A credit risk analyst at Bank XYZ is tasked with evaluating the credit risk of large corporations, relying on credit ratings provided by two distinct rating agencies, Agency X and Agency Y. The analyst has collected the credit ratings for 30 companies, with the ratings segmented into four groups as follows:

Rating categories:

1. High investment grade
2. Mid investment grade
3. Low investment grade
4. Non-investment grade

In order to visually compare these rating categories, the analyst charts the ratings for each company from both agencies, resulting in a graph named "Corporate Ratings: Agency X vs. Agency Y":

Corporate Ratings: Agency X vs. Agency Y 5 Y 4 3 Rating - Agency X

Given this data visualization, what statistical method should the analyst employ to effectively estimate the correlation between the rating categories assigned by Agency X and Agency Y?