Optimal Sample Allocation in Group-Randomized Mediation Studies with a Group-Level Mediator

We derive sample-allocation formulas that maximize the power of several mediation tests in two-level–group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under parameter values commonly seen in the literature. However, the optimal sample allocation can be heavily influenced by the group-to-individual cost ratio, the ratio of the treatment-mediator to mediator-outcome path coefficients, and the outcome variance structure. We illustrate these findings with a hypothetical group-randomized trial examining a school-discipline reform policy. To encourage utilization of the sample allocation formulas we implement them in the R package PowerUpR and powerupr Shiny application.     

Mediation Effects In 2-1-1 Multilevel Model: Evaluation Of Alternative Estimation Methods

We compared six common methods in estimating the 2-1-1 (level-2 independent, level-1 mediator, level-1 dependent) multilevel mediation model with a random slope. They were the Bayesian with informative priors, the Bayesian with non-informative priors, the Monte-Carlo, the distribution of the product, the bias-corrected, and the bias-uncorrected parametric percentile residual bootstrap. The Bayesian method with informative priors was superior in relative mean square error (RMSE), power, interval width, and interval imbalance. The prior variance and prior mean were also varied and examined. Decreasing the prior variance increased the power, reduced RMSE and interval width when the prior mean was the true value, but decreasing the prior variance reduced the power when the prior mean was set incorrectly. The influence of misspecification of prior information of the b coefficient on multilevel mediation analysis was greater than that on coefficient a. An illustrate example with the Bayesian multilevel mediation was provided.     

Alternative Methods for Assessing Mediation in Multilevel Data: The Advantages of Multilevel SEM

Multilevel modeling (MLM) is a popular way of assessing mediation effects with clustered data. Two important limitations of this approach have been identified in prior research and a theoretical rationale has been provided for why multilevel structural equation modeling (MSEM) should be preferred. However, to date, no empirical evidence of MSEM's advantages relative to MLM approaches for multilevel mediation analysis has been provided. Nor has it been demonstrated that MSEM performs adequately for mediation analysis in an absolute sense. This study addresses these gaps and finds that the MSEM method outperforms 2 MLM-based techniques in 2-level models in terms of bias and confidence interval coverage while displaying adequate efficiency, convergence rates, and power under a variety of conditions. Simulation results support prior theoretical work regarding the advantages of MSEM over MLM for mediation in clustered data.     

Estimation of a Nonlinear Intervention Phase Trajectory for Multiple-Baseline Design Data

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (ΔLevels) model and a model involving a quadratic function (Quadratic) for the nonlinear intervention phase data were also estimated. In addition, a simulation study was conducted to assess Markov chain Monte Carlo estimation of the logistic model and compare its trajectory recovery with use of the ΔLevels and Quadratic models. While most of the logistic model's parameter values were recovered well, trajectory recovery was very reasonable using the simpler Quadratic model. Results are discussed along with recommendations for practitioners and directions for future research.     

Optimal Design for Two-Level Random Assignment and Regression Discontinuity Studies

An important concern when planning research studies is to obtain maximum precision of an estimate of a treatment effect given a budget constraint. When research designs have a multilevel or hierarchical structure changes in sample size at different levels of the design will impact precision differently. Furthermore, there will typically be differential costs of enrolling additional units at different levels of the hierarchy. The optimal design problem in multilevel research studies involves determining the optimal sample size at each level of the design given specified design parameters and a specified marginal cost of recruitment at each level. The current work extends existing results by considering optimal design for (a) unbalanced random assignment designs and (b) regression discontinuity designs.     

Power Analysis in Two-Level Unbalanced Designs

Previous work on statistical power has discussed mainly single-level designs or 2-level balanced designs with random effects. Although balanced experiments are common, in practice balance cannot always be achieved. Work on class size is one example of unbalanced designs. This study provides methods for power analysis in 2-level unbalanced designs with random effects. Overall, the nesting affects power negatively, the treatment affects power positively, and the Level-2 units affect power more than Level-1 units. Computing power assuming balanced designs provides reasonable estimates only when imbalance is mild or moderate. When imbalance is large or extreme, computing power assuming balanced designs produces larger estimates of power. The use of the harmonic mean provides accurate estimates of power in unbalanced 2-level designs even when imbalance is large.     

