"...as usual..." depends on information you didn't share:
1. What is your definition of 'usual'?
2. Are the zero and one, true numeric values or a proxy for a categorical response? If the response is a categorical response, then modeling and analysis will take a very different flow compared to a numeric response.
3. If the zero/one response values are numeric, are there possible values between zero and one? Or did the measurement system not discriminate these in between values?
4. Would also help if you shared the design and information regarding the practical problem at hand. Analysis should be aimed at the practical problem at hand. Not too mention the specific design that was used to explore the system.
Lots of questions before substantive advice can be given...and I'm sure I've left out a few of those questions...love to hear others thoughts.