Modeling Diagnostic Assessments with Bayesian Networks

This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models are reviewed, as they affect applications to diagnostic assessment. The paper discusses how Bayesian network models are set up with expert information, improved and calibrated from data, and deployed as evidence-based inference engines. Aimed at a general educational measurement audience, the paper illustrates the flexibility and capabilities of Bayesian networks through a series of concrete examples, and without extensive technical detail. Examples are provided of proficiency spaces with direct dependencies among proficiency nodes, and of customized evidence models for complex tasks. This paper is intended to motivate educational measurement practitioners to learn more about Bayesian networks from the research literature, to acquire readily available Bayesian network software, to perform studies with real and simulated data sets, and to look for opportunities in educational settings that may benefit from diagnostic assessment fueled by Bayesian network modeling.     

Automated soil resources mapping based on decision tree and Bayesian predictive modeling

INTRODUCTION Land resources management and ecologicalenvironmental decision-making requires knowl-edge about the spatial distribution, and quantity andquality of soil resources. Soil maps have tradition-ally been made by interpretation of remotely sensedimagery supported by ground surveys. Thus, soilmapping becomes expensive, labor-intensive, andtime-consuming exercises. Moreover, it also issubjective, and may result in inconsistencies in theassignment of soil type boundaries or nam…     

Automated soil resources mapping based on decision tree and Bayesian predictive modeling

This article presents two approaches for automated building of knowledge bases of soil resources mapping.These methods used decision tree and Bayesian predictive modeling,respectively to generate knowledge from training data.With these methods,building a knowledge base for automated soil mapping is easier than using the conventional knowledge acquisition approach.The knowledge bases built by these two methods were used by the knowledge classifier for soil type classification of the Longyou area,Zhejiang Province,China using TM bi-temporal imageries and GIS data.To evaluate the performance of the resultant knowledge bases,the classification results were compared to existing soil map based on field survey.The accuracy assessment and analysis of the resultant soil maps suggested that the knowledge bases built by these two methods were of good quality for mapping distribution model of soil classes over the study area.     

Software Packages for Bayesian Multilevel Modeling

Multilevel modeling is a statistical approach to analyze hierarchical data that consist of individual observations nested within clusters. Bayesian method is a well-known, sometimes better, alternative of Maximum likelihood method for fitting multilevel models. Lack of user friendly and computationally efficient software packages or programs was a main obstacle in applying Bayesian multilevel modeling. In recent years, the development of software packages for multilevel modeling with improved Bayesian algorithms and faster speed has been growing. This article aims to update the knowledge of software packages for Bayesian multilevel modeling and therefore to promote the use of these packages. Three categories of software packages capable of Bayesian multilevel modeling including brms, MCMCglmm, glmmBUGS, Bambi, R2BayesX, BayesReg, R2MLwiN and others are introduced and compared in terms of computational efficiency, modeling capability and flexibility, as well as user-friendliness. Recommendations to practical users and suggestions for future development are also discussed.     

基于贝叶斯网络的网络交互教学成效评价系统

网络交互质量是影响网络教学效果的重要因素。已有的网络交互教学成效评价系统缺乏对学习过程的监控和对学习者的良好建模,评价大多凭借专家经验,评估的主观随意性大,评价结果与实际值存在一定的误差。贝叶斯网络有很强大的解决不确定问题的处理水平,是目前基于概率的不确定表达和智能推理方面最有效的理论模型之一。基于贝叶斯网络的网络交互教学成效评价系统,基于领域知识关系构建贝叶斯网络学生模型,并引入模糊数学变换方法对学生认知水平进行评估。能减少不正常因素的干扰,提高对学生认知能力评价的精确度．实现对网络教学交互的质量评估和个性化导学。     

Digital Module 11: Bayesian Psychometric Modeling https://ncme.elevate.commpartners.com

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their capabilities more broadly conceived, as well as fitting models to characterize the psychometric properties of tasks. The approach is first developed in the context of estimating a mean and variance of a normal distribution before turning to the context of unidimensional item response theory (IRT) models for dichotomously scored data. Dr. Levy illustrates the process of fitting Bayesian models using the JAGS software facilitated through the R statistical environment. The module is designed to be relevant for students, researchers, and data scientists in various disciplines such as education, psychology, sociology, political science, business, health, and other social sciences. It contains audio-narrated slides, diagnostic quiz questions, and data-based activities with video solutions as well as curated resources and a glossary.     

