The study tested "the hypothesis that reduced stability relative to opposite-sex families may explain part or all of any increased emotional distress experienced by children in same-sex families." https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2500537
"Risk was elevated in the presence of parent psychological distress (RR 2.7, CI 1.8-4.3, p (t) < .001), moderated by family instability (RR 1.3, CI 1.2-1.4) and unaffected by stigmatization (RR 2.4, CI 1.4-4.2), though these all had significant direct effects on emotional problems." https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2500537
Zack Ford called the study "Hugely Flawed" over the absence of legal marriage certificates. However, it seems to me that the study was on biological parentage by both opposite-sex parents versus same-sex. Most of his critique was not with the data and findings (the science) but with the policy suggestions in that they didn't address all of the other types of living arrangements Ford mentioned (though the study did address them, and one may draw his or her own policy conclusions). Ford wrote as if there is something inherently sinister in that. I disagree.