Education

this is a discussion that is pretty much like politics - two very equal and opposing sides -

Alaska has very liberal laws when it comes to home schooling...here is info on it

http://www.hslda.org/laws/analysis/Alaska.pdf

I am not sure if there is "research" but I homeschooled my kids. My oldest was taught by me her whole life except for 2 years of christian school.
There was a homeschool support group in our area and many of the parents were teachers.
I am not sure why you ask about homeschooling but if I had it to do over again I would not have put my kids in public school when I did. At the time I saw no other choice because I was recently widowed. My youngest daughter was in 4th grade, my oldest son was in 1st. My youngest son has been in public school since kindergarten. There is so much junk that you don't have to deal with in public school if you are able to do it. It is a huge commitment but the kids are better off. They have none of the peer pressure etc that our kids deal with in public school.
There are benefits such as athletics etc that the kids may miss out on but some of the school systems allowed us to participate.
I think if a teacher decides to homeschool that is great. They already have some of the training etc that we who aren't teachers don't have . We teach our kids to talk etc, who better than to educate?
There are some cases though , that the parents don't educate their children. They say they  are homeschooling but are not. I have no college degree but my kids were tested every year to make sure they were keeping up. They always tested above where they needed to be. But they enjoyed more free time. We usually started our year about a month after public schools and ended a month before. We had a week for Thanksgiving and 2 for Christmas.School for the younger kids was done around noon and the older kids were done when they finished their work. They worked at their own pace, which allowed them to be ahead or take more time if they didn't understand something.My youngest could read and write, add and subract when he started kindergarten. He was ahead then and as a 9th grader now..is still at the top of his class.