I have a logistic regression model. My DV has two levels, 1 and 0. I don't think that is a linear model.
But of course it is a linear model. It is a generalized linear model. It is a logistic multiple linear regression, like this:
log(p/(1-p)) = beta_0 + beta_1*x_1 + beta_2*x_2
It is linear in the parameter. i.e. the beta:s.
But it has a non-linear link function: the stuff with "log(p/(1-p))". If you solve that equation, that is maninulate it so that you only get "p" on the left hand side, then you will get:
p = (exp(beta_0 + beta_1*x_1 + beta_2*x_2))/(1 + exp(beta_0 + beta_1*x_1 + beta_2*x_2))
If you plot that curve against x_1 (let x_2 be a constant) you will get an S-shaped curve.
You can check if the factor levels of x_1 are approximately on a line:
log(p/(1-p)) = beta_0 + factor(x_1)_i + beta_2*x_2
Anyway, it will maybe be a good enough approximation.