def test_ic():
#test information criteria
#consistency check
ics = [aic, aicc, bic, hqic]
ics_sig = [aic_sigma, aicc_sigma, bic_sigma, hqic_sigma]
for ic, ic_sig in zip(ics, ics_sig):
assert_(ic(np.array(2),10,2).dtype == np.float, msg=repr(ic))
assert_(ic_sig(np.array(2),10,2).dtype == np.float, msg=repr(ic_sig) )
assert_almost_equal(ic(-10./2.*np.log(2.),10,2)/10,
ic_sig(2, 10, 2),
decimal=14)
assert_almost_equal(ic_sig(np.log(2.),10,2, islog=True),
ic_sig(2, 10, 2),
decimal=14)
#examples penalty directly from formula
n, k = 10, 2
assert_almost_equal(aic(0, 10, 2), 2*k, decimal=14)
#next see Wikipedia
assert_almost_equal(aicc(0, 10, 2),
aic(0, n, k) + 2*k*(k+1.)/(n-k-1.), decimal=14)
assert_almost_equal(bic(0, 10, 2), np.log(n)*k, decimal=14)
assert_almost_equal(hqic(0, 10, 2), 2*np.log(np.log(n))*k, decimal=14)
def test_ic():
# test information criteria
# examples penalty directly from formula
n = 10
k = 2
assert_almost_equal(aic(0, 10, 2), 2*k, decimal=14)
# next see Wikipedia
assert_almost_equal(aicc(0, 10, 2),
aic(0, n, k) + 2*k*(k+1.)/(n-k-1.), decimal=14)
assert_almost_equal(bic(0, 10, 2), np.log(n)*k, decimal=14)
assert_almost_equal(hqic(0, 10, 2), 2*np.log(np.log(n))*k, decimal=14)
def test_ic():
# test information criteria
# examples penalty directly from formula
n = 10
k = 2
assert_almost_equal(aic(0, 10, 2), 2 * k, decimal=14)
# next see Wikipedia
assert_almost_equal(aicc(0, 10, 2),
aic(0, n, k) + 2 * k * (k + 1.) / (n - k - 1.),
decimal=14)
assert_almost_equal(bic(0, 10, 2), np.log(n) * k, decimal=14)
assert_almost_equal(hqic(0, 10, 2), 2 * np.log(np.log(n)) * k, decimal=14)
def test_ols():
# More comprehensive tests against OLS estimates
mod = RecursiveLS(endog, dta['m1'])
res = mod.fit()
mod_ols = OLS(endog, dta['m1'])
res_ols = mod_ols.fit()
# Regression coefficients, standard errors, and estimated scale
assert_allclose(res.params, res_ols.params)
assert_allclose(res.bse, res_ols.bse)
# Note: scale here is computed according to Harvey, 1989, 4.2.5, and is
# the called the ML estimator and sometimes (e.g. later in section 5)
# denoted \tilde \sigma_*^2
assert_allclose(res.filter_results.obs_cov[0, 0], res_ols.scale)
# OLS residuals are equivalent to smoothed forecast errors
# (the latter are defined as e_t|T by Harvey, 1989, 5.4.5)
# (this follows since the smoothed state simply contains the
# full-information estimates of the regression coefficients)
actual = (mod.endog[:, 0] -
np.sum(mod['design', 0, :, :] * res.smoothed_state, axis=0))
assert_allclose(actual, res_ols.resid)
# Given the estimate of scale as `sum(v_t^2 / f_t) / (T - d)` (see
# Harvey, 1989, 4.2.5 on p. 183), then llf_recursive is equivalent to the
# full OLS loglikelihood (i.e. without the scale concentrated out).
desired = mod_ols.loglike(res_ols.params, scale=res_ols.scale)
assert_allclose(res.llf_recursive, desired)
# Alternatively, we can constrcut the concentrated OLS loglikelihood
# by computing the scale term with `nobs` in the denominator rather than
# `nobs - d`.
scale_alternative = np.sum(
(res.standardized_forecasts_error[0, 1:] *
res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs
llf_alternative = np.log(
norm.pdf(res.resid_recursive, loc=0,
scale=scale_alternative**0.5)).sum()
assert_allclose(llf_alternative, res_ols.llf)
# Prediction
actual = res.forecast(10, design=np.ones((1, 1, 10)))
assert_allclose(actual, res_ols.predict(np.ones((10, 1))))
# Sums of squares, R^2
assert_allclose(res.ess, res_ols.ess)
assert_allclose(res.ssr, res_ols.ssr)
assert_allclose(res.centered_tss, res_ols.centered_tss)
assert_allclose(res.uncentered_tss, res_ols.uncentered_tss)
assert_allclose(res.rsquared, res_ols.rsquared)
# Mean squares
assert_allclose(res.mse_model, res_ols.mse_model)
assert_allclose(res.mse_resid, res_ols.mse_resid)
assert_allclose(res.mse_total, res_ols.mse_total)
# Hypothesis tests
actual = res.t_test('m1 = 0')
desired = res_ols.t_test('m1 = 0')
assert_allclose(actual.statistic, desired.statistic)
assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15)
actual = res.f_test('m1 = 0')
desired = res_ols.f_test('m1 = 0')
assert_allclose(actual.statistic, desired.statistic)
assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15)
