How to create a scatter plot of partial rank correlation

Hello,

I have a question regarding a partial rank correlation.

I would like to use "partialcorr" function to find correlation between X and Y after controlling for Z and visualize it on a scatter plot. As far as I understood the calculation, I can plot it as below.

X = variable 1

Y = variable 2

Z = Confounder

mdl_Z_X = fitlm(Z,X);

mdl_Z_Y = fitlm(Z,Y);

plot(mdl_Z_X.Residuals.Raw,mdl_Z_Y.Residuals.Raw);

I calculated the correlation in both ways to make sure they match each other

R1 = partialcorr(X,Y,Z,"type","Pearson")

R2 = corr(mdl_Z_X.Residuals.Raw, mdl_Z_Y.Residuals.Raw, "type", "Pearson")

And they were matched (R1 = R2). However, When I switched it to "Spearman", the correlation coefficient did not match. What I mean is ...

R1 = partialcorr(X,Y,Z,"type","Spearman")

R2 = corr(mdl_Z_X.Residuals.Raw, mdl_Z_Y.Residuals.Raw, "type", "Spearman")

R1 and R2 were a different value. I also tried to convert X and Y variables into rank variables as if ...

X = [2.5 3.1 6.5 1.2]

Xrank = [2 3 4 1]

The conversion seemed working somewhat as the correlation coefficient became closer to the coefficient from the "partialcorr" function, but it still did not match. Since the algorithm of a built-in function is hidden by MATLAB, I would really appreciate if someone knows how I can create a scatter plot of partial rank correlation.

Thank you in advance.

[俊荣 韩]

hello,

Thank you for your example shown here, and I got a lot of help. I tried your code and did a bit of improvement

"R1 and R2 were a different value. I also tried to convert X and Y variables into rank variables as if ...

X = [2.5 3.1 6.5 1.2]

Xrank = [2 3 4 1]"

The rank of X should be descended when conducting Spearman. It's ascending in your example.

And the R2 calculation with resduals of X and Y should use Pearson,

R2 = corr(mdl_Z_X.Residuals.Raw, mdl_Z_Y.Residuals.Raw, "type", "Pearson")

Then, the R1 and R2 were the same.