OVerall Scores

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rodbro
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OVerall Scores

Post by rodbro »

Hello There,

How would you calc. the overall score for the latent variables (loyality, Satisfaction, Image, etc.)

Hope tp hear from you.

Regards
Kenneth
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jjsailors
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Post by jjsailors »

Hi Kenneth,

In PLS latent variables are the weighted sum of their indicators. This is always the case, regardless of whether the latent variables are specified as having formative or reflective indicators. So to compute latent variable scores you simply sum the product of each indicator and it's weight (never the loading).

Hope this helps.

John
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The University of St. Thomas
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Diogenes
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Post by Diogenes »

If you are modelling from your raw data, Smart-PLS shows the LV´s scores in the output.

Best regards.
Prof. Dr. Diogenes de Souza Bido
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Post by rodbro »

Hello,

Thank you for your time!

Do I understand this correct:

I use the outer weights to calc. the overall index?

So it is (w1/w1+w2)*W1 + (w2/w1+w2)*W2= overall score for W?

If you sum the LV's scores you got allmost 0! How Do I use the LV scores?

Regards
Kenneth
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Diogenes
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Post by Diogenes »

As prof. John said:

In PLS latent variables are the weighted sum of their indicators

If you have a LV with two indicators

(formative) i1 ==> LV1 <== i2 or (reflective) i1 <== LV1 ==> i2

The score will be: LV1 = w1 * i1 + w2 * i2

Best Regards.
Prof. Dr. Diogenes de Souza Bido
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Post by rodbro »

Hello Professor Diogenes Bido

Thank you for your time again.

You can't be sure, that the out weights sum to 1.
So now you have:

w1=0,88, w2=0,5, Mean(W1)=88, mean(W2)=50 (rescalen 0-100)

w1 <== LV1 ==> w2

The score for this LV1 have to be:

(w1/w1+w2)*W1 + (w2/w1+w2)*W2= 74,34

I can't see what else it could be.

Is this correct
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Diogenes
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Post by Diogenes »

Let´s try...

When you said that
that the out weights sum to 1.
I understand (now) that you are using "RELATIVE weights".
Some people use "relative weights" like a way of comparation of the relative importance of each indicator.

We don´t use relative weights to compute the scores.

A exemple could help:

If a observation has this values to my indicators (or manifested variables): i1 = 4 and i2 = 5

And the weights are w1 = 0,88 and w2 = 0,50

The score will be: LV1 = w1 * i1 + w2 * i2
LV1 = 0,88 * 4 + 0,50 * 5 = 6,02 (unstandardized)

Best Regards.
Prof. Dr. Diogenes de Souza Bido
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Post by rodbro »

Hello Professor Diogenes Bido

I not sure about this.

I'm calc. the overall scores for the ecsi model. So lets take the overall score for Image.

There is 5 image questions there overall will make the Image index. But there is only 2 qustions to make the Quality index.

If you do not use relative weights the score for Image will allways be allot higher than the score for Quality simply because there is 3 more question.

So I'm quit sure, that you have to use relative weights when you calculate the overall score in the esci model.

What do you think about this?

Maybe it will be possible to get the overall scores directly from smartpls - I think this will help a lot of people.


Regards
Kenneth Larsen
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Post by jjsailors »

rodbro wrote:
There is 5 image questions there overall will make the Image index. But there is only 2 qustions to make the Quality index.

If you do not use relative weights the score for Image will allways be allot higher than the score for Quality simply because there is 3 more question.
In PLS weights are scaled so that Latent Variables have unit variance so if you look at a latent variable with 2 indicators, their weights will tend to be larger than the weights associated with the indicators of a latent variable with 5 measures.

John
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The University of St. Thomas
Opus College of Business
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Post by rodbro »

Hello,

Thank you all for your time.

How would you calc. the score for the LV in the esci model, when you have got the output from smartpls?

People did answer the questionaire from a scale from 1-10 and all the answers has been rescale to 0-100.

You now got the model and output from smartpls - but how will you calc. the overall score for LV?

Regards

Kenneth
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Post by jjsailors »

rodbro wrote:Hello,

How would you calc. the score for the LV in the esci model, when you have got the output from smartpls?
Under "Calculation Results" you will find a field called "Latent Variable Scores" that will list the latent variable scores for each observation. You can simply highlight, copy, and paste into whatever program you want the scores in.

These are calculated, as Diogenes wrote, as LV1 = w1 * i1 + w2 * i2 etc. Keep in mind that the reported weights are based on the standardized data so the i1 and i2 etc above would be the standardized manifest variable scores. If you do this it should match exactly what is in the SMART PLS output.

If you want to calculate LV scores based on unstandardized data, simply divide the weights by the standard deviation for each variable, then do the multiplication and summation as above.

John
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Associate Professor of Marketing
The University of St. Thomas
Opus College of Business
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Post by rodbro »

Dear John J. Sailors,

Thank you for your time.

I did try to standalize my data and calc. the pls model again. I simply can't see that the Latent scores should be correct. There is negative numbers beetween, and that should not be possible.

This is a normal ecsi model, so I hope someone has the answer for calc. the index for the LV - Image, Loyalitly, Satisfaction, etc.

The only solution I can see is to use relative weights.

Regards

Kenneth
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Post by jjsailors »

rodbro wrote:There is negative numbers beetween, and that should not be possible.
Again, the weights are calculated such that latent variables have unit variance and a zero mean. If you unstandardize the weights and apply them to the raw data, you will not have the "issue" of negative latent variable scores.
John J. Sailors, PhD
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The University of St. Thomas
Opus College of Business
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Post by cringle »

Dear all,

the index value calculation (using unstandardized weights that are normed to sum up to one) is described in the following article (see the appendix for a formal presentation):

author = Anderson, Eugene W. / Fornell, Claes
title = Foundations of the American Customer Satisfaction Index
full reference: viewtopic.php?t=21

We will provide the index value computation and unstandardized LV-scores in the upcoming release (soon).

Best
Christian
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Post by rodbro »

Dear Christian,

Could you please tell me where I can see the overall scores in smartpls?`

Did you manage to include them in the new version?

Regards
Kenneth
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