ABOUT THE COURSE: Multivariate Procedures with R is designed to equip the learners with necessary theory and application of multivariate procedures in academic, research, and business domains with appropriate examples. The comprehensive content is designed to manually compute various multivariate statistics for learning and R-based computations for application. An important highlight of the course is reporting the results in formal documents such as research reports, journal articles, and class projects. INTENDED AUDIENCE: Students, research scholars, faculty, industry personnel PREREQUISITES: Basic knowledge of statistics. The course will provide a review of the basic concepts of statisticsINDUSTRY SUPPORT: The course will be useful to businesses and service industries
Overview
Syllabus
Week 1:
1. Course Brief - A brief description of the course content; Downloading and installing R and R Studio
2. Exploring R - A description of the basic utilities available in R and R Studio
3. R preliminaries - Using R as a computational tool; Illustrative use of R for data handling
4. Using Simple Commands - Some examples of R-commands
5. Working with R - Importing data into R; Simple applications for data handling
Week 2:
6. Basic Statistical Concepts - Measurement scales; Null hypothesis statistical testing (NHST)
7. Practical Significance of Results - Statistical power of a test; Effect size; Statistical and practical significance of results
8. Univariate Data - Univariate statistical analysis: Z-test, t-test, F-test, correlations
9. Multivariate Techniques - An overview of multivariate techniques: selecting an appropriate multivariate technique for a given dataset
10. Data Manipulation - Scaling data: Mean-centering and standardizing data
Week 3:
11. Data Preparation - Visual (graphical) examination of data: box-plot, stem and leaf plot, histogram; Missing values; Outliers
12. Examining the Data - Examining the data for univariate and multivariate assumptions
13. Transformations for Non-normal Data - Transformations for skewed data; Selecting between square-root, inverse, and logarithmic transformations; Interpreting results based on the transformed data
Week 4:
14. Analytical Models - Descriptive, graphical, and mathematical models
15. Principal Components Analysis (PCA) - Introduction to different factor analysis techniques; Basic concepts; manually doing PCA; Factor structure and rotation of factor structure
16. Performing Principal Components Analysis - Using R-packages for computing PCA in R; Interpreting the R-output
Week 5:
17. Exploratory Factor Analysis (EFA) - Introduction to EFA; Comparison of PCA and EFA; Performing EFA; Higher order factor analysis
18. Application of Factor Analysis - Issues in PCA and EFA; Illustrative applications of PCA and EFA
19. Confirmatory Factor Analysis (CFA) - Objectives of CFA; Comparison of CFA and EFA; Performing CFA and interpretation of R-output
Week 6:
20. Regression Analysis - Bivariate and multiple regression analysis; Assumptions of regression analysis; Multicollinearity and its effect on the regression model
21. Performing regression analysis - Interpretation of R-Output; Multivariate multiple regression analysis
22. Cluster analysis - Objectives of cluster analysis; Similarity measures; Hierarchical clustering; the concept of dendrogram
Week 7:
23. Performing Cluster Analysis - Interpreting R-output
24. Discriminant Analysis - Objectives of discriminant analysis; comparison with regression analysis and clustering
25. Performing Discriminant Analysis - Two-group discriminant analysis; Multiple group discriminant analysis
Week 8:
26. Logistic Regression - Objectives of logistic regression; Logistic regression model; Receiver Operating Characteristic (ROC) Curve
27. Performing Logistic Regression - Interpretation of R-Output
28. Analysis of Variance (ANOVA) - Univariate ANOVA; Factorial ANOVA designs; Analysis of covariance (ANCOVA)
Week 9:
29. Computing ANOVA and ANCOVA - Interpretation of R-output
30. Multivariate analysis of variance (MANOVA) - Analytical approach to MANOVA; Wilks lambda and other statistics to test the statistical significance of MANOVA results
31. Computing and interpreting MANOVA - Computing MANOVA for two groups and multiple groups; Interpretation of R-output
Week 10:
32. Canonical Correlation Analysis (CCA) - Introduction to CCA; Statistical tests for significance testing
33. Performing Canonical Correlation Analysis - Illustrative example and interpretation of R-output
34. Multidimensional scaling (MDS) - Spatial models; Similarity and distance; multidimensional map
Week 11:
35. Performing Multidimensional Scaling - Interpretation of R-output
36. Correspondence Analysis - Basic concepts; Creating perceptual maps
37. Conjoint Analysis - The concept of utility (worth); Assessing part worth and whole worth based on the product attributes
Week 12:
