Stats:
If you have some linear model:
$y_i=\beta_0+\beta_1x_{i1}+...+\beta_px_{ip}$

Is testing a joint some null hypothesis like
$Ho:\beta_0=\beta_1=...=\beta_p=0$ using an ANOVA test the same as doing it with a likelihood ratio test (a.k.a. deviance test)? When would you use one versus the other?

Question

Stats:
If you have some linear model:
$y_i=\beta_0+\beta_1x_{i1}+...+\beta_px_{ip}$

Is testing a joint some null hypothesis like 
$Ho:\beta_0=\beta_1=...=\beta_p=0$ using an ANOVA test the same as doing it with a  likelihood ratio test (a.k.a. deviance test)? When would you use one versus the other?

kirbykirby · Answer

I am guessing that in linear models, they give the same result (but I would like a convincing argument if that's true. But, we use a deviance test for generalized linear models because you can't "separate" the sums of squares into two components easily like you can in linear models?

kirbykirby · Answer

Actually I should say something more like $\beta_1=...=\beta_p=0$ for Ho,. It would be hard to imagine including the intercept.