+If now we want to modelise heterogeneous populations, let $K$ be the number of
+populations and $\omega=(\omega_1,\cdots,\omega_K)$ their weights such that
+$\omega_{j}\geq 0$, $j=1,\ldots,K$ and $\sum_{j=1}^{K}\omega{j}=1$.
+Define, for $j=1,\ldots,K$, the regression coefficients in the $j$-th population
+by $\beta_{j}\in\R^{d}$ and the intercept in the $j$-th population by
+$b_{j}\in\R$. Let $\omega =(\omega_{1},\ldots,\omega_{K})$,
+$b=(b_1,\cdots,b_K)$, $\beta=[\beta_{1} \vert \cdots,\vert \beta_K]$ the $d\times K$
+matrix of regression coefficients and denote $\theta=(\omega,\beta,b)$.
+The model of population mixture of binary regressions is given by: