Model	Expression	Description
Log of mean of cell counts = log(μijk)	λ + λiW + λjU + λkS	Complete independence among the three factors (pair-wise independent). No interaction term is included.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ik}}^{\mathit{WS}}$	Underweight is partially independent of stunting and wasting. This model contains the interaction between wasting and stunting
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{jk}}^{\mathit{US}}$	Wasting is partially independent of stunting and underweight. This model contains the interaction between underweight and stunting.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{UW}}$	Stunting is partially independent of wasting and underweight. This model contains the interaction between underweight and wasting.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{jk}}^{\mathit{US}}+{\lambda }_{\mathit{ik}}^{\mathit{WS}}$	Wasting & underweight are conditionally independent of stunting. This model contains the interaction terms between underweight and stunting; stunting and wasting.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{WU}}+{\lambda }_{\mathit{ik}}^{\mathit{WS}}$	Stunting and underweight are conditionally independent of wasting. This model contains the interaction terms between wasting and underweight; wasting and stunting.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{WU}}+{\lambda }_{\mathit{jk}}^{\mathit{US}}$	Stunting & wasting are conditionally independent of underweight. This model contains the interaction terms between wasting and underweight; underweight and stunting.
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{WU}}+{\lambda }_{\mathit{ik}}^{\mathit{WS}}+{\lambda }_{\mathit{jk}}^{\mathit{US}}$	Homogenous associations (every factor interacts with each other factor, but there is no interaction between all three factors)
	$\lambda +{\lambda }_i^W+{\lambda }_j^U+{\lambda }_k^S+{\lambda }_{\mathit{ij}}^{\mathit{WU}}+{\lambda }_{\mathit{ik}}^{\mathit{WS}}+{\lambda }_{\mathit{jk}}^{\mathit{US}}+{\lambda }_{\mathit{ijk}}^{\mathit{WUS}}$	All possible relationships between the factors are included.