Inverted U-shaped LV --> Neep help for my PhD Thesis

[RobertusMaximus]

Hi there,

I´m desperately looking for help regarding a LV with an inverted U-shaped relationship within other LVs with linear relationship.
I´m measuring the impact of three LVs on Brand Image. 2 of the LV have a linear relationship and 1 of the three LVs has a inverted U-shaped relationship.
So I have LV1 ---> Brand Image = linear, LV2 ---> Brand Image = linear, LV3 ---> Brand Image = nonlinear. The 3 LVs are each Determined by 2 other LVs.

The full model looks like:

Determinant1/Determinant2 ---> LV1/LV2/LV3(nonlinear) ---> Brand Image


Is there any chance to calculate the effects of all three LV simultaneously with regard to the one nonlinear LV?

If yes, how do I have to proceed to take the non linear LV into account?


I´m super super thankful for any advice regarding my "problem"

Many many thanks in advance and best regards

Robert

[RobertusMaximus]

Hello,

no one here with any idea??

Would be great to get a hint, I`m still stuck.

Thanks in advance!

Robert

[jmbecker]

If you expect an inverted u-shape (i.e., a simple quadratic non-linear relationship), then you can simply add a quadratic effect (similar to a moderation effect) and estimate your quadratic relation for the one LV that you expect to have a nonlinear relation.

[RobertusMaximus]

Thanks for your advice.
I used the 2 stage approach by Henseler et al. to analyze quadratic effects. (I have a reflective model, but I saw, that it can also be used for reflective models, right?!)
After calculating the 2 Steps I also calculated the f^2 manually as follows:

(R^2 of model with nonlinear term - R^2 of model without nonlinear term)/ (1- R^2 of model with nonlinear term)

--> The value for my f^2 is 0,0046 wich is due to relatively similar R^2 values of both models (with and without nonlinear term)

--> In conclusion for me this is the Indicator, that there is NO NONLINEAR relationship in my data and I proceed calculating my model
without the quadratic effect and assume a lineare relationship of all LVs.

Is this the right implication out of the given data (f^2) ??

Thanks again for your help and cheers to cologne!

[jmbecker]

1) Two-Stage approach is also ok for reflective constructs if statistical power is of your main concern.

2) You should also assess the significance of the quadratic effect. Your very small f² indicates that the quadratic effect is not substantial, but if it is also not significant you will have an even stronger argument against a non-linear shape. In this regard also the use of two-stage approach is justified.

3) You can also directly get the f² of the quadratic effect from SmartPLS 3. There is no need to calculate it yourself.