Table 1 Possible log-linear models of the three-way table of Emotional (E), Physical (P), and Sexual (S) violence
Model expression | Description |
|---|---|
\(log(\mu_{ijk})=\lambda + \lambda ^{E}_{i}+ \lambda^{P}_{j}+\lambda^{S}_{k}\) | 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 |