Michael Moore, Nick Broomfield and Louis Theroux are great examples of what Bill Nichols describes as the participatory mode of Documentary.
The participatory mode of Documentary welcomes direct engagement between filmmaker and subject(s) - the filmmaker becomes part of the events being recorded The filmmakers impact on the events being recorded is acknowledged, indeed, it is often celebrated. (Bill Nichols).
This style is often referred to as 'Interactive' style of Documentary.