扬州地区工业设计现状及其发展策略探究

工业设计作为新兴的产业力量能够对经济发展起到极大的推动作用.而当前扬州地区现状是工业设计观念淡薄、缺乏高素质的专业人才、设计环境不容乐观、专业服务平台空白.因此,发展扬州的工业设计产业可从建立相关交流平台、广泛深入宣传、确定优先发展项目、加大高素质人才培养力度这几方面入手.     

Using Multilevel Regression Mixture Models to Identify Level-1 Heterogeneity in Level-2 Effects

This article proposes a novel exploratory approach for assessing how the effects of Level-2 predictors differ across Level-1 units. Multilevel regression mixture models are used to identify latent classes at Level 1 that differ in the effect of 1 or more Level-2 predictors. Monte Carlo simulations are used to demonstrate the approach with different sample sizes and to demonstrate the consequences of constraining 1 of the random effects to 0. An application of the method to evaluate heterogeneity in the effects of classroom practices on students is used to show the types of research questions that can be answered with this method and the issues faced when estimating multilevel regression mixtures.     

Between-School Variation in Students' Achievement,Motivation, Affect,and Learning Strategies: Results from 81 Countries for Planning Group-Randomized Trials in Education

To plan group-randomized trials where treatment conditions are assigned to schools, researchers need design parameters that provide information about between-school differences in outcomes as well as the amount of variance that can be explained by covariates at the student (L1) and school (L2) levels. Most previous research has offered these parameters for U.S. samples and for achievement as the outcome. This paper and the online supplementary materials provide design parameters for 81 countries in three broad outcome categories (achievement, affect and motivation, and learning strategies) for domain-general and domain-specific (mathematics, reading, and science) measures. Sociodemographic characteristics were used as covariates. Data from representative samples of 15-year-old students stemmed from five cycles of the Programme for International Student Assessment (PISA; total number of students/schools: 1,905,147/70,098). Between-school differences as well as the amount of variance explained at L1 and L2 varied widely across countries and educational outcomes, demonstrating the limited generalizability of design parameters across these dimensions. The use of the design parameters to plan group-randomized trials is illustrated.     

PowerUp!: A Tool for Calculating Minimum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies

Abstract

This paper and the accompanying tool are intended to complement existing supports for conducting power analysis tools by offering a tool based on the framework of Minimum Detectable Effect Sizes (MDES) formulae that can be used in determining sample size requirements and in estimating minimum detectable effect sizes for a range of individual- and group-random assignment design studies and for common quasi-experimental design studies. The paper and accompanying tool cover computation of minimum detectable effect sizes under the following study designs: individual random assignment designs, hierarchical random assignment designs (2-4 levels), block random assignment designs (2-4 levels), regression discontinuity designs (6 types), and short interrupted time-series designs. In each case, the discussion and accompanying tool consider the key factors associated with statistical power and minimum detectable effect sizes, including the level at which treatment occurs and the statistical models (e.g., fixed effect and random effect) used in the analysis. The tool also includes a module that estimates for one and two level random assignment design studies the minimum sample sizes required in order for studies to attain user-defined minimum detectable effect sizes.     

Accuracy of Estimates and Statistical Power for Testing Meditation in Latent Growth Curve Modeling

The latent growth curve modeling (LGCM) approach has been increasingly utilized to investigate longitudinal mediation. However, little is known about the accuracy of the estimates and statistical power when mediation is evaluated in the LGCM framework. A simulation study was conducted to address these issues under various conditions including sample size, effect size of mediated effect, number of measurement occasions, and R ₂ of measured variables. In general, the results showed that relatively large samples were needed to accurately estimate the mediated effects and to have adequate statistical power, when testing mediation in the LGCM framework. Guidelines for designing studies to examine longitudinal mediation and ways to improve the accuracy of the estimates and statistical power were discussed.     

