Multivariate Statistics

Study Course Description

Course Description Statuss:Approved

Course Description Version:4.00

Study Course Accepted:14.03.2024 11:36:29

Study Course Information
Course Code:		SL_119		LQF level:		Level 7
Credit Points:		2.00		ECTS:		3.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Andrejs Ivanovs
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		23 Kapselu street, 2nd floor, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		6	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		12
Classes (count)		6	Class Length (academic hours)		2	Total Contact Hours of Classes		12
Total Contact Hours								24
Part-Time - Semester No.1
Lectures (count)		6	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		6
Classes (count)		6	Class Length (academic hours)		2	Total Contact Hours of Classes		12
Total Contact Hours								18
Study course description
Preliminary Knowledge:
Higher mathematics, probability, statistics, linear models, basic knowledge of R programming.
Objective:
The aim of the course is to introduce the tools and concepts of multivariate data analysis with a strong focus on applications with R program.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Introduction to multivariate analysis, multivariate dataset examples, Covariance, correlation, multivariate normal distribution. Repetition of basic linear algebra elements: determinants, inverse, eigenvalues and eigenvectors, decompositions and quadratic forms.			Lectures		1.00	auditorium
2	Visualizing of multivariate data with R. Practicing matrix algebra calculations in R.			Classes		1.00	computer room
3	Principal components (PC) analysis. A geometrical approach to reducing data matrix dimension. Definition, interpretation and inference on principal components. Normalized principal components.			Lectures		1.00	auditorium
4	Real-world data example analysis in R: calculating PCs, determining statistical significance, drawing plots to interpreting PCs.			Classes		1.00	computer room
5	Factor analysis. Orthogonal factor model. Interpretation of factors. Test for the number of common factors. Comparison with PC analysis.			Lectures		1.00	auditorium
6	Factor analysis in R: estimating the factor model, testing the number of factors, drawing plots to interpret factors.			Classes		1.00	computer room
7	Discriminant analysis. Classes, labels and classification accuracy measures. Linear and quadratic discriminant analysis.			Lectures		1.00	auditorium
8	Discriminant analysis in R.: estimation, interpretation, comparison of methods.			Classes		1.00	computer room
9	Cluster analysis. Proximity between objects, distance functions. Various clusterization algorithms.			Lectures		1.00	auditorium
10	Cluster analysis in R: realizing and comparing various clusterization algorithms. Determining the optimal number of clusters.			Classes		1.00	computer room
11	Multivariable linear regression. Multivariate normality tests.			Lectures		1.00	auditorium
12	Multivariable linear regression in R: estimation, testing and interpretation.			Classes		1.00	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Introduction to multivariate analysis, multivariate dataset examples, Covariance, correlation, multivariate normal distribution. Repetition of basic linear algebra elements: determinants, inverse, eigenvalues and eigenvectors, decompositions and quadratic forms.			Lectures		1.00	auditorium
2	Visualizing of multivariate data with R. Practicing matrix algebra calculations in R.			Classes		1.00	computer room
3	Principal components (PC) analysis. A geometrical approach to reducing data matrix dimension. Definition, interpretation and inference on principal components. Normalized principal components.			Lectures		1.00	auditorium
4	Real-world data example analysis in R: calculating PCs, determining statistical significance, drawing plots to interpreting PCs.			Classes		1.00	computer room
5	Factor analysis. Orthogonal factor model. Interpretation of factors. Test for the number of common factors. Comparison with PC analysis.			Lectures		1.00	auditorium
6	Factor analysis in R: estimating the factor model, testing the number of factors, drawing plots to interpret factors.			Classes		1.00	computer room
7	Discriminant analysis. Classes, labels and classification accuracy measures. Linear and quadratic discriminant analysis.			Lectures		1.00	auditorium
8	Discriminant analysis in R.: estimation, interpretation, comparison of methods.			Classes		1.00	computer room
9	Cluster analysis. Proximity between objects, distance functions. Various clusterization algorithms.			Lectures		1.00	auditorium
10	Cluster analysis in R: realizing and comparing various clusterization algorithms. Determining the optimal number of clusters.			Classes		1.00	computer room
11	Multivariable linear regression. Multivariate normality tests.			Lectures		1.00	auditorium
12	Multivariable linear regression in R: estimation, testing and interpretation.			Classes		1.00	computer room
Assessment
Unaided Work:
1. Review of compulsory and additional literature to expand the knowledge acquired in lectures and classes. 2. Students will be expected to prepare five R based home assignments related to each of the topics: a. Principal components analysis (2nd practical class). b. Factor analysis (3rd practical class). c. Discriminant analysis (4th practical class). d. Cluster analysis (5th practical class). e. Multivariable linear regression (6th practical class).
Assessment Criteria:
Assessment on the 10-point scale according to the RSU Educational Order: • 5 home assignments to be handed in – 70%. • Written Exam – 30%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		Student: • has gained an in-depth knowledge of the theoretic probabilistic concepts related to multivariate analysis. • illustrates the visualization techniques describing the multivariate data. • assesses the most important multivariate techniques such as principal components analysis, factor analysis, cluster analysis and discriminant analysis.
Skills:		• Implements appropriate multivariate data visualizations in R programme. • Can independently apply multivariate data analysis techniques in R programme, to carry out research activities or highly qualified professional functions.
Competencies:		• Can compare and understand the aims of various multivariate data analysis methods and choose the most appropriate for the analysis of the data set. • Can generate hypothesis and make analysis-based decisions related to multivariate data.
Bibliography
No.	Reference
Required Reading
1	W. K. Haerdle Härdle, L. Simar, Applied Multivariate Statistical Analysis. Springer. 2015
2	D. Zelterman. Applied Multivariate Statistics with R. Springer, Statistics for biology and health series, 2015
Additional Reading
1	R. A. Johnson, D.W. Wickern, Applied Multivariate Statistical Analysis, 6th edition. Prentice & Hall, 2007
2	T. Hothorn, B. Everitt, An Introduction to Applied Multivariate Analysis with R. Springer, Use R! series, 2011