Geostatistics and Statistical Analysis in Geography

  1. Spatial Regression Analysis
    1. Limitations of Ordinary Least Squares with Spatial Data
      1. Violation of Independence Assumption
        1. Spatial Autocorrelation in Residuals
          1. Consequences for Inference
          2. Spurious Correlation
            1. False Relationships due to Spatial Structure
              1. Confounding Effects
              2. Unreliable Significance Tests
                1. Inflated Type I Error Rates
                  1. Biased Standard Errors
                  2. Inefficient Estimates
                    1. Loss of Precision
                      1. Suboptimal Predictions
                    2. Diagnosing Spatial Dependence
                      1. Residual Analysis
                        1. Moran's I Test on Residuals
                          1. Spatial Correlograms
                            1. Residual Mapping
                            2. Lagrange Multiplier Tests
                              1. LM-Lag Test
                                1. LM-Error Test
                                  1. Robust LM Tests
                                  2. Likelihood Ratio Tests
                                    1. Information Criteria Comparison
                                    2. Spatial Regression Models
                                      1. Spatial Lag Model
                                        1. Model Specification
                                          1. Spatial Autoregressive Parameter
                                            1. Interpretation of Coefficients
                                              1. Direct and Indirect Effects
                                              2. Spatial Error Model
                                                1. Model Specification
                                                  1. Spatial Error Parameter
                                                    1. Interpretation of Coefficients
                                                      1. Error Structure Modeling
                                                      2. Spatial Durbin Model
                                                        1. Model Specification
                                                          1. Spatially Lagged Explanatory Variables
                                                            1. Direct and Indirect Effects
                                                              1. Total Effects
                                                              2. General Spatial Model
                                                                1. Combined Lag and Error Components
                                                                  1. Model Identification
                                                                  2. Spatial Autoregressive Moving Average Models
                                                                  3. Estimation Methods
                                                                    1. Maximum Likelihood Estimation
                                                                      1. Log-Likelihood Functions
                                                                        1. Concentrated Likelihood
                                                                          1. Numerical Optimization
                                                                          2. Instrumental Variables
                                                                            1. Two-Stage Least Squares
                                                                              1. Generalized Method of Moments
                                                                              2. Bayesian Estimation
                                                                                1. Prior Specification
                                                                                  1. Posterior Inference
                                                                                2. Geographically Weighted Regression
                                                                                  1. Addressing Spatial Heterogeneity
                                                                                    1. Local Model Fitting
                                                                                      1. Spatial Non-stationarity
                                                                                      2. Concept of Local Coefficients
                                                                                        1. Spatial Variation in Relationships
                                                                                          1. Local R-squared Values
                                                                                          2. Weighting Schemes
                                                                                            1. Gaussian Weights
                                                                                              1. Bi-square Weights
                                                                                                1. Exponential Weights
                                                                                                2. Bandwidth Selection
                                                                                                  1. Fixed Bandwidth
                                                                                                    1. Constant Spatial Scale
                                                                                                      1. Distance-Based
                                                                                                      2. Adaptive Bandwidth
                                                                                                        1. Variable Spatial Scale
                                                                                                          1. Nearest Neighbor-Based
                                                                                                          2. Cross-Validation Methods
                                                                                                            1. Information Criteria
                                                                                                            2. Model Diagnostics
                                                                                                              1. Local Multicollinearity
                                                                                                                1. Residual Analysis
                                                                                                                  1. Model Comparison
                                                                                                                  2. Mapping and Interpreting Results
                                                                                                                    1. Visualization of Local Coefficients
                                                                                                                      1. Interpretation of Spatial Patterns
                                                                                                                        1. Significance Testing

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                                                                                                                    5. Measuring and Modeling Spatial Autocorrelation

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                                                                                                                    7. Advanced Topics in Geostatistics