Multilevel design efficiency in educational effectiveness research

In educational effectiveness research, multilevel data analyses are often used because research units (most frequently, pupils or teachers) are studied that are nested in groups (schools and classes). This hierarchical data structure complicates designing the study because the structure has to be taken into account when approximating the accuracy of estimation and the power for statistical testing, which should be sufficient to reach meaningful conclusions. Accuracy and power, both referred to as efficiency, can be optimized by carefully choosing the number of units to sample at each of the levels, taking into account the available resources and costs of sampling at these levels. We complement the findings that are found in the literature with regard to designing multilevel studies and propose a simulation approach that can be used to help making study-specific decisions.     

The Role of Centering for Interaction of Level 1 Variables in Multilevel Structural Equation Models

This article examined the role of centering in estimating interaction effects in multilevel structural equation models. Interactions are typically represented by product term of 2 variables that are hypothesized to interact. In multilevel structural equation modeling (MSEM), the product term involving Level 1 variables is decomposed into within-cluster and between-cluster random components. The choice of centering affects the decomposition of the product term, and therefore affects the sample variance and covariance associated with the product term used in the maximum likelihood fitting function. The simulation study showed that for an interaction between a Level 1 variable and a Level 2 variable, the product term of uncentered variables or the product term of grand mean centered variables produced unbiased estimates in both Level 1 and Level 2 models. The product term of cluster mean centered variables produced biased estimates in the Level 1 model. For an interaction between 2 Level 1 variables, the product term of cluster mean centered variables produced unbiased estimates in the Level 1 model, whereas the product term of grand mean centered variables produced unbiased estimates for the Level 1 model. Recommendations for researchers who wish to estimate interactions in MSEM are provided.     

任务型教学模式下高中英语阅读课教学设计的策略

新课程标准倡导在英语教学中采用任务型教学模式,让学生学会用英语做事,培养学生的交际能力。这就要求教师依据教学内容并结合课程的总体目标,有创造性地和灵活地使用教材,设计贴近学生实际的教学活动,吸引和组织他们积极参与,并在此过程中培养发展学生的创新精神和培养学生用英语解决实际问题的能力。     

H1-003铣齿机数控化改造设计

在多年使用H1-003铣齿机的基础上,发现其存在的一些不足,通过分析铣齿机的工作原理,提出数控化改造设计的原理、思路和方法,成功地实现了对该铣齿机的数控化改造。经加工试验表明,改造后的铣齿机扩大了加工范围,增强了刚性,大大提高了机床性能,具有很高的性价比和实用性。     

网络课程实验环节教学设计与实践

对网络教育中普遍存在实践环节相对薄弱的问题进行分析,简述在工程测量课程中进行实验环节教学设计的实践,指出实验教学在网络教育中的重要作用,并对加强实验环节提出几点建议。     

文化产业政策背景下广西艺术设计人才的培养

广西艺术设计人才培养的现状是人才培养从单一走向多样,办学规模扩大的同时存在人才质量下降的隐患,人才培养模式重叠混合,人才培养的国际合作少。文化产业的发展离不开艺术设计人才的培养,其培养的策略是：营造＂兼容并蓄＂的多元文化环境;培养策略与国家产业政策相适应;加快从量到质的转变;调整教学体系,适应市场对艺术设计人才的需求;注重特色办学,实行国际联合办学。     

梧州旅游形象设计与推广策略研究

形象是旅游地的生命,也是形成竞争优势的最有力的工具。良好形象的设计和推广,是旅游目的地开拓市场的重要手段,也是旅游地的巨大财富和无形资产。文章以梧州的旅游发展现状、游客的感知形象调查情况为基础,对梧州的旅游形象定位,旅游形象系统的建设和旅游形象推广力度、技术等方面存在的问题进行分析,并为如何解决这些问题提出探讨性策略。     

火电厂取水管道设计及常见问题的处理

以江西数个火电厂取水管道工程为例,详细介绍了取水管道敷设时容易遇见的问题,针对存在的问题给出了有效的处理方法,为其他取水管道工程的设计提供了参考。     

调频调宽脉冲开关电源触发电路的设计

采用2片555时基电路，其中一片控制频率，另一片控制占空比．产生频率为30Hz～10MHz连续可调；在10MHz频带宽度内，占空比为1％～99％连续可调的矩形触发脉冲，且频率和占空比均可独立调节．