The Chow test is often suggested to test if the coefficients of two linear regressions differ or if a single linear regressions is more appropriate.
However, Chow test assumes equality of the variances of the regressions' residuals, which might not be the case in practice. For this reason, Wald test is suggested.
The wikipedia-page of the Wald test, however, states that the Wald test is a) not invariant to parametrization (what ever this means), b) uses two approximations, and c) requires an estimate under the null hypothesis. Because of these limitations, Wikipedia suggests to use log likelihood test instead.
So, why should I bother to use the Chow or Wald test in the first place, if I could (presumably) use the log likelihood test for the same purpose?
