Calculate Chatterjee's Rank Correlation Coefficient

This function calculates Chatterjee's rank correlation coefficient, which measures the association between two variables. It is particularly useful for identifying monotonic relationships between variables, even if they are not linear.

Usage

xicor(x, y, ties = FALSE)

Arguments

x

A numeric vector representing the independent variable.

y

A numeric vector representing the dependent variable.

ties

A logical value indicating whether to handle ties in the data. Default is FALSE.

If ties = TRUE, the function adjusts for tied ranks (repeated values in the data). This is important when there are many tied values in either x or y, as it ensures accurate calculation by considering the maximum rank for tied observations.

If ties = FALSE, the function assumes that there are no ties, or that ties can be handled without additional computational effort. This option can offer better performance when ties are rare or absent.

Value

A numeric value representing Chatterjee's rank correlation coefficient.

Details

Unlike Pearson's correlation (which measures linear relationships), Chatterjee's coefficient can handle non-linear monotonic relationships. It is robust to outliers and can handle tied ranks, making it versatile for datasets with ordinal data or tied ranks. This makes it a valuable alternative to Spearman's and Kendall's correlations, especially when the data may not meet the assumptions required by these methods.

By default, ties = FALSE is set to prioritize computational efficiency, as handling ties requires additional processing. In cases where ties are present or likely (such as when working with ordinal or categorical data), it is recommended to set ties = TRUE.

Examples

xicor(x = pq_data$Collaboration_hours, y = pq_data$Internal_network_size, ties = TRUE)
#> [1] 0.1703689
xicor(x = pq_data$Collaboration_hours, y = pq_data$Internal_network_size, ties = FALSE)
#> [1] 0.1721492