ó áp7]c@s$dZddlZdd„Zdd„Zdd„Zdd„Zdd„Zdd „Zdd „Z ddd „Z ddd „Z dd „Z d„Z d„Zd„Zd„Zed„Zed„Zed„Zed„Zeeee eee e e eeeeeeeee gZdS(s“some measures for evaluation of prediction, tests and model selection Created on Tue Nov 08 15:23:20 2011 Author: Josef Perktold License: BSD-3 iÿÿÿÿNicCs9tj|ƒ}tj|ƒ}tj||dd|ƒS(s†mean squared error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- mse : ndarray or float mean squared error along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. itaxis(tnpt asanyarraytmean(tx1tx2R((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytmse scCs:tj|ƒ}tj|ƒ}tjt||d|ƒƒS(s‘root mean squared error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- rmse : ndarray or float root mean squared error along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. R(RRtsqrtR(RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytrmse*scCs>tj|ƒ}tj|ƒ}tjtj||ƒd|ƒS(sLmaximum absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- maxabs : ndarray or float maximum absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. R(RRtmaxtabs(RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytmaxabsGscCs>tj|ƒ}tj|ƒ}tjtj||ƒd|ƒS(sGmean absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- meanabs : ndarray or float mean absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. R(RRRR (RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytmeanabscscCs>tj|ƒ}tj|ƒ}tjtj||ƒd|ƒS(sMmedian absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- medianabs : ndarray or float median absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. R(RRtmedianR (RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt medianabsscCs5tj|ƒ}tj|ƒ}tj||d|ƒS(sAbias, mean error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- bias : ndarray or float bias, or mean difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. R(RRR(RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytbias›scCs5tj|ƒ}tj|ƒ}tj||d|ƒS(sYmedian bias, median error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- medianbias : ndarray or float median bias, or median difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. R(RRR (RRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt medianbias·scCs;tj|ƒ}tj|ƒ}tj||d|d|ƒS(s@variance of error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- vare : ndarray or float variance of difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. tddofR(RRtvar(RRRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytvareÓscCs;tj|ƒ}tj|ƒ}tj||d|d|ƒS(sTstandard deviation of error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- stde : ndarray or float standard deviation of difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. RR(RRtstd(RRRR((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytstdeïscCsòtj|ƒ}tj|ƒ}|dkrQtj|ƒ}tj|ƒ}d}ntj||ƒ}|j|}tj|dtjddgƒƒjt ƒ}t dƒg|j }|||lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyR( s   / cCsd|d|S(s‹Akaike information criterion Parameters ---------- llf : float value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aic : float information criterion References ---------- http://en.wikipedia.org/wiki/Akaike_information_criterion gÀg@((tllfR%t df_modelwc((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytaic:scCs d|d||||dS(s´Akaike information criterion (AIC) with small sample correction Parameters ---------- llf : float value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aicc : float information criterion References ---------- http://en.wikipedia.org/wiki/Akaike_information_criterion#AICc gÀg@gð?((R)R%R*((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytaiccSscCsd|tj|ƒ|S(sªBayesian information criterion (BIC) or Schwarz criterion Parameters ---------- llf : float value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- bic : float information criterion References ---------- http://en.wikipedia.org/wiki/Bayesian_information_criterion gÀ(Rtlog(R)R%R*((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pytbiclscCs&d|dtjtj|ƒƒ|S(syHannan-Quinn information criterion (HQC) Parameters ---------- llf : float value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- hqic : float information criterion References ---------- Wikipedia doesn't say much gÀi(RR-(R)R%R*((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pythqic…scCs0|stj|ƒ}n|td||ƒ|S(sÔAkaike information criterion Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. The information criteria should be used to compare only comparable models. For example, AIC is defined in terms of the loglikelihood as :math:`-2 llf + 2 k` in terms of :math:`\hat{\sigma}^2` :math:`log(\hat{\sigma}^2) + 2 k / n` in terms of the determinant of :math:`\hat{\Sigma}` :math:`log(\|\hat{\Sigma}\|) + 2 k / n` Note: In our definition we do not divide by n in the log-likelihood version. TODO: Latex math reference for example lecture notes by Herman Bierens See Also -------- References ---------- http://en.wikipedia.org/wiki/Akaike_information_criterion i(RR-R+(tsigma2R%R*tislog((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt aic_sigma s4cCs0|stj|ƒ}n|td||ƒ|S(sAkaike information criterion (AIC) with small sample correction Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aicc : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- http://en.wikipedia.org/wiki/Akaike_information_criterion#AICc i(RR-R,(R0R%R*R1((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt aicc_sigmaÙscCs0|stj|ƒ}n|td||ƒ|S(sBayesian information criterion (BIC) or Schwarz criterion Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- bic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- http://en.wikipedia.org/wiki/Bayesian_information_criterion i(RR-R.(R0R%R*R1((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt bic_sigmaüscCs0|stj|ƒ}n|td||ƒ|S(sÀHannan-Quinn information criterion (HQC) Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- hqic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- xxx i(RR-R/(R0R%R*R1((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt hqic_sigmas(t__doc__tnumpyRRRR R RRRRRR(R+R,R.R/tFalseR2R3R4R5t__all__(((s>lib/python2.7/site-packages/statsmodels/tools/eval_measures.pyt s,         /     9 # # (