My question relates mostly around the practical differences between General Linear Modeling (GLM) and Generalized Linear Modelling (GZLM).
In my case it would be a few continuous variables as covariates and a few factors in an ANCOVA, versus GZLM. I want to examine the main effects of each variable, as well as one three-way interaction that I will outline in the model. I can see this hypothesis being tested in an ANCOVA, or using GZLM. To some extent I understand the math processes and reasoning behind running a General Linear Model like an ANCOVA, and I somewhat understand that GZLMs allow for a link function connecting the linear model and the dependent variable (ok, I lied, maybe I don't really understand the math).
What I really don't understand are the practical differences or reasons for running one analysis and not the other when the probability distribution used in the GZLM is normal (i.e., identity link function?). I get very different results when I run one over the other. Could I run either? My data is somewhat non-normal, but works to some extent both in the ANCOVA and the GZLM. In both cases my hypothesis is supported, but in the GZLM the p value is "better".
My thought was that an ANCOVA is a linear model with a normally distributed dependent variable using an identity link function, which is exactly what I can input in a GZLM, but these are still different.
Please shed some light on these questions for me, if you can!
Based on the first answer I have the additional question:
If they are identical except for the significance test that it utilized (i.e., F test vs. Wald Chi Square), which would be most appropriate to use? ANCOVA is the "go-to method", but I am unsure why the F test would be preferable. Can someone shed some light on this question for me?