Detect multicollinearity in real-life, non-normally distributed data

Question

I am currently trying to figure out whether my data (consisting of thousands of rows, some is numerical, and some are categorical, and some are ordinal) has multicollinearities or not.

One thing I have noticed is that my data is not normally distributed, based on the Shapiro-Wilk test. As is the case with mostly (if not all) real world data, as answered here

But based on several posts, including this one, many suggests the ANOVA (Categorical vs Numerical) or the Chi-Squared (Categorical vs Categorical ) tests to detect whether or not there are multicollinearities, without implying (at least not specifically) to ensure the data has normal distribution.

My questions are:

1. Can we actually use these methods parametric methods for non-normally distributed data?
2. Other than statistical tests, is there a computational model/algorithm to detect multicollinearities in data, parametric or non-parametric? I've read that decision trees algorithms like Random Forests and XGBoost disregards multicollinearities and can also give feature importance information.

Answer 1

As with most contexts - it depends.

Often non-normally distributed data is transformed to be more normally distributed if the algorithm has strict requirements.

Sometimes the normality assumption is ignored.