Yes, involvement from both parents seems to be the major factor regardless of sex. There is likely additional research needed on why fathers disengage more when the mother has primary custody. With a majority of single parent households being headed by mothers, it seems another area ripe for research is how unlikely it is that the majority of fathers are disengaged to create such a large effect on the whole single mother cohort. Likewise, with the way custody tends to be grated in court, you would expect single father households to have a higher percentage of unengaged mothers due if it was determined that the mothers were the lesser choice for child welfare. I would guess looking at outcomes where one parent died would mostly control for that support mechanism.