How do I calculate xscores in Proc PLS?

[KR029]

I am using Proc PLS for PCR. Below is the code I'm using: 

I would like to understand how to calculate the "xscore=factors" columns using my raw data.

I have output for model effect loading and model effect weights, but I don't understand how I can use this to calculate the factors that I have outputted in the output file. 

What is a formula that I can use to calculate the factors to match the columns in the output file using my raw input data? 

[Reeza]

Just a quick note, I've moved your post to the Statistical Procedures forum, for better responses.

[PaigeMiller]

Scores are computed using the centered and scaled x-values (in other words, each x-variable has a mean of zero and a variance of 1).

Then the score in dimension i for a single observation is the vector multiplication of loadings (p) times centered and scaled data values (x) transposed

Ti = p*x'

[KR029]

Thank you for your response Paige. I have tried that, and the numbers are not matching. 

Below are the first few rows of data. The Var 1 -- Var 8 variables I have here are standardized to meet the criteria. 

If I take a linear combination of Var1 -- Var 8 with the model effect loadings seen below, I calculate much larger factors than the ones in the data. Please explain how this works. 

Thank you so much for you help on this!

[PaigeMiller]

Show your math. Show the results.

Make the actual input data available as a .CSV file or a SAS data set.

[KR029]

CSV is attached with std variables, loading, and my calculations. 

[PaigeMiller]

In your spreadsheet, in cell Y2, I use the formula =SUMPRODUCT(B2:I2,P2:W2) and I get the exact same value as in cell X2

[KR029]

Yes, I calculated cell X2 doing the same in an attempt to match factor 1, which is cell L2. But doing the sumproduct with loading weights and standardized variables does not give me factor 1. 

[PaigeMiller]

I believe the difference is a scaling factor, that the variance of column L over the entire data set (not just the 10 rows you show) must be equal to 1. Or it must be equal to eigenvalue 1, I don't really remember now, but it should be easy for you to confirm.