def __init__(self,
y,
x,
intercept=True,
weights=None,
nw_lags=None,
nw_overlap=False):
import scikits.statsmodels.api as sm
self._x_orig = x
self._y_orig = y
self._weights_orig = weights
self._intercept = intercept
self._nw_lags = nw_lags
self._nw_overlap = nw_overlap
(self._y, self._x, self._weights, self._x_filtered, self._index,
self._time_has_obs) = self._prepare_data()
if self._weights is not None:
self._x_trans = self._x.mul(np.sqrt(self._weights), axis=0)
self._y_trans = self._y * np.sqrt(self._weights)
self.sm_ols = sm.WLS(self._y.values,
self._x.values,
weights=self._weights.values).fit()
else:
self._x_trans = self._x
self._y_trans = self._y
self.sm_ols = sm.OLS(self._y.values, self._x.values).fit()
def _check_wls(self, x, y, weights):
result = ols(y=y, x=x, weights=1/weights)
combined = x.copy()
combined['__y__'] = y
combined['__weights__'] = weights
combined = combined.dropna()
endog = combined.pop('__y__').values
aweights = combined.pop('__weights__').values
exog = sm.add_constant(combined.values, prepend=False)
sm_result = sm.WLS(endog, exog, weights=1/aweights).fit()
assert_almost_equal(sm_result.params, result._beta_raw)
assert_almost_equal(sm_result.resid, result._resid_raw)
self.checkMovingOLS('rolling', x, y, weights=weights)
self.checkMovingOLS('expanding', x, y, weights=weights)
ols_fit = sm.OLS(data.endog, data.exog).fit() # perhaps the residuals from this fit depend on the square of income incomesq = data.exog[:, 2] plt.scatter(incomesq, ols_fit.resid) plt.grid() # If we think that the variance is proportional to income**2 # we would want to weight the regression by income # the weights argument in WLS weights the regression by its square root # and since income enters the equation, if we have income/income # it becomes the constant, so we would want to perform # this type of regression without an explicit constant in the design #data.exog = data.exog[:,:-1] wls_fit = sm.WLS(data.endog, data.exog[:, :-1], weights=1 / incomesq).fit() # This however, leads to difficulties in interpreting the post-estimation # statistics. Statsmodels does not yet handle this elegantly, but # the following may be more appropriate # explained sum of squares ess = wls_fit.uncentered_tss - wls_fit.ssr # rsquared rsquared = ess / wls_fit.uncentered_tss # mean squared error of the model mse_model = ess / (wls_fit.df_model + 1) # add back the dof of the constant # f statistic fvalue = mse_model / wls_fit.mse_resid # adjusted r-squared rsquared_adj = 1 - (wls_fit.nobs) / (wls_fit.df_resid) * (1 - rsquared)
#use correction #sandwich estimators of parameter covariance matrix print 'heteroscedasticity corrected standard error of beta estimates' print res2.HC0_se print res2.HC1_se print res2.HC2_se print res2.HC3_se #print res.predict #plt.plot(x1, res2.fittedvalues, '--') #WLS knowing the true variance ratio of heteroscedasticity #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ print '\nWLS' res3 = sm.WLS(y2, X[:, [0, 2]], 1. / w).fit() print 'WLS beta estimates' print res3.params print 'WLS stddev of beta' print res3.bse #print res.predict #plt.plot(x1, res3.fittedvalues, '--.') #Detour write function for prediction standard errors #Prediction Interval for OLS #--------------------------- covb = res2.cov_params() # full covariance: #predvar = res2.mse_resid + np.diag(np.dot(X2,np.dot(covb,X2.T))) # predication variance only
# generate dataset
nsample = 50
x1 = np.linspace(0, 20, nsample)
X = np.c_[x1, (x1-5)**2, np.ones(nsample)]
np.random.seed(0)#9876789) #9876543)
beta = [0.5, -0.01, 5.]
y_true2 = np.dot(X, beta)
w = np.ones(nsample)
w[nsample*6/10:] = 3
sig = 0.5
y2 = y_true2 + sig*w* np.random.normal(size=nsample)
X2 = X[:,[0,2]]
# estimate OLS, WLS, (OLS not used in these tests)
res2 = sm.OLS(y2, X2).fit()
res3 = sm.WLS(y2, X2, 1./w).fit()
#direct calculation
covb = res3.cov_params()
predvar = res3.mse_resid*w + (X2 * np.dot(covb,X2.T).T).sum(1)
predstd = np.sqrt(predvar)
prstd, iv_l, iv_u = wls_prediction_std(res3)
np.testing.assert_almost_equal(predstd, prstd, 15)
# testing shapes of exog
prstd, iv_l, iv_u = wls_prediction_std(res3, X2[-1:,:], weights=3.)
np.testing.assert_equal( prstd[-1], prstd)
prstd, iv_l, iv_u = wls_prediction_std(res3, X2[-1,:], weights=3.)
np.testing.assert_equal( prstd[-1], prstd)
def age_model(indices): return sm.WLS(logwage[indices], age_design(indices), weights = w[indices])
print len(indf)
print len(indm)
#With each of these models, typically do some
#commands to look more at the models, like summary(),
#, anova for the model on its own or betwen two models to see
#how much additional explantory power you get with the added
#variables, and plots to look at residuals, qqplot, and hist of residuals
#Currently can't do anova or lowess in python, and the qqplots are annoying
#to make.
#Initial model, only look at log(hrwage)~sex
X1 = hrdat['sex']==2
X1 = sm.add_constant(X1, prepend=True)
model1 = sm.WLS(np.log(hrdat['hrwage']), X1, weights = hrdat['A_ERNLWT'])
results1 = model1.fit()
print results1.summary()
#More complicated model, log(hrwage)~sex+educ+age+PTFT
n = len(hrdat)
logwage = np.log(hrdat['hrwage'])
w = hrdat['A_ERNLWT']
X2 = np.hstack((sm.categorical(hrdat['sex'])[:,2:],
sm.categorical(hrdat['educ'])[:,2:],
hrdat['age'].reshape(n,1),
