Though weightages taken seems reasonable,Here’s how you can refine and validate your synthetic indicator weights through both conceptual improvement and statistical methods:

Refining the Model Conceptually

Consult Stakeholders or Experts:Involve banking professionals or regulators to weigh in on the importance of each dimension and indicator. This can provide practical insights and ensure alignment with industry priorities.

Regulatory Frameworks: Cross-reference weights with guidelines like Basel III or national banking regulations. For instance, higher weights on liquidity and capital quality are consistent with global standards emphasizing financial stability.

Scenario Testing: Apply the weights to sample banks under different scenarios (e.g., economic downturn, high-interest environments). Ensure the synthetic indicator reflects intuitive changes in bank performance under these conditions.

Adjust Weights Dynamically: Consider dynamic weighting based on bank size, market conditions, or regional factors. For example, smaller banks might need higher emphasis on liquidity.

Statistical Validation

1. Principal Component Analysis (PCA):

Goal: Check if the dimensions and sub-indicators capture the maximum variance in the dataset.

Steps: Standardize your dataset.

Run PCA on all indicators.

Compare the PCA loadings with your proposed weights.

Adjust weights if highly loading indicators are underweighted.

2. Correlation Analysis:

Goal: Ensure sub-indicators within a dimension are moderately correlated to avoid redundancy or overemphasis.

Steps: Compute the correlation matrix for indicators within each dimension.

If two indicators are highly correlated, consider reducing their individual weights or combining them into a single composite indicator.

3. Sensitivity Analysis:

Goal: Determine how sensitive the synthetic indicator is to changes in weights.

Steps: Vary each weight (e.g., ±5%) while keeping others constant.

Assess changes in the composite score and rank order of banks.

4. Regression Analysis:

Goal: Validate weights based on real-world outcomes like credit ratings or financial performance.

Steps: Use the synthetic indicator as an independent variable to predict known outcomes.

Adjust weights to maximize explanatory power (e.g., R²).

5. Shapley Value Decomposition:

Goal: Quantify the contribution of each dimension and indicator to the final score.

Steps: Use game-theoretic approaches to compute Shapley values for each indicator based on its marginal contribution.

Compare these values to your weights to ensure alignment.

Tools for Analysis

Software: Python, R, or statistical software like STATA.

Key Libraries for Python:PCA: sklearn.decomposition.PCA

Correlation Matrix: pandas.corr()

Regression: statsmodels or sklearn.linear_model

Shapley Analysis: shap library

Thank you very much.

Your opinions and methodologies proposed will be taken into account in future works.

Kind regards.