'Transforms the log of observation probabilities in terms of the
Lagrange multiplier to the log \'star\' of the probabilities.
Parameters
eta : float
Lagrange multiplier
est_vect : ndarray (n,k)
Estimating equations vector
wts : nx1 array
Observation weights
Returns
data_star : array
The weighted logstar of the estimting equations
Notes
This function is only a placeholder for the _fit_Newton.
The function value is not used in optimization and the optimal value
is disregarded when computing the log likelihood ratio.'

def _log_star(self, eta, est_vect, weights, nobs):

    data_star = (np.log(weights) + (np.sum(weights) + np.dot(est_vect, eta)))
    idx = (data_star < (1.0 / nobs))
    not_idx = (~ idx)
    nx = (nobs * data_star[idx])
    data_star[idx] = ((np.log((1.0 / nobs)) - 1.5) + (nx * (2.0 - (nx / 2))))
    data_star[not_idx] = np.log(data_star[not_idx])
    return data_star
