def test_multiple_regression_big_small(self):
''' test multiple regression with a small array, and a large array
'''
for n in [50, 500000]:
x, y, x_with_intercept = make_arrays(n=n, k=10)
lstsq_fit = lstsq(x_with_intercept, y)
regressor_fit = linregress(x, y)
# check the betas are tightly correlated
corr = numpy.corrcoef(lstsq_fit[0][:-1], regressor_fit.coef_[:-1])[0, 1] ** 2
self.assertTrue(corr > 0.99999)
abs_diff = difference(lstsq_fit[0][:-1], regressor_fit.coef_[:-1])
self.assertTrue(abs_diff.max() < 1e-5)
def test_multiple_regression(self):
''' check a single large regression with many different linear models.
Skip p-value checks for other tests, as statsmodels is too slow. Also,
this uses arrasy of random numbers, i.e. random betas and p-values.
'''
x, y, x_with_intercept = make_arrays(n=5000, k=250)
# mainly compare lstsq from scipy with regressor, but lstsq lacks p-values
# so we need statsnmodels OLS for p-values, but that is very slow
lstsq_fit = lstsq(x_with_intercept, y)
regressor_fit = linregress(x, y)
sm_fit = OLS(y, x_with_intercept).fit()
sk_fit = LinearRegression().fit(x, y)
# check that the betas are very tightly correlated
corr = numpy.corrcoef(lstsq_fit[0][:-1],
regressor_fit.coef_[:-1])[0, 1]**2
self.assertTrue(corr > 0.9999999)
# check that lstsq betas correlate with sk_fit betas for extra sanity
corr = numpy.corrcoef(lstsq_fit[0][:-1], sk_fit.coef_)[0, 1]**2
self.assertTrue(corr > 0.9999999)
# check the beta values are very close. They aren't identical, as this
# package uses 32-bit floats, but the others convert to 64-bit doubles.
# Differences should be on the order of 1e-8, which is the usual delta
# between a 64-bit float and its 32-bit representation (for values
# around 0.5). Float differences accumulate to around 2e-6 at most,
# which makes a bigger relative difference for betas near zero.
abs_diff = difference(lstsq_fit[0][:-1], regressor_fit.coef_[:-1])
self.assertTrue(abs_diff.max() < 5e-6)
# check the p-values are nearly identical in log10 space, and correlate
p_delta = abs(
numpy.log10(regressor_fit.pvalue) - numpy.log10(sm_fit.pvalues))
self.assertTrue(p_delta.max() < 1e-3)
corr = numpy.corrcoef(numpy.log10(regressor_fit.pvalue),
numpy.log10(sm_fit.pvalues))[0, 1]**2
self.assertTrue(corr > 0.9999999)
def test_regression_correlated(self):
''' check multiple regresion, where y-values depend on the x columns
'''
x, y, x_with_intercept = make_arrays(n=50000, k=10)
# define some effect sizes (which decline across the columns)
betas = numpy.logspace(0, -10, num=x.shape[1])
y = (x * betas).sum(axis=1)
lstsq_fit = lstsq(x_with_intercept, y)
regressor_fit = linregress(x, y)
# check differences versus the predefined betas
diff = difference(betas, regressor_fit.coef_[:-1])
self.assertTrue(diff.max() < 5e-6)
corr = numpy.corrcoef(betas, regressor_fit.coef_[:-1])[0, 1] ** 2
self.assertTrue(corr > 0.9999999)
# and check difference versus lstsq fit
corr = numpy.corrcoef(lstsq_fit[0][:-1], regressor_fit.coef_[:-1])[0, 1] ** 2
self.assertTrue(corr > 0.9999999)