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Theory and Implementation of Sensitivity Analyses Based on Their Algebraic Representation in the Graph Model

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Journal of Systems Science and Systems Engineering 2019年第5期28卷 580-601页

作者： Jinshuai Zhao Haiyan Xu Keith W.Hipel Baohua Yang College of Economics and Management Nanjing University of Aeronautics and Astronautics Nanjing 211106 China College of Computer Science and Technology Jiangsu Normal University Xuzhou 221116 China Department of Systems Design Engineering University of Waterloo Waterloo Canada School of Business Jiangsu Normal University Xuzhou 221116 China

Sensitivity analyses based on an algebraic representation in the graph model for conflict resolution (GMCR) are generalized for ascertaining the robustness of stability results by varying decision makers' preference ranking.The ordinal preferences in GMCR are advantageous to carry out sensitivity analyses with respect to systematically identifying the influence of preference alterations upon the four basic stabilities consisting of Nash stability,general metarationality,symmetric metarationality and sequential stability.The proposed algebraic representation of the four basic stabilities is not only effective and convenient for computer implementation of sensitivity analysis,but also makes it easier to understand the meaning of the four stabilities when compared with the existing matrix representation.Further,these sensitivity analyses results are embedded into the latest version of the decision support system NUAAGMCR,which can be used to study real-world conflicts.To illustrate how these contributions to sensitivity analyses can be applied in practice and provide valuable strategic insights,they are used to investigate the civil war conflict in South Sudan.

关键词： Sensitivity analyses algebraic expression graph model ordinal preference conflict resolution

Investigating the relationship between crash severity,traffic barrier type,and vehicle type in crashes involving traffic barrier

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Journal of Traffic and Transportation Engineering(English Edition) 2020年第1期7卷 125-136页

作者： Amirarsalan Mehrara Molan Mahdi Rezapour Khaled Ksaibati Department of Civil and Environmental Engineering California Polytechnic State UniversitySan Luis ObispoCA 93407USA Wyoming Technology Transfer Center Department of Civil and Architectural EngineeringUniversity of WyomingLaramieWY 82071USA

Roadside safety is one of the important components of highway systems due to its considerable rate of high-severity crashes.Traffic barriers play a key role in reducing the crash severity and saving more lives on roadsides but choosing an inappropriate traffic barrier could decrease traffic barriers’efficiency.This paper investigated the variables affecting crash severity in different traffic barrier types(cable,guardrail,and rigid)and vehicle types(truck,and non-truck).For this purpose,an ordinal logistic regression approach was conducted on the crash data collected between 2007 and 2016 in Wyoming.According to the results,different traffic barrier types show different relationships to crash severity based on posted speed limit at the site.In guardrail segments,a high-severity crash is more likely when the posted speed limit is more than 55 mph;however,cable barrier crashes were less severe in high-speed limit(>55 mph)areas.While light vehicles were more vulnerable to crashes hitting rigid barriers,no significant difference was found between performances of cable and rigid barriers in terms of truck crash severity.The analytical models proposed in this study would make a clear view for designers and decision-makers in selecting the most appropriate traffic barrier.Also,the effective factors introduced in each model could be used to rank the risk posed by existing traffic barrier segments based on traffic barrier type,truck volume percentage,and other highway characteristics.

关键词： Traffic barrier Roadside safety Truck Crash severity ordinal logistic regression Wyoming

An analysis of Chinese Super League partial results

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Science China Mathematics 2009年第6期52卷 1139-1151页

作者： BRILLINGER David R Department of Statistics University of California Berkeley CA 94720 USA

Some of the history of soccer/world football in China is presented. Then consideration turns to the 2008 Chinese Super League. It has 16 teams. The results from the first half of the season, i.e. 15 rounds, are studied. The response of interest for a specific game is whether the home team won, tied or lost, who the home team was, and who the opponent was. The response is ordinal-valued. A generalized linear model is fit and then, given the remaining fixtures, used to predict the final standings of the season. Other explanatories, such as round number, are considered for inclusion in the model. Simulation is employed to estimate probabilities of interest.

