Interpretation of latent variable scores

[oliverschilke]

Dear all:

How do I interpret the latent variable scores, which are provided as a PLS output.

In my survey, I used a 5-point scale. However, the LV scores seem to fall between -2.x and +2.x.

What is the minimum and the maximum of the LV scores for my data? Is it possible to convert the LV score back to my initial 5-point scale?

Thanks,
Oliver

[stefanbehrens]

Hi Oliver,

you have to keep in mind that PLS works with standardized scores for the MVs and also produces standardized scores for the LVs. That is, each LV has a mean of 0 and a std-dev of 1 across all cases. That's why the observed ranges are not what you were expecting to find.

To produce LV-estimates closer to your original 5-point scale you would have to do the following: Simply write down the weights of all indicators for your LV of interest and then calculate the non-standardized LV-scores manually in Excel:

LV = w1*MV1 + w2*MV2 + ... +wn*MVn

Hope this helps.
Cheers,
Stefan

[oliverschilke]

Hi Stefan!

Thanks a lot, this helps!

2 more questions:

1) How can I calculate the LV score if the LV is a second order factor?
2) Do you know a source for the procedure you have proposed?

Thanks,
Oliver

[stefanbehrens]

Well...

a source I don't have for you. It's just following the logic of the PLS algorithm. In a regular PLS run, MVs would first be standardized, before LV-scores are calculated based on the weights. This procedure results in standardized LV-scores, i.e. mean=0, stddev=1. Thus, in principle, I don't see why the LV-scores should be calculated in any different way using non-standardized MVs. A precondition, however, obviously would be that all your MVs had the same scale (e.g., 7-point Likert).

Regarding 2nd-order LVs: How are you operationalizing your 2nd-order LV in the PLS model? If you are re-using indicators of the 1st-order LVs for this then you could calculate non-standardized scores in the same way as outline above.

Cheers,
S.

[oliverschilke]

Dear Stefan,

I am indeed re-using indicators of the 1st-order for the 2nd-order construct (that is, the hierarchical component model (Lohmöller 1989; Wold 1980)).

Now I'm wondering: Can I really use the outer weights for calculating the non-standardized LV-scores - although the LVs are modeled as reflective constructs?

Moreover, the sum of all outer weights associated with the construct (in your formula wn) is > 1 (in my case 1.88). Applying your formula, for some cases the LV score is above 5, which is kind of strange since I used a 5 point scale for all items.

Thanks,
Oliver

[stefanbehrens]

Hi Oliver,

well, first of all, PLS doesn't really differentiate the way it calculates LV-scores for reflective or formative LVs. Both are simply a weighted sum of their MVs. Hence, no concern there.

With regard to the sum of weights:
The sum of all weights doesn't add up to 1 because PLS produces standardized LV-scores. Thus, weights are adjusted by the algorithm in order to get mean=0, stddev=1. In order to create artificial scores within your scale limits, you could adjust the weights proportionately to get sum_of_weights=1. In your case, the new adjusted weights (w_a) would be w_a= w_PLS / 1.88. However, you have to be aware that this will deflate the stddev of your artificial scores by the same factor (1.88). Also, you have to be careful with the interpretation of these artificial LV-scores since applying the same anchors you used for the Likert-scales in the first place may be problematic.

What are you trying to use the composite scores for anyway?

Cheers,
Stefan

[jamarin]

With this version you can get the unstandardised latent variable scores in the INDEX values/results of the standard report

this report place above of PLS/calculation results/Latent Variable scores (this are standardized)

[bwilson]

Hi Oliver,

What are you trying to use the composite scores for anyway?

Cheers,
Stefan

Hi,
The advice of Stefan is very high quality throughout.

c.f.,
Handbook of Partial Least Squares
http://www.springer.com/statistics/comp ... 40-32825-4

Chapter by Wilson
Using PLS to Investigate Interaction Effects Between
Higher Order Branding Constructs.

All the best,