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

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

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

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

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