I agree with Christin, but I have a couple of things to add. I certainly don't think of the Duggers, the hillbilly politician family with 19 kids and still growing, according to Michelle Dugger, with the huge house that their A&E lifestyle bought. I think a minimalist family would tend to have fewer children, probably at the most three unless multiple births were involved, as well as live a basic lifestyle. Maybe drive a used Chevy or Honda, don't eat out often, some of them would home school their children, which would require fewer clothes and shoes. They might have a TV, but not cable and they would have a computer only because it is required for their children in school.
A minimalist family might grow part of its own food and maybe raise a few chickens, but that wouldn't be required to be considered minimalist.
I also think of a two-parent household because a single parent, especially if it is a woman, in this situation is not thought of as minimalist. It is thought of as deprived or in poverty.