# R squared in structural equation modeling

#### Stef Van Puyenbroeck

##### New Member
Hello

I recently started working with structural equation modeling. I am doing a study for which I tested a model like this:
Var1 --> var2--> var3 --> var4. All variables are latent variables and have several indicators.

Now, the R² of var3 is +-40% in this case. However, something strange happens when I test the model:
Var1 --> var2 --> var3.

In this case, although the variables BEFORE var3 remain exactly the same, the R² of var3 becomes much smaller (+-28%).

Does anyone know a possible explanation for this? I've already checked whether this is due to missings in var4 but this is not the case. I've also checked this using another software program than the one I normally use (lavaan package in R) and found the same.

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#### hlsmith

##### Less is more. Stay pure. Stay poor.
Do you know that each child variable only has a single parent, so they are in a line like you have in your post?

Are you family with D-separation (D= direct), Var 4 its independent of Var 1 and Var 2 | Var 3. So if they are in a direct line Var 1 and Var 2 should not influence Var 4 if you have Var 3 in the model. This may also be called Markovian Process, I believe.

How do your data fit into this?

#### Stef Van Puyenbroeck

##### New Member
Thanks for your reply. However, I still don't see how this would lead to an increase in my R² of var3? Could be me though.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
So you are calculating the R^2 of Var 3. How are you calculating the R^2 in the first model when Var3 is not the dependent variable. They appear to be different models.

Var3 = Var1 + Var2
Var4 = Var1 + Var2 + Var3

And you are getting these from single linear regression models. I have not done a SEM before, though I know there are different approaches.

I also know that some approaches have a unique linear model for each endogenous variable, then you insert all of the model together to get the model for the last node (child) in the model. You probably need to provide some more details.

Thanks!

#### evelyn13

##### New Member
It's not clear about your model, are var2 and var3 acting as mediators in the model (i.e. is there a direct relationship between var1 and var4?) All this will impact on how R^2 is calculated.
R^2 will always increase as the number of variables increases in a model.

Also more importantly, as hlsmith pointed out, you have two models with different dependent variables it appears. Therefore you can't really compared the r^2 values...
R^2 is the an indicator of overall model fit, not just the fit of one variable in the model.

#### noetsi

##### No cake for spunky
Also if your samples for the two dependent variables is different than R squared can't be compared regardless I believe.

#### Ben Pierce

##### New Member
Greetings,
I am running two models that predict the same set of outcomes (DV's). I am attempting to compare the standardized coefficients across models for the same outcome, and was wondering if there are test statistics available to do so (e.g., to determine whether the standardized association between a latent variable and an outcome is statistically significantly different between models 1 and 2). Does anyone have a reccomendation?
Thanks and best regards,
B

#### hlsmith

##### Less is more. Stay pure. Stay poor.
You can use an F-test to compare two linear models.