Table 1.

Possible log-linear models of the three-way table of Emotional (E), Physical (P), and Sexual (S) violence

Model expression	Description
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S$	Mutual independence model (pair of variables are independent, both conditionally and marginally)
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{EP}}$	Sexual violence is partially independent of Emotional and Physical violence. This model contains the interaction between Emotional and Physical violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ik}}^{\mathit{ES}}$	Physical violence is partially independent of Emotional and Sexual violence. This model contains the interaction between Emotional and Sexual violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{jk}}^{\mathit{PS}}$	Emotional violence is partially independent of Physical and Sexual. This model contains the interaction between Physical and Sexual violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{EP}}+{\lambda }_{\mathit{ik}}^{\mathit{ES}}$	Physical and Sexual violence are conditionally independent of Emotional. This model contains the interaction terms between Emotional and physical violence; Emotional and Sexual violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{EP}}+{\lambda }_{\mathit{jk}}^{\mathit{PS}}$	Emotional and Sexual violence are conditionally independent of Physical violence. This model contains the interaction terms between Emotional and Physical violence; Physical and Sexual violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ik}}^{\mathit{ES}}+{\lambda }_{\mathit{jk}}^{\mathit{PS}}$	Emotional and Physical violence are conditionally independent of Sexual violence. This model contains the interaction terms between Emotional and Sexual violence; Physical and Sexual violence
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{EP}}+{\lambda }_{\mathit{ik}}^{\mathit{ES}}+{\lambda }_{\mathit{jk}}^{\mathit{PS}}$	Homogenous associations (every violence of the three interacts with each other, but there is no interaction between all three violence)
$log({\mu }_{\mathit{ijk}})=\lambda +{\lambda }_i^E+{\lambda }_j^P+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{EP}}+{\lambda }_{\mathit{ik}}^{\mathit{ES}}+{\lambda }_{\mathit{jk}}^{\mathit{PS}}+{\lambda }_{\mathit{ijk}}^{\mathit{EPS}}$	All possible interaction between violence

log(µ_ijk) = log of expected cell counts; E = Emotional; P = Physical; S = Sexual; λ^E_i,λ_j^P,λ^S_k = the effect of Emotional, Physical and Sexual violence respectively. Similar for the interaction term. For instance, λ^EP_ij represent the interaction effect among Emotional and Physical violence