Path comparision with Wald Test

[PascalHessler]

Hey,
so I have a case where we are interested if one path has a higher effect than another one. In "Normal" regression, you can just use the Wald test for this. Technically this should be possible for pls-sem to (Both paths are to one construct).
I would like to have the option to use the Wald test, but I was not sure if this is an "issue" of this package, so I am posting it here. What do you think?
Best regards

[soumyaray]

Dear @PascalHessler thank you for your excellent enquiry. I have not used the Wald test in practice and am mostly familiar with it as a test of an individual coefficient, or a set of coefficients, being significantly different from zero. It would be great if you can share a resource of the Wald test being use to compare the relative level of two coefficients. Searching casually, I also see people offering t-tests for comparing coefficients. If there is well vetted and accepted method available in practice, we might consider incorporating it into SEMinR – though we are quite conservative about adding new methods as many prove to be problematic over the course of time.

In principle, any test that only needs to know the estimated coefficients and their respective standard errors is implementable. The regular PLS estimation can provide the coefficients and bootstrapping can provide their standard errors. If you have a formula for a relevant test, you (or we) can readily compute it with these. Again, if you can provide a reference that offers a clear cut description of the procedure you are interested in, we can at least work with you to put together an ad hoc function that you can use – and later debate if it should be formally included as a publicly exported function of SEMinR.

[PascalHessler]

Hi, @soumyaray,

so i implemented the test for my model. After some smaller issues I achieved my goal :) Perhaps you can add this in the commented out section in the package?

# b <- coef.boot_seminr_model(boot_obj = boot_pls, endogenous = "LOY")
# S <- vcov.boot_seminr_model(boot_obj = boot_pls, endogenous = "LOY")
# Tests the joined hypotheses of 'SAT->LOY' == 0 and 'COM->LOY' == 0
# Corresponding L Matrix = [0 1 0, 0 0 1]
# wald.test(b=b, Sigma=S, Terms=c(2,3))

# If you want to test if to pathes are equal to each other you need to provide the L argument representing the linear combinations 
# of the coefficients to be tested
# For example: 'SAT->LOY'=='COM->LOY'  would correspond to a Matrix [0  1 -1]
# wald.test(b=b, Sigma=S, L= matrix(c(0,1,-1), nrow = 1))

Perhaps this helps someone else in the future :)

[soumyaray]

Thanks so much @PascalHessler – could you link me to any resources discussing the L matrix and nrows parameter you used in more detail? The help file for wald.test is very brief on them and doesn't help me understand your example quite yet.

[PascalHessler]

Hey @soumyaray it is based on the article shared above: https://cran.r-project.org/web/packages/clubSandwich/vignettes/Wald-tests-in-clubSandwich.html.
Basically 0 1 - 1 Represents "Sat->Loy" - "Com->Loy " = 0. A standard t-test for only Sat->Loy = 0 would be represented by 0 1 0

Hope this helps.

the nrows parameter is not from the package just setting the dimensions of the matrix to consist out of one row. If not R would create one column and 3 rows

[soumyaray]

perfect – i'll give this a read when i have a moment. It seems to be that setting the values of L could be the kind of thing for which we could provide a high level function that makes it easier.

[PascalHessler]

Yes that would be much easier. The clubsandwich provides such functions but they are not compatible, since they not only return the matrix but add addintional information.