def METHOD_NAME():
    # start with ICRS model, fit with both models
    # compare parameter values and uncertainties
    model_ICRS = get_model(io.StringIO(modelstring_ICRS))
    toas = pint.simulation.make_fake_toas_uniform(
        MJDStart, MJDStop, NTOA, model=model_ICRS, error=1 * u.us, add_noise=True
    )
    fit_ICRS = WLSFitter(toas, model_ICRS)
    fit_ECL = WLSFitter(toas, model_ICRS.as_ECL())
    fit_ECL.fit_toas()
    fit_ICRS.fit_toas()
    m1 = fit_ICRS.model
    m2 = fit_ECL.model.as_ICRS()
    for p in ("RAJ", "DECJ", "PMRA", "PMDEC"):
        assert np.isclose(m1.__getitem__(p).value, m2.__getitem__(p).value)
        # do a generous test here since the uncertainties could change
        assert np.isclose(
            m1.__getitem__(p).uncertainty, m2.__getitem__(p).uncertainty, rtol=0.5
        )