2025/2026
Многомерный анализ данных
Статус:
Маго-лего
Когда читается:
4 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
3
Контактные часы:
40
Course Syllabus
Abstract
This course takes a modern, data-analytic approach to the multivariate data. Multivariate data analysis (MVA) encompasses statistical techniques that are used to analyze several variables at once. The course covers some basic notions of statistics with the development into several domains: cluster analysis, principle component analysis, factor analysis, canonical corelation analysis, discriminant analysis. All the topic of the course are supplemented by the examples of MVA application to different types of data. This course serves as an important prerequisite for the course in structural equation modeling.
Learning Objectives
- To develop a comprehensive understanding of the statistical principles and mathematical foundations underlying multivariate techniques, including their assumptions, limitations, and appropriate research applications.
- To master the selection, application, and critical interpretation of key multivariate methods (cluster analysis, PCA, factor analysis, CCA, and discriminant analysis).
- To gain practical experience implementing multivariate methods using R, including data preparation, data diagnostics, visualization, and reporting of results.
Expected Learning Outcomes
- Have the skill to work with statistical software, required to analyze the data.
- Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods.
- Have the skill to meaningfully develop an appropriate model for the research question.
- Be able to criticize constructively and determine existing issues with applied linear models in published work.
- Be able to explore the advantages and disadvantages of various linear modeling instruments, and demonstrate how they relate to other methods of analysis.
- Be able to work with major linear modeling programs, especially R and SAS, so that they can use them and interpret their output.
- Have an understanding of advanced methods of linear models and related multivariate extensions.
- Know complex methods of aggregating data and dimensionality reduction.
- Know innovative, effective methods for presenting the results from statistical investigations of empirical data.
- Know new insights into the regression analysis.
- Know various modern extensions to the traditional linear model.
Course Contents
- Introduction to multivariate data analysis
- Basic statistics
- Some basic notations
- Graphical representation of multivariate data
- Cluster analysis
- Principal component analysis
- Factor analysis
- Canonical correlations
- Discriminant analysis
Bibliography
Recommended Core Bibliography
- Analysis of multivariate and high-dimensional data, Koch, I., 2014
- Brown, B. (2012). Multivariate Analysis for the Biobehavioral and Social Sciences : A Graphical Approach. Hoboken, N.J.: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=405437
- Chatterjee, S., Hadi, A. S., & Ebooks Corporation. (2012). Regression Analysis by Example (Vol. Fifth edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=959808
- Rencher, A. C., & Christensen, W. F. (2012). Methods of Multivariate Analysis (Vol. Third Edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=472234
Recommended Additional Bibliography
- Berry, W. D., & Sanders, M. S. (2000). Understanding Multivariate Research : A Primer For Beginning Social Scientists. Boulder, Colo: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421170
- Essentials of research methods in human sciences. Vol.2: Multivariate analysis, Metsamuuronen, J., 2017
- Izenman, A. J. (2008). Modern Multivariate Statistical Techniques : Regression, Classification, and Manifold Learning. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=275789