def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
        """
        Gradient of the log likelihood function at y, given link(f) w.r.t link(f)

        .. math::
            \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\beta (\\log \\beta y_{i}) - \\Psi(\\alpha_{i})\\beta\\\\
            \\alpha_{i} = \\beta y_{i}

        :param link_f: latent variables (f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata which is not used in gamma distribution
        :returns: gradient of likelihood evaluated at points
        :rtype: Nx1 array

        """
        grad = self.beta*np.log(self.beta*y) - special.psi(self.beta*link_f)*self.beta
        #old
        #return -self.gp_link.dtransf_df(gp)*self.beta*np.log(obs) + special.psi(self.gp_link.transf(gp)*self.beta) * self.gp_link.dtransf_df(gp)*self.beta
        return grad