The Impacts of Ignoring a Crossed Factor in Analyzing Cross-Classified Data

Cross-classified random-effects models (CCREMs) are used for modeling nonhierarchical multilevel data. Misspecifying CCREMs as hierarchical linear models (i.e., treating the cross-classified data as strictly hierarchical by ignoring one of the crossed factors) causes biases in the variance component estimates, which in turn, results in biased estimation in the standard errors of the regression coefficients. Analytical studies were conducted to provide closed-form expressions for the biases. With balanced design data structure, ignoring a crossed factor causes overestimation of the variance components of adjacent levels and underestimation of the variance component of the remaining crossed factor. Moreover, ignoring a crossed factor at the kth level causes underestimation of the standard error of the regression coefficient of the predictor associated with the ignored factor and overestimation of the standard error of the regression coefficient of the predictor at the (k?1)th level. Simulation studies were also conducted to examine the effect of different structures of cross-classification on the biases. In general, the direction and magnitude of the biases depend on the level of the ignored crossed factor, the level with which the predictor is associated at, the magnitude of the variance component of the ignored crossed factor, the variance components of the predictors, the sample sizes, and the structure of cross-classification. The results were further illustrated using the Early Childhood Longitudinal Study-Kindergarten Cohort data.     

Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model

Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve modeling (GCM). This study introduces a cross-classified multiple membership growth curve model (CCMM-GCM) for modeling, for example, academic achievement trajectories in the presence of student mobility. Real data are used to demonstrate and compare growth curve model estimates using the CCMM-GCM and a conventional GCM that ignores student mobility. Results indicate that the CCMM-GCM represents a promising option for modeling growth for multiple membership data structures.     

Hierarchical Classes Modeling of Rating Data

Hierarchical classes (HICLAS) models constitute a distinct family of structural models for N-way N-mode data. All members of the family include N simultaneous and linked classifications of the elements of the N modes implied by the data; those classifications are organized in terms of hierarchical, if–then-type relations. Moreover, the models are accompanied by comprehensive, insightful graphical representations. Up to now, the hierarchical classes family has been limited to dichotomous or dichotomized data. In the present paper we propose a novel extension of the family to two-way two-mode rating data (HICLAS-R). The HICLAS-R model preserves the representation of simultaneous and linked classifications as well as of generalized if–then-type relations, and keeps being accompanied by a comprehensive graphical representation. It is shown to bear interesting relationships with classical real-valued two-way component analysis and with methods of optimal scaling. The research reported in this paper was supported by the Research Fund of the University of Leuven (GOA/00/02 and GOA/05/04) and by the Fund for Scientific Research-Flanders (project G.0146.06). Eva Ceulemans is a Post-doctoral Researcher supported by the Fund for Scientific Research, Flanders. The authors gratefully acknowledge the help of Gert Quintiens and Kaatje Bollaerts in collecting the data used in Section 4 and of Jan Schepers in additional analyses of these data.     

Modeling Dependence Structures for Response Times in a Bayesian Framework

A multivariate generalization of the log-normal model for response times is proposed within an innovative Bayesian modeling framework. A novel Bayesian Covariance Structure Model (BCSM) is proposed, where the inclusion of random-effect variables is avoided, while their implied dependencies are modeled directly through an additive covariance structure. This makes it possible to jointly model complex dependencies due to for instance the test format (e.g., testlets, complex constructs), time limits, or features of digitally based assessments. A class of conjugate priors is proposed for the random-effect variance parameters in the BCSM framework. They give support to testing the presence of random effects, reduce boundary effects by allowing non-positive (co)variance parameters, and support accurate estimation even for very small true variance parameters. The conjugate priors under the BCSM lead to efficient posterior computation. Bayes factors and the Bayesian Information Criterion are discussed for the purpose of model selection in the new framework. In two simulation studies, a satisfying performance of the MCMC algorithm and of the Bayes factor is shown. In comparison with parameter expansion through a half-Cauchy prior, estimates of variance parameters close to zero show no bias and undercoverage of credible intervals is avoided. An empirical example showcases the utility of the BCSM for response times to test the influence of item presentation formats on the test performance of students in a Latin square experimental design.

