Algorithm for the fitting of the parameters

1: Inititialize α(0), β(0)

2: for l = 1 to L do

3:  for k = 1 to K do

4:    ${\theta }_k^{(1)}=\arg {\min }_{{\theta }_k}{\sum }_{(i,j)\in I_k}{(y_{\mathit{ijk}}-f({\alpha }_i^{(0)}{t}_{\mathit{ij}}+{\beta }_i^{(0)};{\theta }_k))}^2$

5:    ${\sigma }_k^{{(1)}^2}=\frac{1}{|I_k-2I-4|}{\sum }_{(i,j)\in I_k}{(y_{\mathit{ijk}}-f({\alpha }_i^{(0)}{t}_{\mathit{ij}}+{\beta }_i^{(0)};{\theta }_k^{(1)}))}^2$

6:  end for

7:  for i = 1 to I do

8:    $({\alpha }_i^{(1)},{\beta }_i^{(1)})=\arg {\min }_{{\alpha }_i,{\beta }_i}{\sum }_{(j,k)\in I_i}\frac{1}{{\sigma }_k^{{(1)}^2}}{(y_{\mathit{ijk}}-f({\alpha }_i{t}_{\mathit{ij}}+{\beta }_i;{\theta }_k^{(1)}))}^2$

9:  end for

10:  α(0) = α(1); β(0) = β(1)

11: end for

12: for k = 1 to K do

13:  if bk < 0 then

14:    $a_k^{(1)}=-a_k^{(1)},b_k^{(1)}=-b_k^{(1)},d_k^{(1)}=d_k^{(1)}+a_k^{(1)}$

15:  end if

16: end for

17: for i = 1 to I do

18:   ${\alpha }_i^{(1)}=\frac{{\alpha }_i^{(1)}}{{\sigma }_N},{\beta }_i^{(1)}=\frac{{\beta }_i^{(1)}-m_N}{{\sigma }_N}$

19: end for