'''Additional functions
prediction standard errors and confidence intervals
A: josef pktd
'''
import numpy as np
from scipy import stats
[docs]def atleast_2dcol(x):
''' convert array_like to 2d from 1d or 0d
not tested because not used
'''
x = np.asarray(x)
if (x.ndim == 1):
x = x[:, None]
elif (x.ndim == 0):
x = np.atleast_2d(x)
elif (x.ndim > 0):
raise ValueError('too many dimensions')
return x
[docs]def wls_prediction_std(res, exog=None, weights=None, alpha=0.05):
'''calculate standard deviation and confidence interval for prediction
applies to WLS and OLS, not to general GLS,
that is independently but not identically distributed observations
Parameters
----------
res : regression result instance
results of WLS or OLS regression required attributes see notes
exog : array_like (optional)
exogenous variables for points to predict
weights : scalar or array_like (optional)
weights as defined for WLS (inverse of variance of observation)
alpha : float (default: alpha = 0.05)
confidence level for two-sided hypothesis
Returns
-------
predstd : array_like, 1d
standard error of prediction
same length as rows of exog
interval_l, interval_u : array_like
lower und upper confidence bounds
Notes
-----
The result instance needs to have at least the following
res.model.predict() : predicted values or
res.fittedvalues : values used in estimation
res.cov_params() : covariance matrix of parameter estimates
If exog is 1d, then it is interpreted as one observation,
i.e. a row vector.
testing status: not compared with other packages
References
----------
Greene p.111 for OLS, extended to WLS by analogy
'''
# work around current bug:
# fit doesn't attach results to model, predict broken
#res.model.results
covb = res.cov_params()
if exog is None:
exog = res.model.exog
predicted = res.fittedvalues
if weights is None:
weights = res.model.weights
else:
exog = np.atleast_2d(exog)
if covb.shape[1] != exog.shape[1]:
raise ValueError('wrong shape of exog')
predicted = res.model.predict(res.params, exog)
if weights is None:
weights = 1.
else:
weights = np.asarray(weights)
if weights.size > 1 and len(weights) != exog.shape[0]:
raise ValueError('weights and exog do not have matching shape')
# full covariance:
#predvar = res3.mse_resid + np.diag(np.dot(X2,np.dot(covb,X2.T)))
# predication variance only
predvar = res.mse_resid/weights + (exog * np.dot(covb, exog.T).T).sum(1)
predstd = np.sqrt(predvar)
tppf = stats.t.isf(alpha/2., res.df_resid)
interval_u = predicted + tppf * predstd
interval_l = predicted - tppf * predstd
return predstd, interval_l, interval_u