     

Modeling fMRI Data: Challenges and Opportunities

We offer an introduction to the five papers that make up this special section. These papers deal with a range of the methodological challenges that face researchers analyzing fMRI data—the spatial, multilevel, and longitudinal nature of the data, the sources of noise, and so on. The papers all provide analyses of data collected by a multi-site consortium, the Function Biomedical Informatics Research Network. Due to the sheer volume of data, univariate procedures are often applied, which leads to a multiple comparisons problem (since the data are necessarily multivariate). The papers in this section include interesting applications, such as a state-space model applied to these data, and conclude with a reflection on basic measurement problems in fMRI. All in all, they provide a good overview of the challenges that fMRI data present to the standard psychometric toolbox, but also to the opportunities they offer for new psychometric modeling.     

Item Response Modeling of Paired Comparison and Ranking Data

The comparative format used in ranking and paired comparisons tasks can significantly reduce the impact of uniform response biases typically associated with rating scales. Thurstone's (1927, 1931) model provides a powerful framework for modeling comparative data such as paired comparisons and rankings. Although Thurstonian models are generally presented as scaling models, that is, stimuli-centered models, they can also be used as person-centered models. In this article, we discuss how Thurstone's model for comparative data can be formulated as item response theory models so that respondents' scores on underlying dimensions can be estimated. Item parameters and latent trait scores can be readily estimated using a widely used statistical modeling program. Simulation studies show that item characteristic curves can be accurately estimated with as few as 200 observations and that latent trait scores can be recovered to a high precision. Empirical examples are given to illustrate how the model may be applied in practice and to recommend guidelines for designing ranking and paired comparisons tasks in the future.     

The Impact of R-Optimized Administration Modeling Procedures on Brazilian Normative Reference Values for Rorschach Scores

To generate normative reference data for the Rorschach Performance Assessment System (R–PAS), modeling procedures were developed to convert the distribution of responses (R) in protocols obtained using Comprehensive System (CS; Exner 2003 Exner, J. E. (2003). The Rorschach: A Comprehensive System. Vol. 1. Basic foundations (4th ed.). Hoboken, NJ: Wiley. [Google Scholar]) administration guidelines to match the distribution of R in protocols obtained using R-Optimized Administration (Meyer, Viglione, Mihura, Erard, &; Erdberg, 2011 Meyer, G. J., Viglione, D. J., Mihura, J. L., Erard, R. E., &; Erdberg, P. (2011). Rorschach Performance Assessment System: administration, coding, interpretation, and technical manual. Toledo, OH: Rorschach Performance Assessment System. [Google Scholar]). This study replicates the R–PAS study, examining the impact of modeling R-Optimized Administration on Brazilian normative reference values by comparing a sample of 746 CS administered protocols to its counterpart sample of 343 records modeled to match R-Optimized Administration. The results were strongly consistent with the R–PAS findings, showing the modeled records had a slightly higher mean R and, secondarily, slightly higher means for Complexity and V-Comp, as well as smaller standard deviations for R, Complexity, and R8910%. We also observed 5 other small differences not observed in the R–PAS study. However, when comparing effect sizes for the differences in means and standard deviations observed in this study to the differences found in the R–PAS study, the results were virtually identical. These findings suggest that using R-Optimized Administration in Brazil might produce normative results that are similar to traditional CS norms for Brazil and similar to the international norms used in R–PAS.     

Structural Equation Modeling Approaches for Analyzing Partially Nested Data

Study designs involving clustering in some study arms, but not all study arms, are common in clinical treatment-outcome and educational settings. For instance, in a treatment arm, persons may be nested in therapy groups, whereas in a control arm there are no groups. Methodological approaches for handling such partially nested designs have recently been developed in a multilevel modeling framework (MLM-PN) and have proved very useful. We introduce two alternative structural equation modeling (SEM) approaches for analyzing partially nested data: a multivariate single-level SEM (SSEM-PN) and a multiple-arm multilevel SEM (MSEM-PN). We show how SSEM-PN and MSEM-PN can produce results equivalent to existing MLM-PNs and can be extended to flexibly accommodate several modeling features that are difficult or impossible to handle in MLM-PNs. For instance, using an SSEM-PN or MSEM-PN, it is possible to specify complex structural models involving cluster-level outcomes, obtain absolute model fit, decompose person-level predictor effects in the treatment arm using latent cluster means, and include traditional factors as predictors/outcomes. Importantly, implementation of such features for partially nested designs differs from that for fully nested designs. An empirical example involving a partially nested depression intervention combines several of these features in an analysis of interest for treatment-outcome studies.     

