In this course, students study major methods of multivariate analysis such as regression analysis, quantification method, principal component analysis and also network analysis in order to deal with phenomenon mathematically based on practical examples. Moreover, students study how to select those methods properly against practical problems through exercises.
This course aims to cultivate the students’ abilities to: select a proper methodology from various mathematical methods in order to cooperate with real problems; decide what necessary data is; develop an effective research plan.
At the end of this course, students will be able to:
1) Understand characteristics and merits of various mathematical methods.
2) Select proper methods for practical complicated problem solving.
3) Develop mathematical research plan which is appropriate for objects and goals.
Multivariate analysis, Network analysis
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
In former part of a class, a lecture about characteristics of mathematical method is done based on an example of practical research. In latter half of a class, an exercise about actual social problems is done. Students consider about what data should be extracted from an object and what method should be applied and also what result will be obtained. At last, a research plan is developed based on result of consideration.
|Course schedule||Required learning|
|Class 1||Guidance||Investigate what methods are included in multivariate analysis, and network analysis.|
|Class 2||Hypothesis testing, analysis of variance||Develop a research plan which utilizes hypothesis testing or analysis of variance.|
|Class 3||Simple regression, multiple regression, mathematical quantification theory class I||Develop a research plan which utilizes simple regression, multiple regression, or mathematical quantification theory class I.|
|Class 4||Factor analysis, principal component analysis||Develop a research plan which utilizes factor analysis or principal component analysis.|
|Class 5||Mathematical quantification theory class III||Develop a research plan which utilizes mathematical quantification theory class III.|
|Class 6||Covariance structure analysis||Develop a research plan which utilizes covariance Structure Analysis|
|Class 7||Discriminant analysis, mathematical quantification theory class II||Develop a research plan which utilizes discriminant analysis or mathematical quantification theory class II.|
|Class 8||Multi-dimensional scaling||Develop a research plan which utilizes multi-dimensional scaling.|
|Class 9||Cluster analysis||Develop a research plan which utilizes Cluster analysis.|
|Class 10||Basis of network||Develop a research plan which utilizes network representation.|
|Class 11||Sub graph, creek||Develop a research plan which utilizes concepts of sub graph or creek.|
|Class 12||Network centrality||Develop a research plan which utilizes Network centrality.|
|Class 13||Structural analysis of network||Develop a research plan which utilizes structural analysis of network.|
|Class 14||Network and randomness||Develop a research plan which utilizes network which includes randomness.|
|Class 15||Small world and scale free||Develop a research plan which utilizes large scale network.|
Eric D. Kolaczyk, “Statistical Analysis of Network Data: Methods and Models”, Springer
T. W. Anderson, “An Introduction to Multivariate Statistical Analysis”, Wiley-Interscience
Feedback sheets are submitted in each class
Students should have successfully completed fundamental linear algebra.
This course consists of the content of science.