"Almost all studies of same-sex parenting have concluded there is “no difference” in a range of outcome measures for children who live in a household with same-sex parents compared to children living with married opposite-sex parents. Recently, some work based on the US census has suggested otherwise, but those studies have considerable drawbacks. Here, a 20 % sample of the 2006 Canada census is used to identify self-reported children living with same-sex parents, and to examine the association of household type with children’s high school graduation rates. This large random sample allows for control of parental marital status, distinguishes between gay and lesbian families, and is large enough to evaluate differences in gender between parents and children. Children living with gay and lesbian families in 2006 were about 65 % as likely to graduate compared to children living in opposite sex marriage families. Daughters of same-sex parents do considerably worse than sons."
In 2012, at the time Professor Mark Regerus study was released, Professor Allen made some observation about the studies of same-sex led households.You can read those here.