# How to test for multicollinearity over matrices?

I plan to test whether there is multicollinearity not between predictors in an individual linear regression model (columns in a matrix) but between the models (over matrices).

The matrices are all the same size (900 by 3, i.e. each model has three predicting vectors that have 900 samples). Let's say they look like this:

Timepoint  Model_A  Model_B  (...)  Model_Z
1          1 7 4    1 2 6           1 3 2
2          5 9 4    1 9 8           0 9 4
3          6 2 8    0 9 7           5 1 7
(...)      (...)    (...)           (...)
900        2 1 1    3 9 1           3 2 2


Is there any problem with simply concatenating them and calculating the Variance Inflation Factor as if it were one big model like so:

Timepoint  Model_AZ
1          1 7 4 1 2 6 1 3 2
2          5 9 4 1 9 8 0 9 4
3          6 2 8 0 9 7 5 1 7
(...)            (...)
900        2 1 1 3 9 1 3 2 2

• Please explain what "between the models (over matrices)" means. Could you perhaps find a different way to describe your problem and its objectives? – whuber Jun 11 '18 at 13:55
• Thank you for the edits, but could you explain what you might mean by a "model"? So far you don't seem to have described any kind of statistical model or procedure at all. – whuber Jun 11 '18 at 15:14