Subjective Priors for Item Response Models: Application of Elicitation by Design

Bayesian methods incorporate model parameter information prior to data collection. Eliciting information from content experts is an option, but has seen little implementation in Bayesian item response theory (IRT) modeling. This study aims to use ethical reasoning content experts to elicit prior information and incorporate this information into Markov Chain Monte Carlo (MCMC) estimation. A six‐step elicitation approach is followed, with relevant details at each stage for two IRT items parameters: difficulty and guessing. Results indicate that using content experts is the preferred approach, rather than noninformative priors, for both parameter types. The use of a noninformative prior for small samples provided dramatically different results when compared to results from content expert–elicited priors. The WAMBS (When to worry and how to Avoid the Misuse of Bayesian Statistics) checklist is used to aid in comparisons.     

Predicting Graduation Rates at 4-year Broad Access Institutions Using a Bayesian Modeling Approach

This study models graduation rates at 4-year broad access institutions (BAIs). We examine the student body, structural-demographic, and financial characteristics that best predict 6-year graduation rates across two time periods (2008–2009 and 2014–2015). A Bayesian model averaging approach is utilized to account for uncertainty in variable selection in modeling graduation rates. Evidence suggests that graduation rates can be predicted by religious affiliation, proportion of students enrolled full-time, socioeconomic status of the student body, enrollment size and institutional revenue and expenditures. Findings also demonstrate that relatively fewer variables predict institutional graduation rates for Latina/o and African American students at 4-year BAIs. We conclude with implications for policy and key recommendations for research focused on 4-year BAIs.     

Bayesian networks modeling for thermal error of numerical control machine tools

The interaction between the heat source location, its intensity, thermal expansion coefficient, the machine system configuration and the running environment creates complex thermal behavior of a machine tool, and also makes thermal error prediction difficult. To address this issue, a novel prediction method for machine tool thermal error based on Bayesian networks （BNs） was presented. The method described causal relationships of factors inducing thermal deformation by graph theory and. estimated the thermal error by Bayesian statistical techniques. Due to the effective combination of domain knowledge and sampled data, the BN method could adapt to the change of running state of machine, and obtain satisfactory prediction accuracy. Experiments on spindle thermal deformation were conducted to evaluate the modeling performance. Experimental results indicate that the BN method performs far better than the least squares （LS） analysis in terms of modeling estimation accuracy.     

Educating teachers about managing classrooms and students

The author defines instruction, classroom management, student socialization, and disciplinary intervention as functions commonly performed by teachers, and suggests guidelines for educating teachers in the latter three functions. A knowledge base reflecting established scientific findings exists to inform teacher education concerning classroom management. No such knowledge base exists concerning student socialization and disciplinary intervention, but principles reflecting a consensus of expert opinion can be identified. The author argues for sustained focus on a single integrated approach, taught as an action system that includes attention not only to propositional knowledge (concerning principles of effective management) but also to procedural knowledge (of how to implement these principles) and conditional knowledge (of when and why to implement them). Other recommended elements include conceptual change teaching designed to confront and correct inappropriate attitudes or beliefs that students may bring with them; emphasizing the basics by concentrating on the most commonly occurring classroom teaching situations; and developing skills as much as possible through the apprenticeship approach (modeling, coaching, scaffolding/fading) but supplementing this as needed with didactic instruction in basic concepts and skills, structured classroom observation and student teaching experiences, and use of case materials and simulation exercises as substitutes for field experiences that cannot be included in the program.     

