Does someone know how a quadratic relationship between two latent constructs can be modelled?
Any input would be great  Thank you
Quadratic path
Quadratic path
GrosseRuyken
 Diogenes
 PLS SuperExpert
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 Joined: Sat Oct 15, 2005 5:13 pm
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 Location: São Paulo  BRAZIL
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Hi,
1) If VL1 is measured by three indicators (X1, X2, X3) we could create a squared VL1 measured by (X1*X1, X2*X2, X3*X3, X1*X2, X1*X3, X2*X3).
First reference: Kenny, David A.; Judd, Charles M. (1984). Estimating the Nonlinear and Interactive Effects of Latent Variables. Psychological Bulletin, Vol. 96, No. I. 201210.
Example: p.328) KLINE, Rex. B. (2005). Principles and practices of Structural Equation Modeling. 2nd Ed. New York, The Guilford Press.
 These product terms must be computed before importing the data to SmartPLS
 It is recommended to centering the MVs before multiply them.
2) MARSH, H.W.; WEN, Z.; HAU, K. Structural Equation Models of Latent Interation and Quadratic Effects. In HANCOCK, G.R.; MUELLER, R.O. (Ed.) (2006). Structural Equation Modeling: a second course. Connecticut: IAP – Information Age Publishing, Inc.
 p.244 = Types of product indicators
 p.248 = Example using just X1*X1; X2*X2; X3*X3 as the indicators of the quadratic LV.
3) One last possibility is
 run the model without the quadratic term
 copy the standardized LV scores
 paste these scores to the original data set
 compute the LV*LV
 import the new data set to SmartPLS
 Use the LV*LV score as a single indicator to the quadratic term.
Best regards
Bido
1) If VL1 is measured by three indicators (X1, X2, X3) we could create a squared VL1 measured by (X1*X1, X2*X2, X3*X3, X1*X2, X1*X3, X2*X3).
First reference: Kenny, David A.; Judd, Charles M. (1984). Estimating the Nonlinear and Interactive Effects of Latent Variables. Psychological Bulletin, Vol. 96, No. I. 201210.
Example: p.328) KLINE, Rex. B. (2005). Principles and practices of Structural Equation Modeling. 2nd Ed. New York, The Guilford Press.
 These product terms must be computed before importing the data to SmartPLS
 It is recommended to centering the MVs before multiply them.
2) MARSH, H.W.; WEN, Z.; HAU, K. Structural Equation Models of Latent Interation and Quadratic Effects. In HANCOCK, G.R.; MUELLER, R.O. (Ed.) (2006). Structural Equation Modeling: a second course. Connecticut: IAP – Information Age Publishing, Inc.
 p.244 = Types of product indicators
 p.248 = Example using just X1*X1; X2*X2; X3*X3 as the indicators of the quadratic LV.
3) One last possibility is
 run the model without the quadratic term
 copy the standardized LV scores
 paste these scores to the original data set
 compute the LV*LV
 import the new data set to SmartPLS
 Use the LV*LV score as a single indicator to the quadratic term.
Best regards
Bido

 PLS Junior User
 Posts: 3
 Joined: Tue Nov 24, 2009 3:55 pm
 Real name and title:
Hi everybody,
I found a quadratic relationship in my research model using SPSS curve estimation. I want to integrate this relationship in my PLS model, now. I understand the procedures explained above (i.e. the calculation of the quadratic LVs), still I am not totally sure how to model it.
Do have to include the original variable (LV1) and the quadratic version (LVq1) of it into the model? If I do so, the effect of LV1 is negative (.2) and the effect of LVq1 is positive (+.7). I am not sure how to interpret this.
What if LV1 is endogenous and has other effects that are linear? How do I have to model this?
It would be great if somebody could help me.
Cheers
Tobi
I found a quadratic relationship in my research model using SPSS curve estimation. I want to integrate this relationship in my PLS model, now. I understand the procedures explained above (i.e. the calculation of the quadratic LVs), still I am not totally sure how to model it.
Do have to include the original variable (LV1) and the quadratic version (LVq1) of it into the model? If I do so, the effect of LV1 is negative (.2) and the effect of LVq1 is positive (+.7). I am not sure how to interpret this.
What if LV1 is endogenous and has other effects that are linear? How do I have to model this?
It would be great if somebody could help me.
Cheers
Tobi

 PLS Expert User
 Posts: 51
 Joined: Tue Nov 04, 2014 5:27 am
 Real name and title: Dr. Bradley Wilson. Senior Lecturer in Advertising. School of Media and Communication. RMIT University.
Re: Quadratic path
Bido's approach is sound.
a more exploratory approach is to use software from Buckler. Neusrel
brad
a more exploratory approach is to use software from Buckler. Neusrel
brad
Bradley Wilson. Ph.D. Senior Lecturer in Advertising. School of Media and Communication. RMIT University. Melbourne, Australia.
SEE: http://www.researchgate.net/profile/Bradley_Wilson2 http://scholar.google.com.au/citations? ... AAAJ&hl=en
SEE: http://www.researchgate.net/profile/Bradley_Wilson2 http://scholar.google.com.au/citations? ... AAAJ&hl=en