Hi Rick, Thank you. Yeah, I have explored how Python calculates Xweights as well, and it seems that it also uses the Euclidean norm. To clarify, I have created a simple raw dataset and SAS code and shared the Xweights (the first component of the SVD of X'Y or X'YY'X) with you below. You will see that the norm of Xweights in Python is 1 (I'm not sure, but I think this proves that it uses the Euclidean norm?), while the norm of Xweights in SAS is always around 1.04XXX. (Again, I have applied mean centering and scaling to the data, so that is not an issue of the difference, it's also not about the algorithm difference as with number of factor = 1, NIPALS algorithm will be the same as SIMPLS, which I have double checked too, it's not a flip of sign as well) DATA regress; INPUT Y X1 X2 X3 X4 X5; DATALINES; 7 0 23 3 4 1 8 2 7 2 3 2 2 0 8 8 3 3 6 0 9 2 5 4 5 0 1 5 2 5 ; RUN; PROC PLS DATA=regress METHOD=SIMPLS nfac = 1 details varss ; MODEL Y = X1 X2 X3 X4 X5; RUN; ods output XWeights = work.pls_xweights run;   Xweights X1 X2 X3 X4 X5 SAS 0.487515 0.259817 -0.783895 0.223089 -0.344725 Python 0.467325566 0.249056761 -0.751431332 0.213850196 -0.330449077     ... View more

Hi Paige, I hope you had a good weekend.   Yeah, the difference in VIP still lies in the scaling. However, since we sometimes interpret VIP score by comparing an absolute value—for example, as a general rule of thumb, if VIP > 1, it indicates a significant variable that impacts the dependent variable—Then this cause a problem as T03 is considered an important variable in SAS but not in Python. Therefore, if possible, it would be helpful to understand how SAS performs the scaling. However, if this is not feasible, it should be fine, as the difference is small.   Variable SAS_XWEIGHT Python_XWEIGHT PYTHON_VIP SAS_VIP T01 -0.0727 -0.0697 0.5402 0.5628 T02 0.1723 0.1653 1.2806 1.3343 T03 0.1321 0.1268 0.9823 1.0235 T04 -0.0649 -0.0623 0.4828 0.5030 T05 0.2256 0.2165 1.6770 1.7474   Thanks, ... View more

Thank you so much Rick. Yeah, I agree that it might be because different software scales xweights differently. And yes, the xweight difference doesn't affect the coefficient or R-squared value, but it does make the VIP scores slightly different, which is a little annoying. Does anyone know how SAS calculates norms? As from what I understand, xweight is obtained from the SVD of X'Y (which has the shape 1 × the number of independent variables). With only one dimension/observation, the easiest way to compute the SVD is by dividing X'Y by its norm. However, I understand (with my limited knowledge on linear algebra) that with only one dimension, there may not be a unique solution, but would be good to know how SAS process it if possible (Ex. with the inner regression coefficient) ... View more

Hi Ksharp,   Thanks for your reply! Interesting, I would like to learn more about how SAS compute SVD differently from Python or R.   Thanks, ... View more

Hi Rick,    Thanks so much for getting back to me. My SAS code is shown as below: proc pls data=regress method=simpls nfac = 1; model Y = A01-A60; run; ods output XWeights = work.pls_xweights run; And here is the comparison of xweights getting from SAS vs Python for the first five dependent variables   Xweights T01 T02 T03 T04 T05 SAS -0.072658 0.172263 0.132138 -0.06494 0.225583 Python -0.069733319 0.165327533 0.12681782 -0.062325287 0.216501385   A quick look I don't think it's the issue of different decimal places between Python or SAS, or with different signs. And the number of components here is one factor only, therefore I don't think their SVD will be different.     Thanks,         ... View more