Hi there,
In this post, we want to look at definition of latent variable and how we can calculate latent variable scores.
In statistics, latent variables are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed (directly measured) [1].
For example, in attached picture, we have ATTR which is latent variable with 3 formative indicators. Each indicator is representative of one question in our questionnaire. Therefore, 3 questions in our questionnaire belong to ATTR. ATTR is abbreviation for Attractiveness. The ATTR can describe the attractiveness of a company's working place. The questions of ATTR are shown in below:
Attractiveness (ATTR)
attr_1: in my opinion [the company] is successful in attracting
high-quality employees.
atr_2 I could see myself working at [the company].
attr_3: I like the physical appearance of [the company] (company,
buildings, shops, etc.).
The data of ATTR's indicators are available in ATTR data.xlsx in the attached.
The data are taken from book named A primer on partial least squares structural equation
modeling ( PLS-SEM) I Joseph F. Hair, Jr. ... [et al., 2014].
Ref:
[1] en.wikipedia.org/wiki/Latent_variable
Now, We follow following steps on attached excel file for our example:
1. Calculate the std-dev sample for each unstandardized indicator as shown in sheet3, cells D2, E2 and F2 of the attached excel file.
2. we calculate the outer loadings / std-dev of each indicator as shown in sheet1, cells E2 ,F2, G2 of the attached excel file.
3. Computation of relative weights as shown in sheet3, cells I2, J2 and K2 of the attached excel file.
4. Then we calculated the unstandardized Latent variable (LV) scores as shown in sheet 2 in cells J2 to J 345. For each case, we calculate unstandardized Latent variable (LV).
5. Finally we standardized the unstandardized LV scores by using the mean value of unstandardized LVs and the population of std-dev of unstandardized LVs as shown in sheet2, cells M2 to M 345.
The results are as same as SmartPLS (v. 3.2.6)> Importance-Performance Map Analysis (IPMA)> Final results > Latent variables > standardized and unstandardized tabs of latent variables
Thanks,
Kamal Karkonasasi
Now, We follow following steps on attached excel file for our example:
1. Calculate the std-dev sample for each unstandardized indicator as shown in sheet3, cells D2, E2 and F2 of the attached excel file.
2. we calculate the outer loadings / std-dev of each indicator as shown in sheet1, cells E2 ,F2, G2 of the attached excel file.
3. Computation of relative weights as shown in sheet3, cells I2, J2 and K2 of the attached excel file.
4. Then we calculated the unstandardized Latent variable (LV) scores as shown in sheet 2 in cells J2 to J 345. For each case, we calculate unstandardized Latent variable (LV).
5. Finally we standardized the unstandardized LV scores by using the mean value of unstandardized LVs and the population of std-dev of unstandardized LVs as shown in sheet2, cells M2 to M 345.
The results are as same as SmartPLS (v. 3.2.6)> Importance-Performance Map Analysis (IPMA)> Final results > Latent variables > standardized and unstandardized tabs of latent variables
Thanks,
Kamal Karkonasasi
Wonderful explanation by Kamal. My question is why did you multiply standard deviation to each indicator value in the first place? Couldn't the unstandardized latent variable score be taken directly?
Check this out:
https://www.smartpls.com/resources/ebook_on_pls-sem.pdf
In sheet 1... A2, A3 and A4 ( 0.420042 0.198091 0.654278 ) values are given... How did you calculate these values?
Thanks for sharing your sheet Kamal.
How do you calculate these values: In sheet 1... A2, A3 and A4 ( 0.420042 0.198091 0.654278 )
Dear all,
I think this link is very helpful:
https://youtu.be/wGjIFC1HlHk
Sorry for my late reply.
Thank you.
Dear Mr. Kamal,
Thank you for sharing the calculation for latent score from SEM model. In your approach, it seems that the error terms are not considered. For instance, the equation may looks like: Attr_1 = 0.420042 * ATTR + ϵ 1. If the var(ϵ 1) is large, then the score of ATTR may differ significantly from your estimated score of ATTR.
Kind regards,
Yen.
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