Calculation and confidence interval of LV index

[i_laerdal]

Hi,

I am writing a master thesis on customer satisfaction. I have two questions relating to LV index:

1) How is it computed? I tried to calculate them manually, to see if I could get the same result as in the SmartPLS report. E.g., I have measured the LV "Expectations" using 3 manifest variables. The LV index reported by SmartPLS is 8.699. I tried to calculate it by multiplying the actual respondents' scores with the outer loadings, and then dividing this number with the number of respondents. However, this gives me a result of 8.13..? What do I do wrong?

2) I have based my model on the EPSI framework. One of the quality criteria of this framework is that "the 95 percent confidence interval for the customer satisfaction index must have a width of not more than 4 units". Would it be correct to use a formula for confidence intervals for means, and to use the latent variable scores (unstandardized) as basis for calculating the variance of the index?

I would be very grateful if someone could give me some hints on these matters!

Best regards,

Ingrid Lærdal

[Diogenes]

Hi Ingrid,

1) SmartPLS computes the paths based in standardized MVs, to do what you want...:
- The standardized scores of each LV are computed using the standardized MV scores and the outer weights, for example:
Satisfaction (std) = w1 * x1 + w2 * x2 + w3 * x3
- To have the unstandardized LV scores, you should use the weights available in the SmartPLS as "Measurement model", and use the raw scores of the MVs.
- The LV index is the average of all scores of that LV.

2) Ok.

Best regards,

Bido

[i_laerdal]

Hi Bido,

Thank you for a fast and informative reply! I tried to calculate the LV indexes, and now it works. Just to confirm - the LV indexes that are reported in SmartPLS are the UNstandardized scores, right?

My understanding of the difference between unstandardized and standardized scores is that the standardized scores takes the standard deviation into consideration. If I want to compare the results I get, e.g. to compare the index I get for the satisfaction-variable to EPSI benchmarks, is it ok to do this based on the unstandardized scores?

Regards,

Ingrid Lærdal

[Diogenes]

Hi, Ingrid

1) UNstandardized => LV in the same scale as the MV. LV Index = average of unstandardized LV scores.
2) Standardized => mean = 0 and standard deviation = 1 (like factor score in SPSS).


Your 1st question = yes
2nd question = yes.

Best regards
Bido