Framework of a Decision-Theoretic Tutoring System for Learning of Mechanics

This paper presents the application of decision-theoretic technique to computer-based tutoring system for elementary mechanics. The technique uses sound probabilistic reasoning and a student model to identify learner's misconception(s). Bayesian belief networks are the building blocks of the student model. The probability values in Bayes' nets are provided by teacher and are based on her judgement, but may be substituted with actual statistics. Evidence on student's mastery of concepts is obtained through her responses to appropriately selected items. Subsequently, Rasch one-parameter model is used to calibrate the item and person parameters (also known as difficulty and ability indices, respectively). The system is able to provide teacher with information for fine-tuning her pedagogical instructions and guide her in coaching students. It is also able to provide students with immediate feedback to improve their proficiencies and ultimately their grades.     

A Bayesian Approach for Estimating Multilevel Latent Contextual Models

In many applications of multilevel modeling, group-level (L2) variables for assessing group-level effects are generated by aggregating variables from a lower level (L1). However, the observed group mean might not be a reliable measure of the unobserved true group mean. In this article, we propose a Bayesian approach for estimating a multilevel latent contextual model that corrects for measurement error and sampling error (i.e., sampling only a small number of L1 units from a L2 unit) when estimating group-level effects of aggregated L1 variables. Two simulation studies were conducted to compare the Bayesian approach with the maximum likelihood approach implemented in Mplus. The Bayesian approach showed fewer estimation problems (e.g., inadmissible solutions) and more accurate estimates of the group-level effect than the maximum likelihood approach under problematic conditions (i.e., small number of groups, predictor variable with a small intraclass correlation). An application from educational psychology is used to illustrate the different estimation approaches.     

何以为师？——实习生的知识转化与身份获得

实习生专业成长过程中的知识转化与身份获得之间是什么关系？本文通过两个案例讨论实习生对教师知识、身份和两者关系的认识,及其对他们知识转化和身份认同的影响。研究发现,对实习生而言,知识与身份相互嵌套、紧密关联。他们对教师工作核心知识的认识在很大程度上决定了他们对教师身份的理解和认同,反之亦然。这表明,教师教育既要注重师范生学科知识的学习,也要注重他们教育性知识的发展。过于狭隘地将教师的学科知识作为其专业活动与教师身份的惟一合法基础,可能阻碍实习生的教师身份认同,误导他们对教育教学的理解。     

Teacher Conceptions and Approaches Associated with an Immersive Instructional Implementation of Computer-Based Models and Assessment in a Secondary Chemistry Classroom

This paper reports on a case study of an immersive and integrated multi-instructional approach (namely computer-based model introduction and connection with content; facilitation of individual student exploration guided by exploratory worksheet; use of associated differentiated labs and use of model-based assessments) in the implementation of coupled computer-based models and assessment in a high-school chemistry classroom. Data collection included in-depth teacher interviews, classroom observations, student interviews and researcher notes. Teacher conceptions highlighted the role of models as tools; the benefits of abstract portrayal via visualizations; appropriate enactment of model implementation; concerns with student learning and issues with time. The case study revealed numerous challenges reconciling macro, submicro and symbolic phenomena with the NetLogo model. Nonetheless, the effort exhibited by the teacher provided a platform to support the evolution of practice over time. Students' reactions reflected a continuum of confusion and benefits which were directly related to their background knowledge and experiences with instructional modes. The findings have implications for the role of teacher knowledge of models, the modeling process and pedagogical content knowledge; the continuum of student knowledge as novice users and the role of visual literacy in model decoding, comprehension and translation.     

