Power Analyses for Moderator Effects in Three-Level Cluster Randomized Trials

Researchers are often interested in whether the effects of an intervention differ conditional on individual- or group-moderator variables such as children's characteristics (e.g., gender), teacher's background (e.g., years of teaching), and school's characteristics (e.g., urbanity); that is, the researchers seek to examine for whom and under what circumstances an intervention works. Furthermore, the researchers are interested in understanding and interpreting variability in treatment effects through moderation analysis as an approach to exploring the sources of the treatment effect variability. This study develops formulas for power analyses to detect the moderator effects in designing three-level cluster randomized trials (CRTs). We develop the statistical formulas for calculating statistical power, minimum detectable effect size difference, and 95% confidence intervals for cluster or cross-level moderation, nonrandomly varying or random slopes, binary or continuous moderators, and designs with or without covariates. We demonstrate how the calculations can be used in the planning phase of three-level CRTs using the software PowerUp!-Moderator.     

Analyzing Different Types of Moderated Method Effects in Confirmatory Factor Models for Structurally Different Methods

An extension of two confirmatory factor models for multitrait-multimethod measurement designs with structurally different methods to the analysis of latent interaction effects is presented: the nonlinear latent difference (NL-LD) model and the nonlinear correlated trait–correlated method-minus-one (NL-CTC[M – 1]) model. Both models are compared with regard to (a) the psychometric definition of the latent variables, (b) the capabilities of explaining latent method effects, and (c) the analysis of latent interaction effects. Using the latent moderated structural equation approach, we show how moderated method effects can be examined in the NL-CTC(M – 1) model. This fine-grained analysis of method effects is not feasible using the classical NL-LD model. We propose an extended version of the NL-LD model, which recovers the results of the NL-CTC(M – 1) model. The different versions of the nonlinear multimethod models are illustrated using real data from a multirater study. Finally, the advantages and challenges of incorporating latent interaction effects in complex CFA–MTMM models are discussed.     

道德具身性的元分析研究

具身认知强调身体的感知觉在认知过程中发挥着重要的作用。有研究者将物理变量的改变使得人们的道德行为和道德判断发生变化这一探讨方向命名为"道德的心理物理学"。元分析研究的目的在于探讨个体的感知觉与道德行为和道德判断之间是否存在联系,以及这种效应是否受到某些变量的影响。元分析纳入42个研究,共包含2962名被试。研究结果表明道德的具身认知效应显著,具体感知觉与道德行为和道德判断之间存在相关(r=0.19,p<0.01)。"被试来源国家"这一变量的调节作用显著(Q=79.454,df=41,p<0.001)。     

A Specification Error Test That Uses Instrumental Variables to Detect Latent Quadratic and Latent Interaction Effects

The relations between the latent variables in structural equation models are typically assumed to be linear in form. This article aims to explain how a specification error test using instrumental variables (IVs) can be employed to detect unmodeled interactions between latent variables or quadratic effects of latent variables. An empirical example is presented, and the results of a simulation study are reported to evaluate the sensitivity and specificity of the test and compare it with the commonly employed chi-square model test. The results show that the proposed test can identify most unmodeled latent interactions or latent quadratic effects in moderate to large samples. Furthermore, its power is higher when the number of indicators used to define the latent variables is large. Altogether, this article shows how the IV-based test can be applied to structural equation models and that it is a valuable tool for researchers using structural equation models.     

Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot. The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix. In this way, joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given. Compared with the general Newton iterative method, the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration. So the convergence domain is bigger than that of the general Newton iterative method. Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector. The inverse displacement analysis of the general 6R (six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm. Because the three non-collinear points can be selected at random, the method can be applied to any other types of serial robots.     

