Empirical and counterfactual conditions for sufficient cause interactions

Abstract

1 SummarySu¢ cient-component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of su¢ cient causes, synergism and su¢ cient cause interactions. Doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of su¢ cient cause interactions. The conditions are novel in that, unlike other conditions in the literature, they make no assumptions about monotonicity. The conditions can also be generalized and the conditions for three-way su¢ cient cause interactions are given explicitly. The statistical tests derived for su¢ cient cause interactions are compared with and contrasted to interaction terms in standard statistical models.

An algebraic interpretation of 2-factor binary sufficient component cause theory

“…Îñíîâîé ðàññìàòðèâàåìîé â ñòàòüå ôîðìàëüíîé ìîäåëè ÿâ-ëÿåòñÿ êîíöåïöèÿ äîñòàòî÷íûõ ïðè÷èí (sucient component cause framework) [9,19], [21,22,23].  ðàáîòå [19] Ê. Ðîòìàí îïðåäå-ëèë ïðè÷èííîñòü êàê ñîáðàíèå ðàçëè÷íûõ ïðè÷èííûõ ìåõàíèçìîâ, êàaeäûé èç êîòîðûõ äîñòàòî÷åí äëÿ ïîëó÷åíèÿ äàííîãî èñõîäà.…”

“…Ñëåäîâàòåëüíî, ìîaeíî ñêàçàòü, ÷òî â êëàññèôèêàöèè Ãðèíëåíäà-Ïóëà íàðóøåíèå ðàâåíñòâà (1) ñëóaeèò õàðàêòåðèñòè-êîé íàëè÷èÿ òîãî èëè èíîãî òèïà âçàèìîäåéñòâèÿ ôàêòîðîâ X 1 , X 2 .  ðàáîòàõ [21,22,23,24] áûë ïðîâåäåí áîëåå òùàòåëüíûé àíà-ëèç êëàññèôèêàöèè Ãðèíëåíäà-Ïóëà.  ñâÿçè ñ ïðîáëåìîé îáíàðó-aeåíèÿ ñèíåðãèçìà, ïîíèìàåìîãî êàê íàëè÷èå äîïîëíèòåëüíîãî ýô-ôåêòà ïðè ñîâìåñòíîì äåéñòâèè ôàêòîðîâ ïî ñðàâíåíèþ ñ ñóììîé ýôôåêòîâ ïðè èõ ðàçäåëüíîì âîçäåéñòâèè, áûëî ïðåäëîaeåíî âûäå-ëèòü êëàññ îòêëèêîâ, êàaeäûé èç êîòîðûõ íàçûâàåòñÿ ¾âûðàaeàþ-ùèì îïðåäåë¼ííóþ âçàèìîçàâèñèìîñòü¿ (denite interdependence) ïðè÷èí.…”

“…Çàìåòèì, ÷òî àíàëèç âçàèìîäåéñòâèÿ íà îñíîâå ðàáîò [21,22,23,24] ïðèâîäèò ê ñëåäóþùèì ñëîaeíîñòÿì: 1) èíòåðïðåòàöèÿ ïîëó÷åííûõ âûâîäîâ íåñîãëàñîâàííà, òàê êàê ñâÿçàíà ñ íåîäíîçíà÷íîñòüþ ñàìîãî ðàçëîaeåíèÿ (2) äëÿ äàííîãî îòêëèêà, ò.å. ñ íåîäíîçíà÷íîñòüþ âîññòàíîâëåíèÿ ðàçëîaeåíèÿ (2) ïî îòêëèêó;…”

“…Òàê êàê ãðóïïà G ïîðîaeäåíà ïðå-îáðàçîâàíèÿìè S 1 , S 2 , êîòîðûå ôîðìàëèçóþò ñâîéñòâà âçàèìîäåé-ñòâèÿ â áèíàðíîì ýêñïåðèìåíòå, òî ïîëó÷åííîå ðàçáèåíèå áóëåâîé àëãåáðû B (x 1 , x 2 ) ÿâëÿåòñÿ íåêîòîðîé êëàññèôèêàöèåé òèïîâ âçà-èìîäåéñòâèÿ ôàêòîðîâ. Íèaeå ìû ñîïîñòàâèì åå ñ èçâåñòíîé êëàñ-ñèôèêàöèåé èç ðàáîò [14], [21,22,23,24].…”

“…Äåéñòâèòåëüíî, èìåííî 10 îòêëèêîâ èç êëàññîâ ñ ýòèìè ïðåäñòàâèòåëÿìè â ðàáîòå [14] îáúåäèíåíû ïîä íà-çâàíèåì îòêëèêîâ, âûðàaeàþùèõ ïðè÷èííóþ âçàèìîçàâèñèìîñòü. Ñìûñëîâîå ñîäåðaeàíèå ýòîãî ïîíÿòèÿ ñîñòîèò â òîì, ÷òî ýôôåêò îò îäíîãî ôàêòîðà íå ìîaeåò áûòü îïðåäåëåí áåç çíàíèÿ î òîì, êàêîâî çíà÷åíèå äðóãîãî ôàêòîðà [14], [21,22,23,24].…”