def test_tau_kacker(self):
# test iterative and two-step methods, Kacker 2004
# PM CA DL C2 from table 1 first row p. 135
# test for PM and DL are also against R metafor in other tests
eff, var_eff = self.eff, self.var_eff
t_PM, t_CA, t_DL, t_C2 = [0.8399, 1.1837, 0.5359, 0.9352]
tau2, converged = _fit_tau_iterative(eff, var_eff,
tau2_start=0.1, atol=1e-8)
assert_equal(converged, True)
assert_allclose(np.sqrt(tau2), t_PM, atol=6e-5)
k = len(eff)
# cochrane uniform weights
tau2_ca = _fit_tau_mm(eff, var_eff, np.ones(k) / k)
assert_allclose(np.sqrt(tau2_ca), t_CA, atol=6e-5)
# DL one step, and 1 iteration, reduced agreement with Kacker
tau2_dl = _fit_tau_mm(eff, var_eff, 1 / var_eff)
assert_allclose(np.sqrt(tau2_dl), t_DL, atol=1e-3)
tau2_dl_, converged = _fit_tau_iter_mm(eff, var_eff, tau2_start=0,
maxiter=1)
assert_equal(converged, False)
assert_allclose(tau2_dl_, tau2_dl, atol=1e-10)
# C2 two step, start with CA
tau2_c2, converged = _fit_tau_iter_mm(eff, var_eff,
tau2_start=tau2_ca,
maxiter=1)
assert_equal(converged, False)
assert_allclose(np.sqrt(tau2_c2), t_C2, atol=6e-5)
def test_pm(self):
res = results_meta.exk1_metafor
eff, var_eff = self.eff, self.var_eff
tau2, converged = _fit_tau_iterative(eff,
var_eff,
tau2_start=0.1,
atol=1e-8)
assert_equal(converged, True)
assert_allclose(tau2, res.tau2, atol=1e-10)
# compare with WLS, PM weights
mod_wls = WLS(eff, np.ones(len(eff)), weights=1 / (var_eff + tau2))
res_wls = mod_wls.fit(cov_type="fixed_scale")
assert_allclose(res_wls.params, res.b, atol=1e-13)
assert_allclose(res_wls.bse, res.se, atol=1e-10)
ci_low, ci_upp = res_wls.conf_int()[0]
assert_allclose(ci_low, res.ci_lb, atol=1e-10)
assert_allclose(ci_upp, res.ci_ub, atol=1e-10)
# need stricter atol to match metafor,
# I also used higher precision in metafor
res3 = combine_effects(eff, var_eff, method_re="pm", atol=1e-7)
# TODO: asserts below are copy paste, DRY?
assert_allclose(res3.tau2, res.tau2, atol=1e-10)
assert_allclose(res3.mean_effect_re, res.b, atol=1e-13)
assert_allclose(res3.sd_eff_w_re, res.se, atol=1e-10)
ci = res3.conf_int(use_t=False)[1]
assert_allclose(ci[0], res.ci_lb, atol=1e-10)
assert_allclose(ci[1], res.ci_ub, atol=1e-10)
assert_allclose(res3.q, res.QE, atol=1e-10)
# the following does not pass yet
# assert_allclose(res3.i2, res.I2 / 100, atol=1e-10) # percent in R
# assert_allclose(res3.h2, res.H2, atol=1e-10)
th = res3.test_homogeneity()
q, pv = th
df = th.df
assert_allclose(pv, res.QEp, atol=1e-10)
assert_allclose(q, res.QE, atol=1e-10)
assert_allclose(df, 9 - 1, atol=1e-10)