Table 4.

Equations for Models 1–4 and 1I-4I

Models	Negative binomial count component	Bernoulli component (zero-inflated "I" models only)
1,1I 2,2I 3,3I 4,4I	$\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a$ $\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w$ $\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w+{\gamma }_2{w}^2$ $\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w+{\gamma }_2{w}^2+{\gamma }_3{w}^3$	$Logit(p)={\delta }_0+{\delta }_{1}a+{\delta }_2\text{Ln}(n)+{\delta }_3\text{Ln}(w)$