Table 4 Equations for Models 1–4 and 1I-4I

1,1I

2,2I

3,3I

4,4I

$\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a$

$\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w$

$\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w+{\gamma }_2{w}^2$

$\text{Ln}({\mu }_{\Lambda })=\text{Ln}({\lambda }_1)+c\text{Ln}(n)+\beta a+{\gamma }_{1}w+{\gamma }_2{w}^2+{\gamma }_3{w}^3$

$Logit(p)={\delta }_0+{\delta }_{1}a+{\delta }_2\text{Ln}(n)+{\delta }_3\text{Ln}(w)$