关于Pykrige中get_statistics的Q1/Q2/cR含义及负R²_score问题咨询

What do Q1, Q2, cR mean? #

These three metrics from Variogram.get_statistics() measure how well your selected variogram model matches the experimental variogram (the spatial correlation structure calculated directly from your temperature data):

• Q1: Mean error between experimental variogram values and the model’s predicted values. This is analogous to the mean error (ME) used in interpolation validation, but it’s specific to variogram model fit. A value near 0 means no systematic bias between the model and experimental variogram.
• Q2: Root mean square error between experimental and model variogram values. This mirrors the RMSE used for interpolation predictions, but applies to variogram fit. Lower Q2 values mean the model’s variogram points are closer to the experimental ones.
• cR: Pearson correlation coefficient between experimental and model variogram values. It quantifies the linear relationship between the two datasets; a value closer to 1 indicates a stronger correlation and better model fit.

None of these directly correspond to normalized RMSE (NRMSE), which scales RMSE by the data’s range or mean for cross-dataset comparisons.

Why is my Krige CV R²_score negative? #

A negative R² score means your kriging model performs worse at predicting temperatures than simply using the average of all observed values. Common causes include:

• Insufficient data: Small datasets lead to unstable experimental variograms and cross-validation splits. Leave-one-out CV with minimal data can produce wildly inconsistent predictions.
• Poor variogram model/parameters: Using the wrong variogram type (e.g., spherical instead of exponential) or poorly tuned parameters (nugget, sill, range) that fail to capture temperature’s actual spatial pattern.
• Violated stationarity assumption: Ordinary kriging assumes constant mean and spatial correlation across the study area. Temperature often breaks this (e.g., elevation gradients, latitudinal trends), so universal kriging with a drift term (like elevation) might be more suitable.
• Outliers: Extreme temperature values can skew the variogram fit and throw off cross-validation results.

Can Q1, Q2, cR be used to find optimal parameters? #

Yes, but pair them with cross-validation metrics for robust results:

• Variogram fit tuning: When optimizing parameters (nugget, sill, range), prioritize models where Q1 is close to 0, Q2 is low, and cR is high. These indicate the model accurately captures your data’s spatial correlation structure.
• Cross-validation check: Even if a model has strong variogram fit stats, validate it with interpolation-focused metrics (R², RMSE, ME) from cross-validation. A good variogram fit doesn’t always guarantee accurate predictions, especially if ordinary kriging’s assumptions are violated.
• Hybrid approach: Use grid search or optimization tools to find parameters that balance strong variogram fit (Q1/Q2/cR) and solid interpolation performance (cross-validation R²/RMSE).

内容的提问来源于stack exchange，提问作者alow wong