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.     

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Abstract

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.     

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.     

问卷数据建模的前传

问卷法是一种常见的实证研究方法。问卷数据建模的前期工作,就像是一栋大楼的奠基工程,基础是否扎实,影响后续的工程质量。本文专门讨论统计模型建立之前要做的事情（重点是量表评价）,内容包括：处理缺失值、评价量表的结构效度和题目删除的适当性、多维量表需要合成总分时检验同质性并计算合成信度、检验共同方法偏差和评价（变量）区分效度、题目打包、检验自变量的多重共线性,最后也涉及建模理据和无关变量控制等。     

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.     

Modeling Clustered Data with Very Few Clusters

Small-sample inference with clustered data has received increased attention recently in the methodological literature, with several simulation studies being presented on the small-sample behavior of many methods. However, nearly all previous studies focus on a single class of methods (e.g., only multilevel models, only corrections to sandwich estimators), and the differential performance of various methods that can be implemented to accommodate clustered data with very few clusters is largely unknown, potentially due to the rigid disciplinary preferences. Furthermore, a majority of these studies focus on scenarios with 15 or more clusters and feature unrealistically simple data-generation models with very few predictors. This article, motivated by an applied educational psychology cluster randomized trial, presents a simulation study that simultaneously addresses the extreme small sample and differential performance (estimation bias, Type I error rates, and relative power) of 12 methods to account for clustered data with a model that features a more realistic number of predictors. The motivating data are then modeled with each method, and results are compared. Results show that generalized estimating equations perform poorly; the choice of Bayesian prior distributions affects performance; and fixed effect models perform quite well. Limitations and implications for applications are also discussed.     

Estimation of a Latent Variable Regression Growth Curve Model for Individuals Cross-Classified by Clusters

The cross-classified multiple membership latent variable regression (CCMM-LVR) model is a recent extension to the three-level latent variable regression (HM3-LVR) model which can be utilized for longitudinal data that contains individuals who changed clusters over time (for instance, student mobility across schools). The HM3-LVR model can include the initial status on growth effect as varying across those clusters and allows testing of more flexible hypotheses about the influence of initial status on growth and of factors that might impact that relationship, but only in the presence of pure clustering of participants within higher-level units. This Monte Carlo study was conducted to evaluate model estimation under a variety of conditions and to measure the impact of ignoring cross-classified data when estimating the incorrectly specified HM3-LVR model in a scenario in which true values for parameters are known. Furthermore, results from a real-data analysis were used to inform the design of the simulation. Overall, it would be recommended for researchers to utilize the CCMM-LVR model over the HM3-LVR model when individuals are cross-classified, and to use a bare minimum of more than 100 clustering units in order to avoid overestimation of the level-3 variance component estimates.     

运用基因表达式编程的自陈量表数据建模

探讨基因表达式编程对自陈量表测量数据的建模方法。运用威廉斯创造力测验和认知需求量表获得400位中学生的测量分数,通过数据清洗,保留383个被试的分数作为建模的数据集。运用哈曼单因素检验方法没有发现共同方法偏差。采用均匀设计方法对基因表达式编程中的5个参数进行优化配置,在测试拟合度最大的试验条件下,找到了测试误差最小的模型。比较基因表达式编程和BP神经网络、支持向量回归机、多元线性回归、二次多项式回归所建模型的预测精度。研究表明,基因表达式编程能用于自陈量表测量数据的建模,该模型比传统方法所建的模型具有更高的预测精度,而且模型是稳健的。     

Modeling Hierarchical Relationships in Hinkle's Implications Grid Data

There have been few attempts to devise suitable methods of analysis for the implications grid devised by Hinkle (1965 Hinkle, D.N. (1965). The change of personal constructs from the viewpoint of a theory of construct implications. Unpublished Ph.D. thesis, The Ohio State University, Columbus. [Google Scholar]). As Hinkle noted (Hinkle, 1965 Hinkle, D.N. (1965). The change of personal constructs from the viewpoint of a theory of construct implications. Unpublished Ph.D. thesis, The Ohio State University, Columbus. [Google Scholar], p. 63), there are three implications needed to define a hierarchical relationship (A → B, B → C, and A → C). Hinkle did not attempt to test this requirement, as neither did the only other published use of the technique (Fransella, 1972). Subsequently, Caputi, Breiger, and Pattison (1990 Caputi, P., Breiger, R., & Pattison, P. (1990). Analyzing implications grids using hierarchical models. International Journal of Personal Construct Psychology, 3, 77–90.[Taylor & Francis Online] , [Google Scholar]) published a technique that explicitly sought to model implications data with respect to this requirement. In this study we use this technique to both (a) evaluate some of the choice points in the technique using data from the 28 implications grids collected by Hinkle and published as an appendix to his thesis, and (b) subsequently analyze this data to examine the hierarchical relationships as defined above. Our evaluation of the choice points showed that the joint modification approach worked best and that there was a clear cut-off to most fully represent the relationships in the raw data. Our analysis via the modeling approach found that there was no difference between the mean number of transitive superordinate constructs implied by subordinate constructs and the mean number of transitive subordinate constructs implied by superordinate constructs in the modeled data, suggesting that the laddered constructs in this study were not necessarily superordinate to the generating constructs.     

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.     

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.     

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.     

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.