38. Structural Equation Modelling (SEM) - Exogenous and endogenous variables; Reflective and formative constructs; inner model and outer model; Statistics related to SEM
39. Performing Structural Equation Modeling - Interpreting R-output and reporting the results
40. Partial Least Squares for SEM (SEM-PLS) - Sample size considerations; SEM-PLS as a technique for data that violates multivariate assumptions; Other approaches to the issue of non-normal data in SEM
1. Course Brief - A brief description of the course content; Downloading and installing R and R Studio
2. Exploring R - A description of the basic utilities available in R and R Studio
3. R preliminaries - Using R as a computational tool; Illustrative use of R for data handling
4. Using Simple Commands - Some examples of R-commands
5. Working with R - Importing data into R; Simple applications for data handling
Week 2:
6. Basic Statistical Concepts - Measurement scales; Null hypothesis statistical testing (NHST)
7. Practical Significance of Results - Statistical power of a test; Effect size; Statistical and practical significance of results
8. Univariate Data - Univariate statistical analysis: Z-test, t-test, F-test, correlations
9. Multivariate Techniques - An overview of multivariate techniques: selecting an appropriate multivariate technique for a given dataset
10. Data Manipulation - Scaling data: Mean-centering and standardizing data
Week 3:
11. Data Preparation - Visual (graphical) examination of data: box-plot, stem and leaf plot, histogram; Missing values; Outliers
12. Examining the Data - Examining the data for univariate and multivariate assumptions
13. Transformations for Non-normal Data - Transformations for skewed data; Selecting between square-root, inverse, and logarithmic transformations; Interpreting results based on the transformed data
Week 4:
14. Analytical Models - Descriptive, graphical, and mathematical models
15. Principal Components Analysis (PCA) - Introduction to different factor analysis techniques; Basic concepts; manually doing PCA; Factor structure and rotation of factor structure
16. Performing Principal Components Analysis - Using R-packages for computing PCA in R; Interpreting the R-output
Week 5:
17. Exploratory Factor Analysis (EFA) - Introduction to EFA; Comparison of PCA and EFA; Performing EFA; Higher order factor analysis
18. Application of Factor Analysis - Issues in PCA and EFA; Illustrative applications of PCA and EFA
19. Confirmatory Factor Analysis (CFA) - Objectives of CFA; Comparison of CFA and EFA; Performing CFA and interpretation of R-output
Week 6:
20. Regression Analysis - Bivariate and multiple regression analysis; Assumptions of regression analysis; Multicollinearity and its effect on the regression model
21. Performing regression analysis - Interpretation of R-Output; Multivariate multiple regression analysis
22. Cluster analysis - Objectives of cluster analysis; Similarity measures; Hierarchical clustering; the concept of dendrogram
Week 7:
23. Performing Cluster Analysis - Interpreting R-output
24. Discriminant Analysis - Objectives of discriminant analysis; comparison with regression analysis and clustering
25. Performing Discriminant Analysis - Two-group discriminant analysis; Multiple group discriminant analysis
Week 8:
26. Logistic Regression - Objectives of logistic regression; Logistic regression model; Receiver Operating Characteristic (ROC) Curve
27. Performing Logistic Regression - Interpretation of R-Output
28. Analysis of Variance (ANOVA) - Univariate ANOVA; Factorial ANOVA designs; Analysis of covariance (ANCOVA)
Week 9:
29. Computing ANOVA and ANCOVA - Interpretation of R-output
30. Multivariate analysis of variance (MANOVA) - Analytical approach to MANOVA; Wilks lambda and other statistics to test the statistical significance of MANOVA results
31. Computing and interpreting MANOVA - Computing MANOVA for two groups and multiple groups; Interpretation of R-output
Week 10:
32. Canonical Correlation Analysis (CCA) - Introduction to CCA; Statistical tests for significance testing
33. Performing Canonical Correlation Analysis - Illustrative example and interpretation of R-output
34. Multidimensional scaling (MDS) - Spatial models; Similarity and distance; multidimensional map
Week 11:
35. Performing Multidimensional Scaling - Interpretation of R-output
36. Correspondence Analysis - Basic concepts; Creating perceptual maps
37. Conjoint Analysis - The concept of utility (worth); Assessing part worth and whole worth based on the product attributes
Week 12:
38. Structural Equation Modelling (SEM) - Exogenous and endogenous variables; Reflective and formative constructs; inner model and outer model; Statistics related to SEM
39. Performing Structural Equation Modeling - Interpreting R-output and reporting the results
40. Partial Least Squares for SEM (SEM-PLS) - Sample size considerations; SEM-PLS as a technique for data that violates multivariate assumptions; Other approaches to the issue of non-normal data in SEM
Taught by
Prof. Narendra K Sharma
