Significant increase in R^2 in 2 nested models through F-test

Frequently asked questions about PLS path modeling.
Post Reply
ElNicolosi
PLS Junior User
Posts: 5
Joined: Tue Jul 02, 2019 8:18 am
Real name and title: Dr. Eleonora Nicolosi

Significant increase in R^2 in 2 nested models through F-test

Post by ElNicolosi » Sat Feb 29, 2020 10:18 am

Hello, I need to test the significance of the increase in R2 of two nested models in SEM-PLS and I am using the following formula:

F=((R2L-R2S)/(dfL-dfS))/((1-R2L)/(N-dfL-1))

where R2L is the R-squared of the endogenous variable from the model with more variables, and R2S is the R-squared of the predicted variable from the model with fewer variables. The quantity dfL-dfS is the difference in the number of variables between the two models. N is the sample size.
However, my problem is what should I consider as variables in my model for the comparison? The indicators of the latent variables or the Latent variables themselves? It would make a huge difference as any latent constructs has 10 indicators. Meanwhile, I have just 4 Latent constructs in the smaller model and 6 in the bigger one. So if I consider indicators I have 60-40 as a difference of variables in the two models. However, if I consider latent constructs I have 6-4. And this, of course, will affect also the degrees of freedom.

Alexg
PLS User
Posts: 12
Joined: Fri May 18, 2018 11:34 am
Real name and title: Mr. Alessandro Grillo

Re: Significant increase in R^2 in 2 nested models through F-test

Post by Alexg » Thu May 07, 2020 12:06 pm

I have the same problem! Did you sort it out at the end?

I assume that we should consider the number of latent variables for the calculation but I am not sure either! Could not find any clear explanation on published papers!

tinGivi3
PLS Junior User
Posts: 5
Joined: Tue Jun 02, 2020 2:57 am
Real name and title: Florentin Givi

Re: Significant increase in R^2 in 2 nested models through F-test

Post by tinGivi3 » Tue Jun 02, 2020 6:34 am

Hi ! Learn From the Multi-Awarded Math Game App! Prodigy math game play free was awarded as one of the best websites for teaching and learning by the American Association of School Librarians in 2018.

Post Reply