创伤骨科的不当医疗

不当医疗问题已经引起社会各界的广泛关注,它包括过度医疗行为、错误医疗行为和缺陷性医疗行为.创伤骨科疾病不当医疗既与医学发展水平和医学本身规律特点有关,又与现行医疗体制、医院经营机制有关,是患者及家属、医务人员和社会等多因素参与,受现行医学科学发展制约的治疗行为.应避免不当医疗,追求适度医疗,尽量达到最优化医疗.     

The Limit of Mental Structures

The development of consistent health behaviors is important for chronic illness prevention and management. The current study experimentally compared two strategies—a personal-rule and a deliberation strategy—designed to help participants consistently perform their intended behaviors over a 7-week period in a real-world setting. Although the personal-rule strategy had theoretical support from behavioral economics and empirical support from both animal and human lab experiments, the deliberation strategy group was significantly more successful than the personal-rule strategy group, both initially (time to first violation, p < .01, Cohen's d = .51) and over the entire 7-week period (overall success, p < .05, Cohen's d = .18). These effects were significant even after controlling for known predictors of behavioral success, including individual-difference variables, person-behavior factors, and resolution-related factors.     

创伤骨科的不当医疗

不当医疗问题已经引起社会各界的广泛关注,它包括过度医疗行为、错误医疗行为和缺陷性医疗行为。创伤骨科疾病不当医疗既与医学发展水平和医学本身规律特点有关,又与现行医疗体制、医院经营机制有关,是患者及家属、医务人员和社会等多因素参与,受现行医学科学发展制约的治疗行为。应避免不当医疗,追求适度医疗,尽量达到最优化医疗。     

Robust Structural Equation Modeling with Missing Data and Auxiliary Variables

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are provided in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from the National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood.     

Multilevel Factor Analysis and Structural Equation Modeling of Daily Diary Coping Data: Modeling Trait and State Variation

This study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data were collected on a large (n = 366) multiethnic sample over the course of 5 days. Intraclass correlation coefficient for the derived factors suggested approximately equal amounts of variability in coping usage at the state and trait levels. MFAs showed that Problem-Focused Coping and Social Support emerged as stable factors at both the within-person and between-person levels. Other factors (Minimization, Emotional Rumination, Avoidance, Distraction) were specific to the within-person or between-person levels but not both. Multilevel structural equation modeling (MSEM) showed that the prediction of daily positive and negative affect differed as a function of outcome and level of coping factor. The Discussion section focuses primarily on a conceptual and methodological understanding of modeling state and trait coping using daily diary data with MFA and MSEM to examine covariation among coping variables and predicting outcomes of interest.     

Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.     

Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation

Psychometrika - In this paper, we propose a joint modeling approach to analyze dependency in parallel response data. We define two types of dependency: higher-level dependency and within-item...     

Modeling Incomplete Longitudinal Substance Use Data Using Latent Variable Growth Curve Methodology

Longitudinal data sets typically suffer from attrition and other forms of missing data. When this common problem occurs, several researchers have demonstrated that correct maximum likelihood estimation with missing data can be obtained under mild assumptions concerning the missing data mechanism. With reasonable substantive theory, a mixture of cross-sectional and longitudinal methods developed within multiple-group structural equation modeling can provide a strong basis for inference about developmental change. Using an approach to the analysis of missing data, the present study investigated developmental trends in adolescent (N = 759) alcohol, marijuana, and cigarette use across a 5-year period using multiple-group latent growth modeling. An associative model revealed that common developmental trends existed for all three substances. Age and gender were included in the model as predictors of initial status and developmental change. Findings discuss the utility of latent variable structural equation modeling techniques and missing data approaches in the study of developmental change.     

Modeling Time-Dependent Association in Longitudinal Data: A Lag as Moderator Approach

We describe a straightforward, yet novel, approach to examine time-dependent association between variables. The approach relies on a measurement-lag research design in conjunction with statistical interaction models. We base arguments in favor of this approach on the potential for better understanding the associations between variables by describing how the association changes with time. We introduce a number of different functional forms for describing these lag-moderated associations, each with a different substantive meaning. Finally, we use empirical data to demonstrate methods for exploring functional forms and model fitting based on this approach.