def test_confint_simult():
# example from book for simultaneous confint
m = [526.29, 54.69, 25.13]
cov = [[5808.06, 597.84, 222.03], [597.84, 126.05, 23.39],
[222.03, 23.39, 23.11]]
nobs = 87
res_ci = confint_mvmean_fromstats(m,
cov,
nobs,
lin_transf=np.eye(3),
simult=True)
cii = [
confint_mvmean_fromstats(m,
cov,
nobs,
lin_transf=np.eye(3)[i],
simult=True)[:2] for i in range(3)
]
cii = np.array(cii).squeeze()
# these might use rounded numbers in intermediate computation
res_ci_book = np.array([[503.06, 550.12], [51.22, 58.16], [23.65, 26.61]])
assert_allclose(res_ci[0], res_ci_book[:, 0], rtol=1e-3) # low
assert_allclose(res_ci[0], res_ci_book[:, 0], rtol=1e-3) # upp
assert_allclose(res_ci[0], cii[:, 0], rtol=1e-13)
assert_allclose(res_ci[1], cii[:, 1], rtol=1e-13)
res_constr = confint_mvmean_fromstats(m,
cov,
nobs,
lin_transf=[0, 1, -1],
simult=True)
assert_allclose(res_constr[0], 29.56 - 3.12, rtol=1e-3)
assert_allclose(res_constr[1], 29.56 + 3.12, rtol=1e-3)
# TODO: this assumes separate constraints,
# but we want multiplicity correction
# test if several constraints or transformations work
# original, flipping sign, multiply by 2
lt = [[0, 1, -1], [0, -1, 1], [0, 2, -2]]
res_constr2 = confint_mvmean_fromstats(m,
cov,
nobs,
lin_transf=lt,
simult=True)
lows = res_constr[0], -res_constr[1], 2 * res_constr[0]
upps = res_constr[1], -res_constr[0], 2 * res_constr[1]
# TODO: check return dimensions
lows = np.asarray(lows).squeeze()
upps = np.asarray(upps).squeeze()
assert_allclose(res_constr2[0], lows, rtol=1e-13)
assert_allclose(res_constr2[1], upps, rtol=1e-13)
def test_mv_mean():
# names = ['id', 'mpg1', 'mpg2', 'add']
x = np.asarray([[1.0, 24.0, 23.5, 1.0], [2.0, 25.0, 24.5, 1.0],
[3.0, 21.0, 20.5, 1.0], [4.0, 22.0, 20.5, 1.0],
[5.0, 23.0, 22.5, 1.0], [6.0, 18.0, 16.5, 1.0],
[7.0, 17.0, 16.5, 1.0], [8.0, 28.0, 27.5, 1.0],
[9.0, 24.0, 23.5, 1.0], [10.0, 27.0, 25.5, 1.0],
[11.0, 21.0, 20.5, 1.0], [12.0, 23.0, 22.5, 1.0],
[1.0, 20.0, 19.0, 0.0], [2.0, 23.0, 22.0, 0.0],
[3.0, 21.0, 20.0, 0.0], [4.0, 25.0, 24.0, 0.0],
[5.0, 18.0, 17.0, 0.0], [6.0, 17.0, 16.0, 0.0],
[7.0, 18.0, 17.0, 0.0], [8.0, 24.0, 23.0, 0.0],
[9.0, 20.0, 19.0, 0.0], [10.0, 24.0, 22.0, 0.0],
[11.0, 23.0, 22.0, 0.0], [12.0, 19.0, 18.0, 0.0]])
res = smmv.test_mvmean(x[:, 1:3], [21, 21])
res_stata = Holder(p_F=1.25062334808e-09,
df_r=22,
df_m=2,
F=59.91609589041116,
T2=125.2791095890415)
assert_allclose(res.statistic, res_stata.F, rtol=1e-10)
assert_allclose(res.pvalue, res_stata.p_F, rtol=1e-10)
assert_allclose(res.t2, res_stata.T2, rtol=1e-10)
assert_equal(res.df, [res_stata.df_m, res_stata.df_r])
# diff of paired sample
mask = x[:, -1] == 1
x1 = x[mask, 1:3]
x0 = x[~mask, 1:3]
res_p = smmv.test_mvmean(x1 - x0, [0, 0])
# result Stata hotelling
res_stata = Holder(
T2=9.698067632850247,
df=10,
k=2,
N=12,
F=4.4082126, # not in return List
p_F=0.0424) # not in return List
res = res_p
assert_allclose(res.statistic, res_stata.F, atol=5e-7)
assert_allclose(res.pvalue, res_stata.p_F, atol=5e-4)
assert_allclose(res.t2, res_stata.T2, rtol=1e-10)
assert_equal(res.df, [res_stata.k, res_stata.df])
# mvtest means diff1 diff2, zero
res_stata = Holder(p_F=.0423949782937231,
df_r=10,
df_m=2,
F=4.408212560386478,
T2=9.69806763285025)
assert_allclose(res.statistic, res_stata.F, rtol=1e-12)
assert_allclose(res.pvalue, res_stata.p_F, rtol=1e-12)
assert_allclose(res.t2, res_stata.T2, rtol=1e-12)
assert_equal(res.df, [res_stata.df_m, res_stata.df_r])
dw = weightstats.DescrStatsW(x)
ci0 = dw.tconfint_mean(alpha=0.05)
nobs = len(x[:, 1:])
ci1 = confint_mvmean_fromstats(dw.mean,
np.diag(dw.var),
nobs,
lin_transf=np.eye(4),
alpha=0.05)
ci2 = confint_mvmean_fromstats(dw.mean,
dw.cov,
nobs,
lin_transf=np.eye(4),
alpha=0.05)
assert_allclose(ci1[:2], ci0, rtol=1e-13)
assert_allclose(ci2[:2], ci0, rtol=1e-13)
# test from data
res = smmv.confint_mvmean(x, lin_transf=np.eye(4), alpha=0.05)
assert_allclose(res, ci2, rtol=1e-13)