Bayesian Meta-Analytic SEM: A One-Stage Approach to Modeling Between-Studies Heterogeneity in Structural Parameters

Meta-analytic structural equation modeling (MASEM) refers to a set of meta-analysis techniques for combining and comparing structural equation modeling (SEM) results from multiple studies. Existing approaches to MASEM cannot appropriately model between-studies heterogeneity in structural parameters because of missing correlations, lack model fit assessment, and suffer from several theoretical limitations. In this study, we address the major shortcomings of existing approaches by proposing a novel Bayesian multilevel SEM approach. Simulation results showed that the proposed approach performed satisfactorily in terms of parameter estimation and model fit evaluation when the number of studies and the within-study sample size were sufficiently large and when correlations were missing completely at random. An empirical example about the structure of personality based on a subset of data was provided. Results favored the third factor structure over the hierarchical structure. We end the article with discussions and future directions.     

Multiple solutions in dyads or alone – Fostering the acquisition of modeling competencies in mathematics

Generating multiple solutions is a promising approach in order to foster deep insight and understanding in mathematical contexts. However, in complex domains, students often struggle to generate just one solution, let alone more than one. This study investigates whether collaboration supports learners to generate multiple solutions, and to what extent collaboration and generating multiple solutions foster the acquisition of modeling competencies. In an experiment, students either learned alone or in dyads which were homogeneous or heterogeneous with respect to the level of prior knowledge, and they were prompted to generate one or multiple solutions in the learning phase (N = 193 seventh and eighth graders). Learning in homogeneous dyads fostered the acquisition of modeling competencies. Being prompted to generate a second solution was beneficial only for learners with high prior knowledge; overall, actually generating a second solution had positive impact.     

Latent variable modeling in the hierarchical modeling framework in longitudinal studies: a fully bayesian approach

This paper presents a strategy for specifying latent variable regressions in the hierarchical modeling framework (LVR-HM). This model takes advantage of the Structural Equation Modeling (SEM) approach in terms of modeling flexibility—regression among latent variables—and of the HM approach in terms of allowing for more general data structures. A fully Bayesian approach via Markov Chain Monte Carlo (MCMC) techniques is applied to the LVR-HM. Through analyzing the data from a longitudinal study of educational achievement, gender difference are explored in the growth of mathematical achievement across grade 7 through grade 10. Allowing for the fact that initial status effect to rates of change may differ for girls and boys, the LVR-HM is specified in a way that rates of change parameters are modeled as a function of initial status parameters and the interaction between initial status and gender.     

Residual Structures in Latent Growth Curve Modeling

This article presents relevant research on Bayesian methods and their major applications to modeling in an effort to lay out differences between the frequentist and Bayesian paradigms and to look at the practical implications of these differences. Before research is reviewed, basic tenets and methods of the Bayesian approach to modeling are presented and contrasted with basic estimation results from a frequentist perspective. It is argued that Bayesian methods have become a viable alternative to traditional maximum likelihood-based estimation techniques and may be the only solution for more complex psychometric data structures. Hence, neither the applied nor the theoretical measurement community can afford to neglect the exciting new possibilities that have opened up on the psychometric horizon.     

A Unified Latent Growth Curve Model

Applying item response theory models to repeated observations has demonstrated great promise in developmental research. By allowing the researcher to take account of the characteristics of both item response and measurement error in longitudinal trajectory analysis, it improves the reliability and validity of latent growth curve analysis. This has enabled the study, to differentially weigh individual items and examine developmental stability and change over time, to propose a comprehensive modeling framework, combining a measurement model with a structural model. Despite a large number of components requiring attention, this study focuses on model formulation, evaluates the performance of the estimators of model parameters, incorporates prior knowledge from Bayesian analysis, and applies the model using an illustrative example. It is hoped that this fundamental study can demonstrate the breadth of this unified latent growth curve model.     

小世界网络条件下合作演化的特性研究

构建一个小世界网络下囚徒困境博弈的演化模型,用Multi-Agent的建模与仿真研究方法,研究网络簇系数、重复博弈轮数及间接信息获取对合作演化动态的影响。结果表明:簇系数、重复博弈轮数对合作演化动态有显著影响,间接信息的获取也明显影响着合作效率。