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_dl(self):
res = results_meta.exk1_dl
eff, var_eff = self.eff, self.var_eff
tau2 = _fit_tau_mm(eff, var_eff, 1 / var_eff)
assert_allclose(tau2, res.tau2, atol=1e-10)
res3 = combine_effects(eff, var_eff, method_re="dl")
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) # fe, re, fe_wls, re_wls
assert_allclose(ci[1][0], res.ci_lb, atol=1e-10)
assert_allclose(ci[1][1], res.ci_ub, atol=1e-10)
assert_allclose(res3.q, res.QE, atol=1e-10)
# I2 is in percent in metafor
assert_allclose(res3.i2, res.I2 / 100, atol=1e-10)
assert_allclose(res3.h2, res.H2, atol=1e-10)
q, pv, df = res3.test_homogeneity()
assert_allclose(pv, res.QEp, atol=1e-10)
assert_allclose(q, res.QE, atol=1e-10)
assert_allclose(df, 9 - 1, atol=1e-10)
# compare FE estimate
res_fe = results_meta.exk1_fe
assert_allclose(res3.mean_effect_fe, res_fe.b, atol=1e-13)
assert_allclose(res3.sd_eff_w_fe, res_fe.se, atol=1e-10)
assert_allclose(ci[0][0], res_fe.ci_lb, atol=1e-10)
assert_allclose(ci[0][1], res_fe.ci_ub, atol=1e-10)
# compare FE, RE with HKSJ adjustment
res_dls = results_meta.exk1_dl_hksj
res_fes = results_meta.exk1_fe_hksj
assert_allclose(res3.mean_effect_re, res_dls.b, atol=1e-13)
assert_allclose(res3.mean_effect_fe, res_fes.b, atol=1e-13)
assert_allclose(res3.sd_eff_w_fe * np.sqrt(res3.scale_hksj_fe),
res_fes.se,
atol=1e-10)
assert_allclose(res3.sd_eff_w_re * np.sqrt(res3.scale_hksj_re),
res_dls.se,
atol=1e-10)
assert_allclose(np.sqrt(res3.var_hksj_fe), res_fes.se, atol=1e-10)
assert_allclose(np.sqrt(res3.var_hksj_re), res_dls.se, atol=1e-10)
# metafor uses t distribution for hksj
ci = res3.conf_int(use_t=True) # fe, re, fe_wls, re_wls
assert_allclose(ci[3][0], res_dls.ci_lb, atol=1e-10)
assert_allclose(ci[3][1], res_dls.ci_ub, atol=1e-10)
assert_allclose(ci[2][0], res_fes.ci_lb, atol=1e-10)
assert_allclose(ci[2][1], res_fes.ci_ub, atol=1e-10)
q, pv, df = res3.test_homogeneity()
assert_allclose(pv, res_dls.QEp, atol=1e-10)
assert_allclose(q, res_dls.QE, atol=1e-10)
assert_allclose(df, 9 - 1, atol=1e-10)