Multivariate Analysis

  1. Data Preparation and Exploration
    1. Data Screening and Quality Assessment
      1. Data Structure Examination
        1. Variable Types and Scales
          1. Data Range and Distribution Checks
          2. Missing Data Analysis
            1. Types of Missingness
              1. Missing Completely at Random (MCAR)
                1. Missing at Random (MAR)
                  1. Missing Not at Random (MNAR)
                  2. Missing Data Patterns
                    1. Imputation Methods
                      1. Mean Imputation
                        1. Regression Imputation
                          1. Multiple Imputation
                            1. Maximum Likelihood Methods
                            2. Deletion Methods
                              1. Listwise Deletion
                                1. Pairwise Deletion
                              2. Outlier Detection and Treatment
                                1. Univariate Outliers
                                  1. Z-Score Method
                                    1. Interquartile Range Method
                                      1. Modified Z-Score
                                      2. Multivariate Outliers
                                        1. Mahalanobis Distance
                                          1. Leverage Values
                                            1. Cook's Distance
                                            2. Outlier Treatment Strategies
                                              1. Deletion
                                                1. Transformation
                                                  1. Winsorization
                                                2. Assumption Checking
                                                  1. Normality Assessment
                                                    1. Univariate Normality
                                                      1. Multivariate Normality
                                                      2. Linearity Assessment
                                                        1. Scatterplot Matrices
                                                          1. Partial Regression Plots
                                                          2. Homoscedasticity Assessment
                                                            1. Residual Plots
                                                              1. Levene's Test
                                                                1. Box's M Test
                                                                2. Multicollinearity Assessment
                                                                  1. Correlation Matrix Inspection
                                                                    1. Variance Inflation Factor
                                                                      1. Condition Index
                                                                        1. Tolerance Values
                                                                      2. Data Transformation
                                                                        1. Standardization
                                                                          1. Z-Score Standardization
                                                                            1. Robust Standardization
                                                                            2. Normalization
                                                                              1. Min-Max Scaling
                                                                                1. Unit Vector Scaling
                                                                                2. Variable Transformations
                                                                                  1. Centering
                                                                                    1. Polynomial Transformations

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                                                                                3. The Multivariate Normal Distribution

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                                                                                5. Principal Component Analysis