电力市场中一类博弈模型的脉冲延迟反馈控制法

针对电力市场中一类非线性博弈模型的混沌问题,通过加入脉冲时间延迟反馈控制,对其稳定性进行研究。第一种形式是对一家投资商引入系统变量的时间延迟反馈控制法,第二种形式是对整个系统引入系统变量的时间延迟反馈控制,并利用Matlab软件对该系统进行数值模拟,验证该方法的有效性。结果表明：时间延迟反馈控制可以有效控制系统的稳定性。     

Multiple Imputation Strategies for Multiple Group Structural Equation Models

Although structural equation modeling software packages use maximum likelihood estimation by default, there are situations where one might prefer to use multiple imputation to handle missing data rather than maximum likelihood estimation (e.g., when incorporating auxiliary variables). The selection of variables is one of the nuances associated with implementing multiple imputation, because the imputer must take special care to preserve any associations or special features of the data that will be modeled in the subsequent analysis. For example, this article deals with multiple group models that are commonly used to examine moderation effects in psychology and the behavioral sciences. Special care must be exercised when using multiple imputation with multiple group models, as failing to preserve the interactive effects during the imputation phase can produce biased parameter estimates in the subsequent analysis phase, even when the data are missing completely at random or missing at random. This study investigates two imputation strategies that have been proposed in the literature, product term imputation and separate group imputation. A series of simulation studies shows that separate group imputation adequately preserves the multiple group data structure and produces accurate parameter estimates.     

Quality assurance of assessment and moderation discourses involving sessional staff

Quality assurance is a major agenda in tertiary education. The casualisation of academic work, especially in teaching, is also a quality assurance issue. Casual or sessional staff members teach and assess more than 50% of all university courses in Australia, and yet the research in relation to the role sessional staff play in quality assurance of student assessment outcomes is scarce. Moderation processes are a pivotal part of robust quality assurance measures. Drawing upon previous work surrounding four discourses of moderation, this pilot project reports the results of research into the role and impact of sessional staff in moderation processes at tertiary level. Qualitative data were gathered through focus interviews. Results, in the form of various moderation discourses, indicate that sessional staff impact the formal quality assurance processes in numerous ways.     

一种用于空间框架结构几何非线性分析的切线刚度矩阵

为了改善空间框架结构的几何非线性分析,根据总势能驻值原理推导了一个三维梁单元,用增量切线刚度矩阵代替传统的增量割线刚度矩阵.新的切线刚度矩阵除了常用的线性刚度和几何刚度矩阵外,还包含2个变形刚度矩阵,这2个矩阵是由每个增量步中轴力和弯距的变化引起的,是单元变形的函数,包含轴向、横向和扭转变形的耦合项.考虑空间转动和弯距的特征,增加一个修正矩阵,使提出的单元通过刚体测试,达到良好的收敛性能.实例显示使用较少的单元模拟构件仍可有效、准确地得到空间框架的轴向扭转和弯扭屈曲的非线性性能.     

From piloting e‐submission to electronic management of assessment (EMA): Mapping grading journeys

The increasing interest in electronic management of assessment is a sign of a gradual institutionalisation of e‐submission and e‐marking technologies in UK Higher Education. The effective adoption of these technologies requires a managed approach, especially a detailed understanding of current assessment practices within the institution and the development of new or adapted business processes. The findings from close participant observation of assessment processes over a 2‐year period across a large Faculty reveal that three independent variables around (1) initial marking, (2) internal quality assurance and (3) the timing of the return of e‐feedback to students, determine variance in grading journeys. Despite the apparent wide variety of processes, five major grading journeys prevail: three varieties of moderation (moderation of multiple markers and moderation of single markers either before or after grades and feedback are released to students); and two forms of second marking (either blind or open to peers). Within an institution, the identification of major workflows is fundamental to both an effective implementation of assessment technologies and in conducting change. The identification of major workflows across UK Higher Education Institutions remains critical to attain the necessary software development from global vendors.     

