Problem with unstandardized LV scores calculation
 Diogenes
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Problem with unstandardized LV scores calculation
I was trying to compute by hand the unstandardized LV scores using Anne Martensen & Lars Grønholdt procedure to compute the unstandardized weights and I had found these results:
1) The scores computed by hand was different from the scores from SmartPLS
2) The correlation between standardized and unstandardized scores was perfect (hand) and was little different when I was using the unstandardized scores from SmartPLS (The error has had little effect for practical matters, but it is a bug).
Professor Christian already found the problem: “SmartPLS uses normed unstandardized outer loadings instead of the outer weights.”
And fixed it for the next release.
==========================
To compute the correct unstandardized follow the example from ECSI model (mobi205.csv)
1) Run the example
2) Copy the standardized outer weights
3) Compute the standardized deviation to each indicator and copy/past to the side of the weight
4) Compute (outer weights / standard deviation for each indicator)
5) Compute the unstandardized weights as “relative weights” to have the unstandardized LV scores in the same scale of the indicators. See the table below:
Indicator Standardized outer weights Standard deviation SOW / s.d. Unstandardized weight
CUEX1 0.5481 1,6218 0,3380 0,4243
CUEX2 0,4950 1,7927 0,2761 0,3467
CUEX3 0.3836 2,1028 0,1824 0,2290
Total = 1,0000
6) Use the unstandardized weights to compute the LV scores.
Best regards.
Bido
1) The scores computed by hand was different from the scores from SmartPLS
2) The correlation between standardized and unstandardized scores was perfect (hand) and was little different when I was using the unstandardized scores from SmartPLS (The error has had little effect for practical matters, but it is a bug).
Professor Christian already found the problem: “SmartPLS uses normed unstandardized outer loadings instead of the outer weights.”
And fixed it for the next release.
==========================
To compute the correct unstandardized follow the example from ECSI model (mobi205.csv)
1) Run the example
2) Copy the standardized outer weights
3) Compute the standardized deviation to each indicator and copy/past to the side of the weight
4) Compute (outer weights / standard deviation for each indicator)
5) Compute the unstandardized weights as “relative weights” to have the unstandardized LV scores in the same scale of the indicators. See the table below:
Indicator Standardized outer weights Standard deviation SOW / s.d. Unstandardized weight
CUEX1 0.5481 1,6218 0,3380 0,4243
CUEX2 0,4950 1,7927 0,2761 0,3467
CUEX3 0.3836 2,1028 0,1824 0,2290
Total = 1,0000
6) Use the unstandardized weights to compute the LV scores.
Best regards.
Bido
Unstandardized LV Scores
Dear Professor Bido,
I tried to compute LV scores as described above but yielded confusing results. I repeat my process to make sure that everything was correct
1. I copied the outer weights from the 'Calculation Results' section of the pls estimation output.
2. I computed s.d. for each indicator in Excel.
3. Outer weight / s.d. for each indicator
4. Computation of relative weight (with sum = 1 for each LV)
5. I then calculated the LV scores by sum(indicator values*rel. weights) for each LV
After doing that, I compared these LV scores to the unstandardized scores from the PLS output. They were all equal. Furthermore, I standardized the (hand) calculated LV scores and compared these to the standardized scores from the output. These scores did not fit´ what went wrong?
To find the error, I tried to reproduce your example in mobi250.csv (you wrote '205'. Is this a typo or an older example file?). My problem was that I could not find the values, you report above for 'standardized outer weights'. Where can I find these values?
Many thanks in advance to anyone who could help me solve this issue.
Best regards
Stephan
I tried to compute LV scores as described above but yielded confusing results. I repeat my process to make sure that everything was correct
1. I copied the outer weights from the 'Calculation Results' section of the pls estimation output.
2. I computed s.d. for each indicator in Excel.
3. Outer weight / s.d. for each indicator
4. Computation of relative weight (with sum = 1 for each LV)
5. I then calculated the LV scores by sum(indicator values*rel. weights) for each LV
After doing that, I compared these LV scores to the unstandardized scores from the PLS output. They were all equal. Furthermore, I standardized the (hand) calculated LV scores and compared these to the standardized scores from the output. These scores did not fit´ what went wrong?
