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Table 1 Possible log-linear models of the three-way table of Emotional (E), Physical (P), and Sexual (S) violence

From: Assessing the prevalence and association between physical, emotional, and sexual of intimate partner violence against women in Nigeria

Model expression Description
\(log(\mu_{ijk})=\lambda + \lambda ^{E}_{i}+ \lambda^{P}_{j}+\lambda^{S}_{k}\) Mutual independence model (pair of variables are independent, both conditionally and marginally)
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{EP}_{ij}\) Sexual violence is partially independent of Emotional and Physical violence. This model contains the interaction between Emotional and Physical violence
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{ES}_{ik}\) Physical violence is partially independent of Emotional and Sexual violence. This model contains the interaction between Emotional and Sexual violence
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{PS}_{jk}\) Emotional violence is partially independent of Physical and Sexual. This model contains the interaction between Physical and Sexual violence
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{EP}_{ij}+\lambda^{ES}_{ik}\) Physical and Sexual violence are conditionally independent of Emotional. This model contains the interaction terms between Emotional and physical violence; Emotional and Sexual violence
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{EP}_{ij}+\lambda^{PS}_{jk}\) 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
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{ES}_{ik}+\lambda^{PS}_{jk}\) 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
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{EP}_{ij}+\lambda^{ES}_{ik} + \lambda^{PS}_{jk}\) Homogenous associations (every violence of the three interacts with each other, but there is no interaction between all three violence)
\(log(\mu_{ijk})=\lambda + \lambda^{E}_{i} + \lambda^{P}_{j} +\lambda^{S}_{k}+ \lambda^{EP}_{ij}+\lambda^{ES}_{ik} + \lambda^{PS}_{jk} + \lambda^{EPS}_{ijk}\) All possible interaction between violence
  1. log(µijk) = log of expected cell counts; E = Emotional; P = Physical; S = Sexual; λEijPSk = the effect of Emotional, Physical and Sexual violence respectively. Similar for the interaction term. For instance, λEPij represent the interaction effect among Emotional and Physical violence