What is the Partial Rank Correlation Coefficient?

The Partial Rank Correlation Coefficient (PRCC) is a statistical measure used in sensitivity analysis to assess the correlation between an input parameter and the output variable of interest, while controlling for the influence of other parameters. It quantifies the strength and direction of the relationship between a parameter and the output variable, taking into account the potential confounding effects of other parameters.

The PRCC is particularly useful when there are multiple input parameters in a model, and it becomes important to determine the individual contribution of each parameter to the output variability. By considering the influence of other parameters, the PRCC provides a more accurate assessment of the direct impact of a parameter on the output variable.

The calculation of the PRCC involves the following steps:

1. Select the input parameter and output variable: Identify the specific input parameter and output variable that you want to analyze in the sensitivity analysis.
2. Perturb the input parameter: Vary the selected input parameter while keeping all other parameters fixed at their original values. The variation can be done using different sampling techniques, such as Latin Hypercube Sampling or Monte Carlo Sampling.
3. Evaluate the rank correlation: Calculate the rank correlation coefficient between the perturbed values of the selected parameter and the output variable. The rank correlation coefficient measures the degree of association between two variables based on their ranks rather than their actual values. Common rank correlation coefficients include Spearman’s rank correlation coefficient and Kendall’s rank correlation coefficient.
4. Control for other parameters: Repeat steps 2 and 3 by perturbing and calculating the rank correlation coefficient for each of the remaining parameters, one at a time. This process allows the assessment of the influence of each parameter on the output variable while accounting for the effects of other parameters.
5. Calculate the Partial Rank Correlation Coefficient: The PRCC is calculated by subtracting the rank correlation coefficient between the perturbed values of the selected parameter and the output variable (step 3) from the rank correlation coefficient obtained when all parameters are considered (step 4). The PRCC represents the unique contribution of the selected parameter to the output variability after accounting for the effects of other parameters.

The PRCC ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation between the parameter and the output variable. A higher absolute value of the PRCC indicates a stronger relationship between the parameter and the output variable.

The PRCC is a valuable tool in sensitivity analysis as it allows for the identification of influential parameters and their individual contribution to the output variability. It helps prioritize parameters for further investigation or control and provides insights into the relative importance of different factors in a complex system.