I found a way to compute unstandardized latent variable scores:
1. Calculate the std-dev for each unstandardized indicator from summary$descriptives 2. Then use the outer loadings / std-dev=x of each indicator from summary$loadings 3. Computation of relative weights (R=x/sum of x's for each scale) 4. Then I calculated the unstandardized lv scores: matrix product of items unstandardized score by R for each scale 5. To check I standardized the unstandardized lv scores by using the mean value and the population of std-dev and recieved the same values as in SmartPLS. And I compute a correlation coefficient between standardized and unstandardized lv scores. Yet I cannot find why the correlation is far from 1 (0.91) for a formative scale.
Do this procedure work for formative scale?
This procedure should work for formative scales as well. However, the correlation between standardized and unstandardized latent variable scores may not be close to 1 for formative scales because formative scales do not have a fixed metric like reflective scales. In reflective scales, the latent variable scores are a linear combination of the standardized indicator scores, so the correlation between standardized and unstandardized latent variable scores is expected to be close to 1. In formative scales, the latent variable scores are a weighted sum of the unstandardized indicator scores, so the correlation between standardized and unstandardized latent variable scores may be lower due to the non-linearity and non-uniqueness of the formative measurement model. Therefore, it is important to assess the validity and reliability of the formative scale using other criteria such as content validity, convergent validity, discriminant validity, and nomological validity.
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