关键词： China forecasting ordinal data simulation soccer Super League world football 2008

The ordinal Interpretation of the Integers and Its Use in Number Theory

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Open Journal of Discrete Mathematics 2019年第4期9卷 165-175页

作者： Nathan Thomas Hamlin Department of Mathematics Washington State University Pullman WA USA

The author recently published a paper which claimed that an ordinal interpretation of numbers had limited applicability for cryptography. A further examination of this subject, in particular to what extent an ordinal interpretation is useful for recurrence sequences, is needed. Hilbert favored an interpretation of the natural numbers that placed their ordinal properties prior to their cardinal properties [1] [2]. The author examines ordinal uses of the integers in number theory in order to discuss the possibilities and limitations of this approach. The author hopes this paper will be useful in clarifying or even correcting some matters that were discussed in his paper of January of 2018. I was trained informally in philosophical realism, and while I think idealism too has a place, at this time in my life I believe that the weight of evidence and usefulness is more on the side of philosophical materialism. I hope this discussion will help supplement for my readers the material in Number in Mathematical Cryptography. I still maintain that a lack of clarity on these matters has hindered progress in cryptography;and it has taken time for me to better understand these things. I hope others who have interest and ability will assist in making these matters clearer. My intention was to work in pure mathematics, and the transition to an applied mindset was difficult for me. As a result, I feel most comfortable in a more middle-of-the road attitude, but have had to slowly move to a more precise analysis of the physical quantities involved. I hope my readers will be patient with my terminology, which is still evolving, and my discussion of things which are more indirectly related, and which are necessary for my expression. These are important things for the mathematical community to understand, and I hope smarter and more knowledgeable people will address my errors, and improve upon the things I might have correct. I am discussing sequences which are sometimes a use of both ordinal and cardinal numbers.

关键词： ordinal Interpretation Integers Number Theory Hilbert’s Theory

农村学校撤并对学生上学距离的影响——基于GIS和ordinal Logit模型的分析

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教育学报 2012年第3期8卷 62-73页

作者：赵丹吴宏超 Bruno Parolin 西北农林科技大学人文学院陕西杨凌712100 华南师范大学教育学院广州510631 澳大利亚新南威尔士大学建筑环境学院

农村义务教育学校布局调整是以撤并小规模学校为主要手段,旨在促进教育资源均衡配置的一项重大教育政策。通过广东省某山区县2003—2009年的学校布局规划数据,从物理距离、时间距离和文化距离的分类视角,运用GIS技术和ordinal Logit模... 详细信息

农村义务教育学校布局调整是以撤并小规模学校为主要手段,旨在促进教育资源均衡配置的一项重大教育政策。通过广东省某山区县2003—2009年的学校布局规划数据,从物理距离、时间距离和文化距离的分类视角,运用GIS技术和ordinal Logit模型分析农村学校撤并对学生上学距离产生的直接影响。研究结果表明:撤并农村学校导致学生上学的物理距离和时间距离增加,偏远学生上学难问题凸显;对学生的文化距离同样产生显著的负面影响。在未来学校布局调整的进程中,县域教育决策者应将关注点从一味追求规模效益转移到教育公平和教育质量上来。要保证农村学生就近入学,设定上学距离的限制;促进学校间教育资源的均衡配置,保证所有学生享受同等质量的教育资源;采用科学的规划程序完善布局调整政策的实施。

关键词：农村学校撤并上学距离 GIS ordinal Logit 学校布局规划

A Comparative Analysis of Generalized Estimating Equations Methods for Incomplete Longitudinal ordinal Data with Ignorable Dropouts

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Open Journal of Statistics 2018年第5期8卷 770-792页

作者： Kago Edwin Ditlhong Oscar Owino Ngesa Abdalla Yusuf Kombo Pan African University Institute of Basic Sciences Technology and Innovation Nairobi Kenya Department of Mathematics and Informatics Taita Taveta University Nairobi Kenya

In longitudinal studies, measurements are taken repeatedly over time on the same experimental unit. These measurements are thus correlated. Missing data are very common in longitudinal studies. A lot of research has been going on ways to appropriately analyze such data set. Generalized Estimating Equations (GEE) is a popular method for the analysis of non-Gaussian longitudinal data. In the presence of missing data, GEE requires the strong assumption of missing completely at random (MCAR). Multiple Imputation Generalized Estimating Equations (MIGEE), Inverse Probability Weighted Generalized Estimating Equations (IPWGEE) and Double Robust Generalized Estimating Equations (DRGEE) have been proposed as elegant ways to ensure validity of the inference under missing at random (MAR). In this study, the three extensions of GEE are compared under various dropout rates and sample sizes through simulation studies. Under MAR and MCAR mechanism, the simulation results revealed better performance of DRGEE compared to IPWGEE and MIGEE. The optimum method was applied to real data set.

