I have the logistic regression model
$$\text{logit}(\pi_i)=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_3+\beta_4x_4+\beta_5x_5$$
when $x_5=x_3\times x_4$.
I set $H_0:\beta_3=\beta_4=\beta_5=0$ and the alternative to be $\beta_3,\beta_4,\beta_5\neq0$.
As the title suggests, I would use Analysis of Deviance, but my (maybe silly) question is: when I determine the models (the full and the sub models), do I include the rest of the parameters $x_1,x_2,x_3$, or do I create a model containing only the predictors $x_3,x_4,x_5$ for the alternative "full" model and the $1$ for the "sub" model?