Wald or F-test

[Alex Caridyas]

I am using GSEM with the svy option (for weights). I am running these models on two separate subsamples and I would like to test whether the effects of the variable on the outcome is statistically different in those two subsamples. I have gone with a Wald test using the following code:

test _b[y0:1.z]=_b[y1:1.z]

The code for my models is along the lines of:

svy:gsem (r<- i.z i.v i.m, ologit) (y<- i.z i.v i.m i.r, ologit)

I am not sure whether, because I am using weights, I should be using an F test?

[Jeff Wooldridge]

All inference here will be based on asymptotics -- whether you use a Wald test or an F test. In the context of asymptotics, W = F/q where q = #restrictions imposed. In your case, it looks like q = 1, so there is literally no difference between a Wald and "F" statistic.

Stata is not consistent about when it reports a Wald (asymptotic chi-square) or F (approximate F) statistic. But it shouldn't matter unless the sample size is very small. And, remember, theoretically the F version of the statistic has no validity over the chi-square. But in some situations it's been seen that using an F approximation gets closer to the exact size of the test. But nothing is every exact except under the classical linear model assumption -- which you definitely do not have here.

[Alex Caridyas]

Understood - thank you for this explanation, Jeff.