关键词： Longitudinal ordinal Data MAR MCAR Multiple Imputation GEE Inverse Probability Weighted GEE Double Robust GEE

THE CAPACITY AND HAUSDORFF DIMENSION OF CUBIC MAP

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Chinese Science Bulletin 1990年第22期35卷 1869-1873页

作者：徐文涛彭守礼 Department of Physics Anhui Institute of Education Hefei 230061 PRC Department of Physics Yunnan University Kunming 650091 PRC

There have been many articles on the quadratic mapping, but only a few on the mapping of higher degree. This article shows how to use inverse iterancy sequence to calculate capacity and Hausdorff dimension with the cu... 详细信息

关键词： inverse iterancy sequence symbolic dynamics ordinal distance function.

Log-Link Regression Models for ordinal Responses

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Open Journal of Statistics 2013年第4期3卷 16-25页

作者： Christopher L. Blizzard Stephen J. Quinn Jana D. Canary David W. Hosmer Department of Public Health University of Massachusetts Amherst USA Flinders Clinical Effectiveness Flinders University Adelaide Australia Menzies Research Institute Tasmania University of Tasmania Hobart Australia

The adjacent-categories, continuation-ratio and proportional odds logit-link regression models provide useful extensions of the multinomial logistic model to ordinal response data. We propose fitting these models with a logarithmic link to allow estimation of different forms of the risk ratio. Each of the resulting ordinal response log-link models is a constrained version of the log multinomial model, the log-link counterpart of the multinomial logistic model. These models can be estimated using software that allows the user to specify the log likelihood as the objective function to be maximized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the unconstrained models produced valid coefficient estimates and standard errors, and the constrained models produced plausible results. Models with a single continuous covariate performed well in data simulations, with low bias and mean squared error on average and appropriate confidence interval coverage in admissible solutions. In an application to real data, practical aspects of the fitting of the models are investigated. We conclude that it is feasible to obtain adjusted estimates of the risk ratio for ordinal outcome data.

关键词： ordinal Risk Ratio Multinomial Likelihood Logarithmic Link Log Multinomial Regression Adjacent Categories Continuation-Ratio Proportional Odds ordinal Logistic Regression

农户恢复村校的需求意愿及影响因素分析——基于ordinal Logit模型的西部三省(区)数据实证

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中国农业大学学报 2017年第9期22卷 191-200页

作者：史耀波赵欣欣岳爱西安理工大学经济与管理学院西安710054 陕西师范大学教育实验经济研究所西安710119

为了解撤点并校后农户对小规模学校的需求意愿,并进一步优化布局调整,通过对西部三省(区)2 760名学生家长的调研,采用ordinal Logit模型,从家庭特征、教育成本、空间变量以及政策因素4个维度对农户是否希望恢复村校的需求意愿以及主要... 详细信息

为了解撤点并校后农户对小规模学校的需求意愿,并进一步优化布局调整,通过对西部三省(区)2 760名学生家长的调研,采用ordinal Logit模型,从家庭特征、教育成本、空间变量以及政策因素4个维度对农户是否希望恢复村校的需求意愿以及主要影响因素进行了研究。结果表明:家庭收入低、上学距离远、在校寄宿、班级规模大和地处山区的家长更加希望恢复村级教学点;村委会支持或受到过捐赠条件下,学生家长更加希望恢复村校。因此,建议在人均收入低以及地理条件较差的偏远山区保留或者恢复村校;同时,在恢复村校决策实施中,农户的广泛参与和村委会支持非常重要,鼓励各地区因地制宜探索建立农村教育的"一事一议"治理模式。

关键词：恢复村校 ordinal Logit模型影响因素政策建议