# Information criteria
# Note: the llf and llf_obs given in the results are based on the Kalman
# filter and so the ic given in results will not be identical to the
# OLS versions. Additionally, llf_recursive is comparable to the
# non-concentrated llf, and not the concentrated llf that is by default
# used in OLS. Compute new ic based on llf_alternative to compare.
actual_aic = aic(llf_alternative, res.nobs_effective, res.df_model)
assert_allclose(actual_aic, res_ols.aic)
actual_bic = bic(llf_alternative, res.nobs_effective, res.df_model)
assert_allclose(actual_bic, res_ols.bic)
def test_ols():
# More comprehensive tests against OLS estimates
mod = RecursiveLS(endog, dta['m1'])
res = mod.fit()
mod_ols = OLS(endog, dta['m1'])
res_ols = mod_ols.fit()
# Regression coefficients, standard errors, and estimated scale
assert_allclose(res.params, res_ols.params)
assert_allclose(res.bse, res_ols.bse)
# Note: scale here is computed according to Harvey, 1989, 4.2.5, and is
# the called the ML estimator and sometimes (e.g. later in section 5)
# denoted \tilde \sigma_*^2
assert_allclose(res.filter_results.obs_cov[0, 0], res_ols.scale)
# OLS residuals are equivalent to smoothed forecast errors
# (the latter are defined as e_t|T by Harvey, 1989, 5.4.5)
# (this follows since the smoothed state simply contains the
# full-information estimates of the regression coefficients)
actual = (mod.endog[:, 0] -
np.sum(mod['design', 0, :, :] * res.smoothed_state, axis=0))
assert_allclose(actual, res_ols.resid)
# Given the estimate of scale as `sum(v_t^2 / f_t) / (T - d)` (see
# Harvey, 1989, 4.2.5 on p. 183), then llf_recursive is equivalent to the
# full OLS loglikelihood (i.e. without the scale concentrated out).
desired = mod_ols.loglike(res_ols.params, scale=res_ols.scale)
assert_allclose(res.llf_recursive, desired)
# Alternatively, we can constrcut the concentrated OLS loglikelihood
# by computing the scale term with `nobs` in the denominator rather than
# `nobs - d`.
scale_alternative = np.sum((
res.standardized_forecasts_error[0, 1:] *
res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs
llf_alternative = np.log(norm.pdf(res.resid_recursive, loc=0,
scale=scale_alternative**0.5)).sum()
assert_allclose(llf_alternative, res_ols.llf)
# Prediction
actual = res.forecast(10, design=np.ones((1, 1, 10)))
assert_allclose(actual, res_ols.predict(np.ones((10, 1))))
# Sums of squares, R^2
assert_allclose(res.ess, res_ols.ess)
assert_allclose(res.ssr, res_ols.ssr)
assert_allclose(res.centered_tss, res_ols.centered_tss)
assert_allclose(res.uncentered_tss, res_ols.uncentered_tss)
assert_allclose(res.rsquared, res_ols.rsquared)
# Mean squares
assert_allclose(res.mse_model, res_ols.mse_model)
assert_allclose(res.mse_resid, res_ols.mse_resid)
assert_allclose(res.mse_total, res_ols.mse_total)
# Hypothesis tests
actual = res.t_test('m1 = 0')
desired = res_ols.t_test('m1 = 0')
assert_allclose(actual.statistic, desired.statistic)
assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15)
actual = res.f_test('m1 = 0')
desired = res_ols.f_test('m1 = 0')
assert_allclose(actual.statistic, desired.statistic)
assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15)
# Information criteria
# Note: the llf and llf_obs given in the results are based on the Kalman
# filter and so the ic given in results will not be identical to the
# OLS versions. Additionally, llf_recursive is comparable to the
# non-concentrated llf, and not the concentrated llf that is by default
# used in OLS. Compute new ic based on llf_alternative to compare.
actual_aic = aic(llf_alternative, res.nobs_effective, res.df_model)
assert_allclose(actual_aic, res_ols.aic)
actual_bic = bic(llf_alternative, res.nobs_effective, res.df_model)
assert_allclose(actual_bic, res_ols.bic)
def bic(self):
"""
(float) Bayes Information Criterion
"""
# return -2*self.llf + self.params.shape[0]*np.log(self.nobs)
return bic(self.llf, self.nobs, self.params.shape[0])
def bic(self):
"""
(float) Bayes Information Criterion
"""
return bic(self.llf, self.nobs_effective, self.df_model)
def bic(self):
"""
(float) Bayes Information Criterion
"""
# return -2*self.llf + self.params.shape[0]*np.log(self.nobs)
return bic(self.llf, self.nobs, self.params.shape[0])
good_ranks += 1
else:
bad_rank_subs.append(sub)
bad_ranks.append(DV_4levels_sub_ranks)
bad_probs.append(DV_vals2)
#Run the logistic regressions
X = sub_df[['gain','loss']]
X['intercept'] = 1.0
y = sub_df.accept
#Run the full model
model_full = sm.Logit(y, X, missing='drop')
result_full = model_full.fit()
#result.summary()
coefficients_full = np.array(result_full.params)
all_coefs.append(coefficients_full)
bic_score_full += bic(result_full.llf,len(y),len(coefficients_full))
#Run the intercept only
model_intercept = sm.Logit(y, X['intercept'], missing='drop')
result_intercept = model_intercept.fit()
bic_score_intercept += bic(result_intercept.llf,len(y),1)
#Run intercept & gain
model_gain = sm.Logit(y, X[['gain', 'intercept']], missing='drop')
result_gain = model_gain.fit()
bic_score_gain += bic(result_gain.llf,len(y),2)
#Run intercept & loss
model_loss = sm.Logit(y, X[['loss', 'intercept']], missing='drop')
result_loss = model_loss.fit()
bic_score_loss += bic(result_loss.llf,len(y),2)
bic_per_sub = [bic(result_full.llf,len(y),len(coefficients_full)), bic(result_intercept.llf,len(y),1),
bic(result_gain.llf,len(y),2), bic(result_loss.llf,len(y),2)]
bic_all.append(bic_per_sub)
