2.-Statistics/R-squared.md

@@ -136,4 +136,20 @@ $$
 R^2_{\text{Nagelkerke}} = \frac{R^2_{\text{Cox-Snell}}}{1 - \left( L_{\text{null\ model}} \right)^{2/n}}
 $$
 
-Each pseudo-R² provides an indication of the model fit, with values closer to 1 indicating a better fit. However, unlike traditional R², pseudo-R² values can vary depending on the model and should be interpreted with caution.
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+### Comparing Different Pseudo-R² Measures
+
+Each pseudo-R² provides an indication of the model fit, with values closer to 1 indicating a better fit. However, unlike traditional \(R^2\), pseudo-\(R^2\) values can vary depending on the type of model, and they don’t have a direct interpretation as the percentage of variance explained like traditional \(R^2\) does in linear regression models.
+
+- **McFadden’s pseudo-\(R^2\)**: Tends to produce values lower than traditional \(R^2\), and values between 0.2 and 0.4 are considered good fits in many contexts.
+  
+- **Cox & Snell’s pseudo-\(R^2\)**: Provides a likelihood-based measure but does not reach 1, making interpretation less straightforward.
+
+- **Nagelkerke’s pseudo-\(R^2\)**: Adjusts Cox & Snell’s measure to allow for a maximum value of 1, making it easier to interpret, but still not as intuitive as traditional \(R^2\).
+
+### Interpreting Pseudo-R² Measures
+
+When comparing models using pseudo-\(R^2\), it's important to note that these measures are relative within the context of a specific model. Unlike traditional \(R^2\), they are not directly comparable across different types of models or datasets. As such, while pseudo-\(R^2\) values can offer insight into model performance, they should be interpreted with caution and supplemented with other evaluation metrics, such as likelihoods or classification accuracy, depending on the model type.
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