Modeling of Nonrecursive Structural Equation Models With Categorical Indicators

Nonrecursive structural equation models generally take the form of feedback loops, involving 2 latent variables that are connected by 2 unidirectional paths, 1 starting with each variable and terminating in the other variable. Nonrecursive models belong to a larger class of path models that require the use of instrumental variables (IVs) to achieve model identification. Prior research has focused on SEM parameter estimation with IVs when indicators were continuous and normally distributed. Much less is known about how estimators function in the presence of categorical indicators, which are commonly used in the social sciences, such as with cognitive and affective instruments. In this study, there was specific interest in comparing the 2-stage least squares (2SLS) estimator and its categorical variant to other recommended estimators. This study compares the performance of several estimation approaches for fitting structural equation models with categorical indicator variables when IVs are necessary to obtain proper model estimates. Across conditions, 1 extension of the nonlinear 2SLS (N2SLS) approach, the nonlinear 3-stage least squares (N3SLS), which accounts for correlated errors among regressors within each model (as does the N2SLS), as well as correlations of errors across models, which N2SLS does not, appears to work the best among methods compared.     

A Nonlinear Structural Equation Mixture Modeling Approach for Nonnormally Distributed Latent Predictor Variables

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we describe a nonlinear structural equation mixture approach that integrates the strength of parametric approaches (specification of the nonlinear functional relationship) and the flexibility of semiparametric structural equation mixture approaches for approximating the nonnormality of latent predictor variables. In a comparative simulation study, the advantages of the proposed mixture procedure over contemporary approaches [Latent Moderated Structural Equations approach (LMS) and the extended unconstrained approach] are shown for varying degrees of skewness of the latent predictor variables. Whereas the conventional approaches show either biased parameter estimates or standard errors of the nonlinear effects, the proposed mixture approach provides unbiased estimates and standard errors. We present an empirical example from educational research. Guidelines for applications of the approaches and limitations are discussed.     

Modeling Nonlinear Structural Equation Models: A Comparison of the Two-Stage Generalized Additive Models and the Finite Mixture Structural Equation Model

Researchers have devoted some time and effort to developing methods for fitting nonlinear relationships among latent variables. In particular, most of these have focused on correctly modeling interactions between 2 exogenous latent variables, and quadratic relationships between exogenous and endogenous variables. All of these approaches require prespecification of the nonlinearity by the researcher, and are limited to fairly simple nonlinear relationships. Other work has been done using mixture structural equation models (SEMM) in an attempt to fit more complex nonlinear relationships. This study expands on this earlier work by introducing the 2-stage generalized additive model (2SGAM) approach for fitting regression splines in the context of structural equation models. The model is first described and then investigated through the use of simulated data, in which it was compared with the SEMM approach. Results demonstrate that the 2SGAM is an effective tool for fitting a variety of nonlinear relationships between latent variables, and can be easily and accurately extended to models including multiple latent variables. Implications of these results are discussed.     

应用Bernstein多项式求解一类分数阶微分方程

给出了基于 Bernstein多项式求解分数阶微分方程的配置方法。首先,在 Bernstein级数的截断式中用tα（0〈α〈1）代替t得到分数阶Bernstein级数截断式,采用Caputo分数阶导数构建分数阶Bernstein级数截断式的矩阵形式。其次,把方程中的每一项用分数阶Bernstein级数截断式转换成矩阵形式,选取配置点,得到相应于非线性代数方程的基本矩阵方程。最后得到由条件矩阵形式和基本矩阵方程构成的新方程组,其解给出了截断项为N的近似解,同时给出了基于残余函数的误差分析。举例说明了这种方法的有效性和可行性。     

Transient Responses of Flexible Non—uniform Spinning Shaft with Nonlinear and Asymmetric Supports

In this paper ,a hybrid approach was developed to investigate the transient responses of a multi-span non-uniform flexble spinning shaft with nonlinear and asymmetric supports.The non-uniform spinning shaft with variable parmeters was modeled as a Bernoulli-Euler beam column with sectional constant cross-section properties by the finite element method.The supporting stiffness behavior of the nonlinear supports was described as a piecewise-linear and asymmetric model.The equations of motion in the matrix form of a multi-span non-uniform spinning shaft with nonlinear and asymmetric supports were formulated using Hamilton‘s principle and the assumed mode method.As an example,a spinning rocket with many variable stiffness supports was numerically simulated by the direct integration method.The transient response and dynamic behavior of this rotate-dynamic system are analyzed.     

