is used to estimate a person-response curve that models how an individual's item endorsement rate decreases as a function of item difficulty. The slope of an individual's person-response curve is used as an indicator of the degree of response consistency or person-fit. I argue that the proposed multilevel modeling approach to person-fit assessment has several potential advantages over traditional techniques. The most important advantage being that the multilevel modeling approach allows explanatory variables to be entered into the model so that the causes of response inconsistency or differential test functioning can be investigated.     

The Multigroup Multilevel Categorical Latent Growth Curve Models

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup multilevel framework and allowed for autoregressive residuals. The parameter in the new model can be estimated using the computer program WinBUGS, which adopts Markov Chain Monte Carlo algorithms. Two simulation studies were conducted. An empirical example was raised and established based on models generated by the results of empirical data, which have been fitted and compared.     

Introduction to the Special Section on Applied Longitudinal Methods in Aging Research

This article introduces articles that appear in the special section on applied longitudinal methods in aging research. These articles apply quantitative statistical techniques such as multilevel modeling and structural equation models to the analysis of longitudinal data. They exemplify how applications of these techniques can advance scientific research on the effects of aging on psychological constructs. ((c) 2003 APA, all rights reserved)     

Studying Multivariate Change Using Multilevel Models and Latent Curve Models

In longitudinal research investigators often measure multiple variables at multiple points in time and are interested in investigating individual differences in patterns of change on those variables. In the vast majority of applications, researchers focus on studying change in one variable at a time. In this article we consider methods for studying relations1.1ips between patterns of change on different variables. We show how the multilevel modeling framework, which is often used to study univariate change, can be extended to the multivariate case to yield estimates of covariances of parameters representing aspects of change on different variables. We illustrate this approach using data from a study of physiological response to marital conflict in older married couples, showing a substantial correlation between rate of linear change on different stress-related hormones during conflict. We also consider how similar issues can be studied using extensions of latent curve models to the multivariate case, and we show how such models are related to multivariate multilevel models.     

Multilevel modelling: Beyond the basic applications

Over the last 30 years statistical algorithms have been developed to analyse datasets that have a hierarchical/multilevel structure. Particularly within developmental and educational psychology these techniques have become common where the sample has an obvious hierarchical structure, like pupils nested within a classroom. We describe two areas beyond the basic applications of multilevel modelling that are important to psychology: modelling the covariance structure in longitudinal designs and using generalized linear multilevel modelling as an alternative to methods from signal detection theory (SDT). Detailed code for all analyses is described using packages for the freeware R.     

密集追踪数据分析：模型及其应用

在心理学、教育学和临床医学等领域, 越来越多的研究者开始关注个体内部的行为、心理、临床效果等随时间而产生的动态变化, 重视针对个体的差异化建模。密集追踪是一种在短时间内对个体进行多个时间节点密集追踪测量的方法, 更适合用于研究个体内部心理过程等的动态变化及其作用机制。近年来, 密集追踪成为心理学研究的一大热点, 但许多密集追踪的研究分析仍停留在较为传统的方法。方法学领域已涌现出较多用于密集追踪数据分析的模型方法, 较为主流的模型包括以动态结构方程模型(Dynamic Structural Equation Model, DSEM)为代表的自上而下的建模方法, 以及以组迭代多模型估计(Group Iterative Multiple Model Estimation, GIMME)为代表的自下而上的建模方法。二者均可以方便地对密集追踪数据中的自回归及交叉滞后效应进行建模。     

Multilevel models for the experimental psychologist: Foundations and illustrative examples

Although common in the educational and developmental areas, multilevel models are not often utilized in the analysis of data from experimental designs. This article illustrates how multilevel models can be useful with two examples from experimental designs with repeated measurements not involving time. One example demonstrates how to properly examine independent variables for experimental stimuli or individuals that are categorical, continuous, or semicontinuous in the presence of missing data. The second example demonstrates how response times and error rates can be modeled simultaneously within a multivariate model in order to examine speed—accuracy trade-offs at the experimental-condition and individual levels, as well as to examine differences in the magnitude of effects across outcomes. SPSS and SAS syntax for the examples are available electronically.     

多层线性模型在纵向研究中的运用

纵向研究中传统统计技术主要是重复测量的方差分析和多元回归分析，但是这两种技术存在一些局限性，不能合理而充分地解释纵向研究资料。近年来出现的多层线性模型能够更有效地利用纵向数据。为促进多层线性模型在纵向研究中的运用，简要论述了传统统计技术的局限，介绍了多层线性模型的原理及其在纵向研究中的作用，以一组模拟数据为例对多层线性模型中各种参数在纵向研究中的含义进行了详细讨论，对于纵向研究中运用多层线性模型时须注意的问题提出了建议。     

Coupling Longitudinal Data and Multilevel Modeling to Examine the Antecedents and Consequences of Jealousy Experiences in Romantic Relationships: A Test of the Relational Turbulence Model

We used longitudinal data and multilevel modeling to examine how intimacy, relational uncertainty, and failed attempts at interdependence influence emotional, cognitive, and communicative responses to romantic jealousy, and how those experiences shape subsequent relationship characteristics. The relational turbulence model ( Solomon & Knobloch, 2004 ) highlights how intimacy, relational uncertainty, and interference from partners influence and reflect reactions to events that occur within romantic relationships. Drawing from the theory, we predicted that (a) relational uncertainty and interference from partners are positively associated with cognitive and emotional jealousies; (b) the intensity of romantic jealousy, relational intimacy, and a partner’s interference is positively associated with the directness of communication about jealousy; (c) relational uncertainty is negatively associated with communicative directness; and (d) cognitive jealousy, emotional jealousy, and the directness of communicative responses to jealousy influence subsequent relationship characteristics. The results of the multilevel modeling revealed mixed support for our predictions. We explore the implications of this study for research on the relational turbulence model, relationship development, and jealousy.     

