Did most early English settlers of America come voluntarily?

This is a very good question because, although most English settlers would seem to have voluntarily settled in America, the vast majority only did so because they were forced out of their native land by religious persecution. Had it not been for such persecution, it's highly unlikely that anywhere near as many settlers would've made the long, hard trip across the Atlantic.
One could approach the question by saying that most of the first settlers may not have chosen to leave England, but they certainly did choose to go to America instead of other havens for religious dissidents.
To make the picture even more complicated, many of such dissidents, most notably the Puritans, believed that it was God's will that they should establish a new kingdom of righteousness on American soil. In that sense, the Puritans and many others like them were answering to what they believed was the call of God rather than making their choice on the basis of the kind of rational deliberation one normally associates with voluntary decisions.