A Simulation Study Evaluating the Generalized Additive Model for Assessing Intervention Effects with Small Samples

Single subject (SS) designs are popular in educational and psychological research. There exist several statistical techniques designed to analyze such data and to address the question of whether an intervention has the desired impact. Recently, researchers have suggested that generalized additive models (GAMs) might be useful for modeling nonlinear effects that are common with SS designs. This study sought to extend the use of GAM from SS to a research design in which individuals may be placed in separate groups and receive different interventions. Results of the simulation study found that using a mixed model form of GAM (GAMM) resulted in higher power for detecting actual effects in the population than was true for either GAM or a Bayesian GAM estimator. Thus, GAMMs are recommended for use with SS designs when interventions are expected to induce nonlinear relationships between time and the outcome variable and individuals receive different treatments.     

University affiliation and the role of the university in the moderation of teaching practice in Botswana

The focus of the paper is on the way in which university affiliation can be used to improve the teaching practice component of teacher training programmes. The model of affiliation used by the University of Botswana is described, and a rationale is offered for procedures used to maintain and improve standards in affiliated institutions. The role of external examining is assessed, the term moderation is defined in the context of affiliation, and the procedures used to moderate teaching practice are scrutinised. Using the moderation reports and data relating to the period 1991–96, the principal issues that have arisen are reviewed and analysed, and their significance is assessed. An evaluation of some of the main outcomes, in terms of the impact made on the affiliated institutions, is then undertaken, in tandem with the way in which experience has brought about modifications made to the moderation procedures. A resume´ is offered of the principal lessons learned to date, and how the University of Botswana model could be replicated. Finally, attention is given to the value of the University of Botswana experience to provide guidelines whereby universities could use a system of teaching practice moderation to raise standards and improve institutional practices in teacher training colleges.     

An Excel Solver Exercise to Introduce Nonlinear Regression

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a “black box” to the students. Thus, although correct models are estimated, students often do not obtain a thorough understanding of the nonlinear estimation process. The exercise presented in this article was created to demonstrate to students the need for nonlinear regression estimation—rather than using linear transformations and Ordinary Least Squares (OLS) and subsequently demonstrate the nonlinear optimization process to estimate nonlinear regression models. Using the spreadsheet exercise, students can see effects on the fit of the model by changing the model parameters as they change the values of the decision variables. After applying the spreadsheet to further exercises, students have expressed a deep understanding of the linear regression software. This exercise is innovative because the active learning exercise requires the students to make the logical connections between the structure of the model, the model's parameters, and the objective function.     

A Nonlinear Dynamic Latent Class Structural Equation Model

In this article, we propose a nonlinear dynamic latent class structural equation modeling (NDLC-SEM). It can be used to examine intra-individual processes of observed or latent variables. These processes are decomposed into parts which include individual- and time-specific components. Unobserved heterogeneity of the intra-individual processes are modeled via a latent Markov process that can be predicted by individual- and time-specific variables as random effects. We discuss examples of sub-models which are special cases of the more general NDLC-SEM framework. Furthermore, we provide empirical examples and illustrate how to estimate this model in a Bayesian framework. Finally, we discuss essential properties of the proposed framework, give recommendations for applications, and highlight some general problems in the estimation of parameters in comprehensive frameworks for intensive longitudinal data.     

Nonlinear identification of electro-magnetic force model

Conventional attractive magnetic force models （proportional to the coil current squared and inversely proportional to the gap squared） cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.