Regression Analysis

  1. Generalized Linear Models
    1. Introduction to GLMs
      1. Limitations of Linear Regression
        1. Motivation for GLMs
          1. Components of GLMs
            1. Random Component
              1. Systematic Component
              2. Exponential Family Distributions
                1. Normal Distribution
                  1. Binomial Distribution
                    1. Poisson Distribution
                      1. Gamma Distribution
                      2. Maximum Likelihood Estimation
                        1. Likelihood Function Construction
                          1. Log-Likelihood Function
                            1. Score Function
                              1. Information Matrix
                                1. Newton-Raphson Algorithm
                                  1. Fisher Scoring Algorithm
                                2. Binary Response Models
                                  1. Linear Probability Model
                                    1. Model Specification
                                      1. Advantages and Limitations
                                        1. Heteroscedasticity Issues
                                          1. Predicted Probabilities Outside Unit Interval
                                          2. Logistic Regression
                                            1. Logit Model Specification
                                              1. Odds and Odds Ratios
                                                1. Interpretation of Coefficients
                                                  1. Marginal Effects
                                                    1. Average Marginal Effects
                                                      1. Marginal Effects at Means
                                                        1. Marginal Effects at Representative Values
                                                        2. Model Diagnostics
                                                          1. Goodness-of-Fit Tests
                                                          2. Probit Regression
                                                            1. Probit Model Specification
                                                              1. Normal CDF Interpretation
                                                                1. Coefficient Interpretation
                                                                  1. Marginal Effects in Probit
                                                                    1. Comparison with Logit
                                                                  2. Count Data Models
                                                                    1. Poisson Regression
                                                                      1. Model Assumptions
                                                                        1. Interpretation of Coefficients
                                                                          1. Incidence Rate Ratios
                                                                            1. Exposure Variables
                                                                            2. Overdispersion in Count Data
                                                                              1. Definition and Detection
                                                                                1. Consequences for Poisson Model
                                                                                  1. Tests for Overdispersion
                                                                                  2. Negative Binomial Regression
                                                                                    1. Model Specification
                                                                                      1. Handling Overdispersion
                                                                                        1. Interpretation of Results
                                                                                          1. Model Selection Criteria
                                                                                          2. Zero-Inflated Models
                                                                                            1. Zero-Inflated Poisson
                                                                                              1. Zero-Inflated Negative Binomial
                                                                                                1. Hurdle Models
                                                                                              2. Categorical Response Models
                                                                                                1. Ordinal Response Models
                                                                                                  1. Ordered Logit Model
                                                                                                    1. Ordered Probit Model
                                                                                                      1. Proportional Odds Assumption
                                                                                                        1. Interpretation of Coefficients
                                                                                                        2. Multinomial Response Models
                                                                                                          1. Multinomial Logit Model
                                                                                                            1. Independence of Irrelevant Alternatives
                                                                                                              1. Interpretation of Coefficients
                                                                                                                1. Relative Risk Ratios
                                                                                                                2. Conditional Logit Models
                                                                                                                  1. Choice-Specific Variables
                                                                                                                    1. Individual-Specific Variables
                                                                                                                      1. Mixed Logit Models

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                                                                                                                  5. Advanced Linear Regression Topics

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                                                                                                                  7. Specialized Regression Techniques