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。     

Collective‐efficacy as a mediator of the relationship of leaders' personality traits and team performance: A cross‐level analysis

The relationship between a leader's personality and his team's performance has been established in organisational research, but the underlying process and mechanism responsible for this effect have not been fully explored. Both the traditional multiple linear regression and the multilevel structural equation model approaches were used in this study to test a proposed mediating model of subordinates' perception of collective efficacy between leader personality and team performance. The results show that the team leader's extraversion and conscientiousness personality traits were related positively to both the team‐average (individual) perception of collective efficacy and team performance, and the collective efficacy mediated the relationship of the leader's personality traits and team performance. This study also discusses how Chinese cultural elements play a role in such a mediating model.     

Modeling competence development in the presence of selection bias

A major challenge for representative longitudinal studies is panel attrition, because some respondents refuse to continue participating across all measurement waves. Depending on the nature of this selection process, statistical inferences based on the observed sample can be biased. Therefore, statistical analyses need to consider a missing-data mechanism. Because each missing-data model hinges on frequently untestable assumptions, sensitivity analyses are indispensable to gauging the robustness of statistical inferences. This article highlights contemporary approaches for applied researchers to acknowledge missing data in longitudinal, multilevel modeling and shows how sensitivity analyses can guide their interpretation. Using a representative sample of N = 13,417 German students, the development of mathematical competence across three years was examined by contrasting seven missing-data models, including listwise deletion, full-information maximum likelihood estimation, inverse probability weighting, multiple imputation, selection models, and pattern mixture models. These analyses identified strong selection effects related to various individual and context factors. Comparative analyses revealed that inverse probability weighting performed rather poorly in growth curve modeling. Moreover, school-specific effects should be acknowledged in missing-data models for educational data. Finally, we demonstrated how sensitivity analyses can be used to gauge the robustness of the identified effects.     

The use of multitreatment modalities in early intervention: A quantitative case study

A quantitative single case study is presented to illustrate how an early intervention program used two therapeutic modalities to treat a depressed mother and her 2-month-old son. Drawing upon an ecological, transactional model of development, the case study utilized a multimethod, longitudinal approach to assess the infant's developmental competence and attachment status, the mother's history and current psychosocial functioning, patterns of mother-infant interaction, and components of the family's social ecology. Measures were administered during a baseline period to assess pre-intervention functioning and were systematically repeated throughout the 2-year period of intervention. The treatment modalities included psychodynamically oriented individual therapy and Parent-Infant Relationship Treatment (PIRT) in which the dyad was also seen by a second therapist to foster more adaptive mother-infant transactional patterns. The findings indicated increased infant developmental competence and a shift from an insecure to a secure attachment classification, improved maternal psychosocial functioning, and a decline in the dyadic interactional pattern of maternal intrusiveness and infant withdrawal. The advantages of using two treatment modalities and a single case approach to evaluation are discussed.     

Beginnings and endings: Therapeutic opportunities in educational settings

This paper is based on its author's experience of working in a Counselling Service with both school and university students. She shows how developmental disturbances in the students' educational lives tended to resonate with developmental disturbances in their earlier lives. She draws on the material from seven students to illustrate her thesis.     

Aggregating and Testing Intra-Individual Correlations: Methods and Comparisons

From a longitudinal study, we have repeatedly measured data from multiple individuals at multiple occasions. For each individual, the relation between 2 variables can be measured by the Pearson’s correlation. The question is how to aggregate the multiple correlations and conduct statistical inference on the aggregated intra-individual correlation. Several methods are proposed to aggregate and test intra-individual correlations: (a) a meta-analysis method based on Fisher’s Z transformed correlations, (b) a meta-analysis method based on the Pearson’s correlations, and (c) a multilevel modeling method using data standardized within each individual. The performance of the methods after bias corrections was compared using simulations with considering factors including numbers of individuals, numbers of time points, population effect sizes, and their distribution forms (homogeneous vs heterogeneous). The results from the simulation studies show that estimation biases were found using the meta-analytic methods and suggestions on when and how to correct biases were provided based on the simulation results. Furthermore, the performance of the 3 methods after necessary bias corrections was found to be comparable and reasonably good, indicating that all 3 methods worked for aggregating and testing intra-individual correlations. An empirical daily diary data set was then used to illustrate the applications of the 3 methods. The assumptions, advantages and disadvantages, and possible extensions of the 3 methods were discussed.     

Get Over It! A Multilevel Threshold Autoregressive Model for State-Dependent Affect Regulation

Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of this model is that the autoregressive parameter is treated as a fixed, trait-like property of a person. We argue that the autoregressive parameter may be state-dependent, for example, if the strength of affect regulation depends on the intensity of affect experienced. To allow such intra-individual variation, we propose a multilevel threshold autoregressive model. Using simulations, we show that this model can be used to detect state-dependent regulation with adequate power and Type I error. The potential of the new modeling approach is illustrated with two empirical applications that extend the basic model to address additional substantive research questions.