Regression Analysis

  1. Specialized Regression Techniques
    1. Time Series Regression
      1. Static Time Series Models
        1. Contemporaneous Relationships
          1. Trend Variables
            1. Seasonal Variables
            2. Distributed Lag Models
              1. Finite Distributed Lag Models
                1. Infinite Distributed Lag Models
                  1. Geometric Lag Models
                    1. Polynomial Distributed Lag Models
                    2. Autoregressive Models
                      1. Autoregressive Distributed Lag Models
                        1. Dynamic Multipliers
                          1. Long-Run vs Short-Run Effects
                          2. Stationarity and Unit Roots
                            1. Definition of Stationarity
                              1. Weak vs Strong Stationarity
                                1. Unit Root Tests
                                  1. Dickey-Fuller Test
                                    1. Augmented Dickey-Fuller Test
                                      1. Phillips-Perron Test
                                      2. Spurious Regression Problem
                                        1. Cointegration Concepts
                                      3. Panel Data Regression
                                        1. Panel Data Structure
                                          1. Individual and Time Dimensions
                                            1. Balanced vs Unbalanced Panels
                                              1. Short vs Long Panels
                                              2. Pooled Cross-Section Models
                                                1. Pooled OLS Estimation
                                                  1. Assumptions and Limitations
                                                  2. Fixed Effects Models
                                                    1. Individual Fixed Effects
                                                      1. Time Fixed Effects
                                                        1. Two-Way Fixed Effects
                                                          1. Within Transformation
                                                            1. LSDV Approach
                                                              1. Interpretation of Fixed Effects
                                                              2. Random Effects Models
                                                                1. Random Effects Assumptions
                                                                  1. GLS Estimation
                                                                    1. Between and Within Variation
                                                                      1. Feasible GLS
                                                                      2. Model Selection in Panel Data
                                                                        1. Hausman Test
                                                                          1. Breusch-Pagan LM Test
                                                                            1. F-Test for Fixed Effects
                                                                            2. Advanced Panel Data Topics
                                                                              1. Dynamic Panel Models
                                                                                1. Instrumental Variables in Panels
                                                                                  1. Difference-in-Differences
                                                                                2. Regularization and Shrinkage Methods
                                                                                  1. The Bias-Variance Tradeoff
                                                                                    1. Overfitting Problems
                                                                                      1. Model Complexity
                                                                                        1. Prediction vs Inference Goals
                                                                                        2. Ridge Regression
                                                                                          1. L2 Penalty Function
                                                                                            1. Ridge Estimator Formula
                                                                                              1. Choosing the Tuning Parameter
                                                                                                1. Properties of Ridge Estimator
                                                                                                  1. Geometric Interpretation
                                                                                                  2. Lasso Regression
                                                                                                    1. L1 Penalty Function
                                                                                                      1. Variable Selection Property
                                                                                                        1. Lasso Solution Path
                                                                                                          1. Coordinate Descent Algorithm
                                                                                                            1. Cross-Validation for Tuning
                                                                                                            2. Elastic Net Regression
                                                                                                              1. Combined L1 and L2 Penalties
                                                                                                                1. Grouping Effect
                                                                                                                  1. Parameter Selection
                                                                                                                    1. Comparison with Ridge and Lasso
                                                                                                                    2. Model Selection with Regularization
                                                                                                                      1. Cross-Validation Approaches
                                                                                                                        1. Information Criteria
                                                                                                                          1. Stability Selection
                                                                                                                        2. Robust and Nonparametric Methods
                                                                                                                          1. Robust Regression
                                                                                                                            1. Motivation for Robust Methods
                                                                                                                              1. M-Estimators
                                                                                                                                1. Huber Regression
                                                                                                                                  1. Least Absolute Deviations
                                                                                                                                    1. Breakdown Point
                                                                                                                                      1. Efficiency vs Robustness
                                                                                                                                      2. Nonlinear Least Squares
                                                                                                                                        1. Nonlinear Model Specification
                                                                                                                                          1. Gauss-Newton Algorithm
                                                                                                                                            1. Levenberg-Marquardt Algorithm
                                                                                                                                              1. Starting Values and Convergence
                                                                                                                                              2. Quantile Regression
                                                                                                                                                1. Conditional Quantiles
                                                                                                                                                  1. Median Regression
                                                                                                                                                    1. Asymmetric Loss Function
                                                                                                                                                      1. Interpretation of Quantile Coefficients
                                                                                                                                                        1. Inference in Quantile Regression
                                                                                                                                                          1. Applications and Advantages

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                                                                                                                                                      8. Practical Applications and Implementation