Individual Co-Effecient of Determination Values R2

[Sussmek]

Hi All,

I've used smartPLS for analysing my model. I have 6 independents variables and 1 dependent variable. The results show that 78% of the variance has been accounted for by the model.

However MY question is as follows,

1) I have seen some articles reporting Individual R2 values for each of the independent variables. Is there anyways I can get the information from smart PLS as to what level of variance is explained by each ( individually) of the 6 independent variables?

Hope my question makes sense!

Thanks in advance!

Sussmek

[jmbecker]

We provide the f² statistic, i.e., the effect size in terms of explained variance.
It calculates as
(R²inlcuded - R²excluded) / (1 - R²included)
Whereas R²exluded means the R² of the dependent variable, when the focal variable is excluded from the model.

This is the more common statistic in this context, which is similar to your objective.

[Sussmek]

Thank You Dr. Becker,

So is it ok, If I use the F2 values as explanation of variance by individual variables. For example in my study " Perceived Usefulness" had a Medium effect and had a f2 value of .187

Can it be implied that 18.7% of variance in the dependent variable was explained by Perceived Usefulness alone?

Thanks Again!

Sussmek

[jmbecker]

You can use f² to assess the impact of each exogenous construct, but the interpretation is not so straight forward, because it is an effect size. You cannot say that a value of 0.187 implies 18.7% of explained variance by that construct, because of the denominator. The numerator of f² reflects the proportion of variance uniquely accounted for by the construct, over and above of all other constructs (Cohen, 1988), but the denominator makes f² hard to interpret.
Actually, it is the proportion of the uniquely explained variance by the construct to the unexplained variance. Given large R² values and large unique contributions, the f² even gets larger that 1 (e.g., for a 0.7 R² and a unique part of a construct of 0.4 would give a f² of 1.333=0.4/0.3).

However, you can get the values for your interpretation (the numerators) by multiplying the f² with (1-R²).

[Sam81]

Hi all,

If let's say we have three independent variables VA, VB, VC and explained variance of each is*
VA 13%
VB 07%
VC 03%

Could we say that statistically VA effect on dependent variable is more than VB and VC? is there any published reference for this kind of interpretation?

Regards,

Sameer

*calculated using the method explained below by "jmbecker" on Fri Aug 14, 2015 8:41 am

[jmbecker]

You could say that VA explains more variance than VB or VC, but you have to test this. Therefore, you should compute the difference of these measure for each bootstrapp sample and then assess whether this difference is significant (different from zero).

[Sam81]

Thanks Dr. Becker for the reply.

When you say "compute the difference of these measure", do you mean something like this:

Bootstrap sample 1: check if explained variance of VA > explained variance of VB
Bootstrap sample 2: check if explained variance of VA > explained variance of VB
.
.
.
Bootstrap sample n: check if explained variance of VA > explained variance of VB

Finally check if 95% of the time explained variance of VA > explained variance of VB? (for 0.05 significance level)

[jmbecker]

Yes, that could be possible, but I would construct confidence intervals for the difference (explained variance of VA - explained variance of VB). The result should be the same, but the confidence interval for the difference is a nicer test of your null hypotheses (the difference in explained variance between VA and VB is not signficantly different from zero).

[Sam81]

Thanks, but how you generate explained variance of VA value by bootstrapping? I thought you do that by PLS Algorithm. Could you please explain the process little bit?

[jmbecker]

First, I would use the f² values, because the include the explained variance of a construct (relative to the unexplained variance).
Then you need to take the data that you find under "Samples" in you bootstrapping results and copy them to (for example) Excel. Then you can calculate the difference in f² for each bootstrap sample between your three constructs and then assess whether this difference is significant (for example using percentile confidence intervals) or a t-statistica using the original difference in f² diveded by the standard deviation of the difference over all bootstrap samples, with degrees of freedom as number of bootstrap samples -1.