To find the error, I tried to reproduce your example in mobi250.csv (you wrote '205'. Is this a typo or an older example file?). My problem was that I could not find the values, you report above for 'standardized outer weights'. Where can I find these values?
Many thanks in advance to anyone who could help me solve this issue.
Best regards
Stephan

 PLS Junior User
 Posts: 1
 Joined: Thu Oct 25, 2007 6:28 pm
 Real name and title:
Hi Stephan Naß,
we calculated the unstandardized and standardized LV Scores the following way:
1. Calculate the stddev for each unstandardized indicator from reportpart: Manifest Variable Scores (Original)
2. Then use the outer loadings / stddev of each indicator from reportpart: Outer Loadings
3. Computation of relative weights like you did.
4. Then we calculated the unstandardized lv scores. The values are the same as in the reportpart: Latent Variable Scores (unstandardized)
5. Finally we standardized the unstandardized lv scores by using the mean value and the population of stddev and recieved the same values as in SmartPLS.
We hope you can follow these steps. For further questions please contact us.
Cheers
SmartPLSTeam
we calculated the unstandardized and standardized LV Scores the following way:
1. Calculate the stddev for each unstandardized indicator from reportpart: Manifest Variable Scores (Original)
2. Then use the outer loadings / stddev of each indicator from reportpart: Outer Loadings
3. Computation of relative weights like you did.
4. Then we calculated the unstandardized lv scores. The values are the same as in the reportpart: Latent Variable Scores (unstandardized)
5. Finally we standardized the unstandardized lv scores by using the mean value and the population of stddev and recieved the same values as in SmartPLS.
We hope you can follow these steps. For further questions please contact us.
Cheers
SmartPLSTeam
Dear SmartPLSTeam and Professor Bido,
Does this mean that I can use the understandized path coefficients reported by SmartPLS? I used OLS with understandized latent variables and obtained different path coefficients. Could you please tell me what has happened? If the unstandardized path coefficients reported by SmartPLS cannot be used, how can I obtain unstandardized path coefficients?
Thanks a lot.
Cheers
Terry
Does this mean that I can use the understandized path coefficients reported by SmartPLS? I used OLS with understandized latent variables and obtained different path coefficients. Could you please tell me what has happened? If the unstandardized path coefficients reported by SmartPLS cannot be used, how can I obtain unstandardized path coefficients?
Thanks a lot.
Cheers
Terry
taiyuan wang
 Diogenes
 PLS SuperExpert
 Posts: 905
 Joined: Sat Oct 15, 2005 5:13 pm
 Real name and title:
 Location: São Paulo  BRAZIL
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Hi Terry,
1) If you run the regression in the SPSS with the unstandardized LV scores from the SmartPLS, the results will be different, because the calculation of the scores in the SmartPLS is not correct in this version.
2) If you want the unstandardized path coefficients, I suggest that you recalculate the unstandardized LV scores, as is explained above and copy/paste them to SPSS to run regression analysis.
Best regards,
Bido
1) If you run the regression in the SPSS with the unstandardized LV scores from the SmartPLS, the results will be different, because the calculation of the scores in the SmartPLS is not correct in this version.
2) If you want the unstandardized path coefficients, I suggest that you recalculate the unstandardized LV scores, as is explained above and copy/paste them to SPSS to run regression analysis.
Best regards,
Bido

 PLS Junior User
 Posts: 1
 Joined: Mon Apr 04, 2011 10:38 pm
 Real name and title:
Calculating LV scores from Relative Weights
What do you mean by "indicator value" when you say calculate the unstandardized LVs by multiplying relative weight by indicator value.
Also, just to confirm, once I've done this, the unstandardized LVs will be the coefficients in my equations correct?
Thank you.
Cinthia
Also, just to confirm, once I've done this, the unstandardized LVs will be the coefficients in my equations correct?
Thank you.
Cinthia