Study here (for those who have access):
http://onlinelibrary...12.02583.x/full
I'll highlight a few things, for those who can't access the whole article:
"In the seat setting, the infant was placed in an infant seat with the parent sitting facing them. For the second setting, the infant was placed on a floor mat on their back with the parent positioned face to face with their infant. For both interactions fathers were instructed to play with the infant in any way they chose without the use of toys or objects, for 3 min." (NB: statistically significant correlations with 12-month-old behaviour were only found in the 'floor' setting)
"Father–infant interactions were assessed using the Global Rating Scales (GRS)..., a video-based assessment of the quality of parent-infant interaction. They were developed to assess differences between mothers with and without postnatal depression.... ...Parental behaviour is rated on four dimensions: sensitivity, intrusiveness, remoteness and behaviour relevant to depression (e.g. sad or tense). The videotaped interactions were scored by a trained researcher who had not been involved in the family visit."
"We selected maternal sensitivity as the key dimension to control for mother-infant interaction, as it is the domain of mother-infant interaction most consistently and strongly associated with adverse child outcome... This was measured by the sensitivity scale of the GRS during mother-infant interactions." (NB: not the entire GRS)
"Infant temperament was measured on the inert-fretful infant scale of the GRS during mother-infant interactions. This scale runs from −2 (withdrawn) to +2 (fretful) and rates the infants' attention to his environment, level of activity and affective state."
What I take away from this study is a suggestion that 'more remote' interactions with a parent tend to increase 'behavioural problems' at 12 months. Their analysis suggests that paternal engagement, yes, may play a role, but I'd point out that their analysis does not in fact exclude or account for maternal engagement, or the interaction between the parents (although they do talk about this in their Discussion).
Further aspects I'd like to see explored:
Are GRS scores (total or separate dimensions) from the father and the mother correlated with each other? How strongly related is each parent's GRS score to the risk of early behavioural problems?
Are GRS scores (total or separate dimensions) from two parents who share direct caretaking responsibilities equally or unequally (regardless of which parent is the 'primary caregiver') correlated with each other? And again, how strongly related is each to the risk of early behavioural problems?
Can one engaged parent with the infant compensate for a 'disengaged' partner? (e.g. as a function of time spent with each parent, or of the 'engaged' parent putting extra effort into being 'maximally engaged'?)
1. Shriek/screaming alone is not indicative of a behavioural problem.
2. The study does not exclude a contribution of the behaviour of the mother (or "second parent" more generally). It does not demonstrate a specific effect of 'paternal behaviour'.