Should I use mantel test to test for signifance between [nxm] matrices?

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Fouad Azar 2022-10-2

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https://ww2.mathworks.cn/matlabcentral/answers/1815975-should-i-use-mantel-test-to-test-for-signifance-between-nxm-matrices

评论： dpb 2022-10-2

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I was looking into the Mantel test, but I'm worried that I was going to get myself into a pitfall.

I read that it would be erronous to use a mantel test for datasets spatial auto-correlation, and I'm not sure if my dataset (I've included an image) falls into this category.

Essetially, what I'm trying to do is to decompose my matrix into vectors which I can multiply together to retrive an analog to the 2d matrix. I want to apply a test to show that there is no significant difference between the original matrix and the matrix that I got from the vector multiplication.

Would the Mantel test show that, or would it be erronous? If so, what test should I apply to test for significance between matrices.

Thanks in advnace!

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Torsten 2022-10-2

编辑：Torsten 2022-10-2

Yes, you derived the second matrix from the original by algebraic operations. You didn't get it without knowledge how it was created. In my opinion, the latter were a situation for a statistical test, the first maybe for numerical optimization.

dpb 2022-10-2

Agree w/ @Torsten; this is not a statistical test, but...since Mantel is an application of regression, I think you could use the computed statistic as a performance measure similar to the Pearson correlation; you just can't draw any statistical conclusions regarding the expected value. It, like Pearson, is an R of [-1 1]; one presumes essentially 1.0 will be the result if the reconstruction is good.

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