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Regular version of the site
Master 2020/2021

## Multidimensional Data Analysis

Area of studies: Applied Mathematics and Informatics
When: 2 year, 3 module
Mode of studies: offline
Master’s programme: Applied Statistics with Network Analysis
Language: English
ECTS credits: 4

### Course Syllabus

#### Abstract

This course will take a modern, data-analytic approach to the multiple regression model. Our coverage of the material will emphasize the ways that graphical tools can augment traditional methods for describing how the conditional distribution of a dependent variable changes along with the values of one or more independent variables. The course will examine the basic nature and assumptions of the linear regression model, diagnostic tools for detecting violations of the regression as-sumptions, and strategies for dealing with situations in which the basic assumptions are violated. #### Learning Objectives

• The goal of the course is to ensure that students understand topics and principles of applied linear models on an advanced level.
• The course gives students an important foundation to develop and conduct their own research as well as to evaluate research of others. #### Expected Learning Outcomes

• Know new insights into the regression analysis.
• Know various modern extensions to the traditional linear model.
• Know complex methods of aggregating data and dimensionality reduction.
• Know innovative, effective methods for presenting the results from statistical investigations of empirical data.
• 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.
• Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods.
• Be able to criticize constructively and determine existing issues with applied linear models in published work.
• Have an understanding of advanced methods of linear models and related multivariate extensions.
• Have the skill to meaningfully develop an appropriate model for the research question.
• Have the skill to work with statistical software, required to analyze the data. #### Course Contents

• Examining data
The first session will introduce the main concepts of preparation for multivariate regression analysis. We will discuss graphical displays, data transformations, and other techniques of multi-dimensional exploratory analysis.
• General Linear Models I: The Basics of Least Squares Regression
The session is a review of basic linear models with an extension to multivariate regression. We will review graphical fitting, least-squares fitting, properties of least-squares estimator, statistical inference, regression models in matrix form, vector geometry and vector presentation of the regression model, the data ellipsoid and model fit.
• General Linear Models II: Effective Presentation I
The session will go in much more detail into topics of categorical predictors, fitted values, inter-actions and effect displays, standardization and relative importance of predictors.
• Regression with Categorical Dependent Variables I
This sessions will provide an understanding of limited dependent variables and problems with the OLS models; binary logit and probit models, fitted probabilities and effect displays.
• Regression with Categorical Dependent Variables II
This session covers ordered probit and logit models, Multinomial logit models, Generalized linear models, Poisson models for count data, Diagnostics for generalized linear models.
• Regression diagnostics I: Unusual observations
This session will show how to examine outliers, leverage, and influence observations; hat values and studentized residuals; and case-deletion statistics.
• Regression Diagnostics II: Nonlinearity, Nonnormality, and Heteroskedasticity
This session will focus on residual plots, visual and maximum likelihood methods for determining transformations, weighted least squares to adjust for nonconstant error variance, robust standard errors. It will also look at variance inflation, principle components analysis, collinearity and model selection, and ridge regression.
• Resampling techniques for regression
This session will introduce bootstrapping and jackknifing, as well as cross-validation.
• Nonlinear regression
This session will examine transformable nonlinearity, polynomial regression, orthogonal poly-nomials, and non-linear least squares.
• Nonparametric regression I: Local polynomial regression
This session will cover local regression (LOESS) and its fitting parameters, robust local regres-sion, and degrees of freedom in local regression, M-estimation and iteratively weighted least squares and bounded influence regression.
• Nonparametric Regression II: Smoothing Splines
This session will introduce the concepts of piecewise regression, cubic smoothing splines, thin plates smoothing splines, and their degrees of freedom.
• Additive regression models (GAM) and graphical regression
This session will look at estimation and backfitting, cross-validation for smoothing parameters, GAM for binary dependent variables, vector GAM for ordered dependent variables. It will also introduce the concepts of model checking plots, visualizing regression with more than two pre-dictors, and sequentially combining predictors. #### Assessment Elements

• Final In-Class or Take-home exam (at the dis-cretion of the instructor)
• Homework Assignments (5 x Varied points)
• In-Class Labs (9-10 x Varied points)
• Quizzes (Best 9 of 10, Varied points) #### Interim Assessment

• Interim assessment (3 module)
0.5 * Final In-Class or Take-home exam (at the dis-cretion of the instructor) + 0.2 * Homework Assignments (5 x Varied points) + 0.2 * In-Class Labs (9-10 x Varied points) + 0.1 * Quizzes (Best 9 of 10, Varied points) #### Recommended Core 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
• 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

• 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