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