B Z@sdZddlmZmZmZmZddlZddlZ ddl m Z ddl m Z mZmZddlmZddlmZddlmZdd lmZdd lmZdd lmZdd lmZd dlmZm Z m!Z!dddddddddddddddddgZ"dd Z#d=d"dZ$d>d#dZ%d?d$dZ&d%d&Z'did'idd(fd)dZ(d@d*dZ)dAd+dZ*dBd,dZ+dCd-dZ,dDd2dZ-dEd3dZ.dFd4dZ/ed5d6ie/_dGd7dZ0e d5d6ie0_dHd9dZ1e!d5d6ie1_dId:dZ2d;dZ3dJd>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> data = sm.datasets.statecrime.load_pandas().data >>> murder = data['murder'] >>> X = data[['poverty', 'hs_grad']] >>> X["constant"] = 1 >>> y = murder >>> model = sm.OLS(y, X) >>> results = model.fit() Create a plot just for the variable 'Poverty': >>> fig, ax = plt.subplots() >>> fig = sm.graphics.plot_fit(results, 0, ax=ax) >>> ax.set_ylabel("Murder Rate") >>> ax.set_xlabel("Poverty Level") >>> ax.set_title("Linear Regression") >>> plt.show() .. plot:: plots/graphics_plot_fit_ex.py NZbo)labelzb-z True valueszFitted values versus %sDr,fitted)colorr2rkgffffff?) linewidthr5alphabest)locZ numpoints)r create_mpl_axmaybe_name_or_idxrrendogexognpZargsortr. endog_namesr fittedvaluesvlines set_title set_xlabel set_ylabellegend)r&exog_idxZy_truer0kwargsfig exog_nameyx1Z x1_argsorttitleprstdiv_liv_ur'r'r(rIs,:   c Cst|}t||j\}}t|}|jj}|jjdd|f}t|\}}}|ddd} | j ||jj ddd|d| j ||j dd d d d | j |||dd dd| j ddd| || || jdd|ddd} | ||jd| jddd| j d|dd| || d|ddd} t|jjjdt} d| |<|jjdd| f} ddlm} t|jjj| |||jjjd| d| d}| j ddd|ddd } t||| d!}| j d"dd|jd#|dd||j dd$|S)%agPlot regression results against one regressor. This plots four graphs in a 2 by 2 figure: 'endog versus exog', 'residuals versus exog', 'fitted versus exog' and 'fitted plus residual versus exog' Parameters ---------- results : result instance result instance with resid, model.endog and model.exog as attributes exog_idx : int index of regressor in exog matrix fig : Matplotlib figure instance, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- fig : matplotlib figure instance Nrobg?)r5r8r2r3r,r4g?)r5r2r8r6gffffff?)r7r5r8zY and Fitted vs. Xlarge)fontsizer9)r:rblack)rKr5zResiduals versus %sresidF)Series)nameindex) obs_labelsr0zPartial regression plot)r0z CCPR PlotzRegression Plots for %s)top)!r create_mpl_figr<rrr@r>r add_subplotr.r=rArBrCrDrErFrWZaxhliner?ZonesshapeboolpandasrYrdataZ orig_endog row_labelsrsuptitle tight_layoutsubplots_adjust) r&rGrIrJZy_namerLrNrOrPr0Z exog_noti exog_othersrYr'r'r(rsL           cCs:t||}t||}t|j|j}|||ffS)aPartial regression. regress endog on exog_i conditional on exog_others uses OLS Parameters ---------- endog : array_like exog : array_like exog_others : array_like Returns ------- res1c : OLS results instance (res1a, res1b) : tuple of OLS results instances results from regression of endog on exog_others and of exog_i on exog_others )rfitrW)r=exog_iriZres1aZres1bZres1cr'r'r(_partial_regressionsrlTFc Kst|\} }t|tr&t|d|}t|trrar~intr?ceilZarray exog_names enumeraterpoprzr`rrCrfrgrh)r&rGgridrIrcrJrKr>Zk_varsnrowsncolsrZ other_namesiidxZothersrir0r'r'r(rs>'        c Cst|\}}t||j\}}t|}|jjdd|f}||j|}||||jdddl m }t ||| }|j} t | t|d}|d|d||f|d||S) aPlot CCPR against one regressor. Generates a CCPR (component and component-plus-residual) plot. Parameters ---------- results : result instance A regression results instance. exog_idx : int or string Exogenous, explanatory variable. If string is given, it should be the variable name that you want to use, and you can use arbitrary translations as with a formula. ax : Matplotlib AxesSubplot instance, optional If given, it is used to plot in instead of a new figure being created. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid. Notes ----- The CCPR plot provides a way to judge the effect of one regressor on the response variable by taking into account the effects of the other independent variables. The partial residuals plot is defined as Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus X_i to show where the fitted line would lie. Care should be taken if X_i is highly correlated with any of the other independent variables. If this is the case, the variance evident in the plot will be an underestimate of the true variance. References ---------- http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm NrRr) add_constant)r0z*Component and component plus residual plotzResidual + %s*beta_%dz%s)r r;r<rrr>r|r.rWstatsmodels.tools.toolsrrrjrrrCrErD) r&rGr0rIrJrLZx1betarmodr|r'r'r(rs*  c Cst|}t||j\}}|dk r.|\}}n4t|dkrVttt|d}d}n t|}d}d}xdt|D]X\}} |jj dd| f dkrd}qp| |||d|} t || | d}| dqpW|jdd d ||jd d |S) aGenerate CCPR plots against a set of regressors, plot in a grid. Generates a grid of CCPR (component and component-plus-residual) plots. Parameters ---------- results : result instance uses exog and params of the result instance exog_idx : None or list of int (column) indices of the exog used in the plot grid : None or tuple of int (nrows, ncols) If grid is given, then it is used for the arrangement of the subplots. If grid is None, then ncol is one, if there are only 2 subplots, and the number of columns is two otherwise. fig : Matplotlib figure instance, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Notes ----- Partial residual plots are formed as:: Res + Betahat(i)*Xi versus Xi and CCPR adds:: Betahat(i)*Xi versus Xi See Also -------- plot_ccpr : Creates CCPR plot for a single regressor. References ---------- See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm NrQg@rr)rGr0rz&Component-Component Plus Residual PlotrT)rUgffffff?)r^)r r_r<rr~rr?rrr>varr`rrCrfrgrh) r&rGrrIrJrrZ seen_constantrrr0r'r'r(r,s*+    c  sB|dk r|}nd}t|\}}|rl|j\|dkr|jjdddf|jjdddfg}n(dk r|dk std|dkr|}|d|dg} | |ddl m } Gfddd| || f|} | | |j d| j| _|j d | j| _|r.|||r>|||S) a Plots a line given an intercept and slope. intercept : float The intercept of the line slope : float The slope of the line horiz : float or array-like Data for horizontal lines on the y-axis vert : array-like Data for verterical lines on the x-axis model_results : statsmodels results instance Any object that has a two-value `params` attribute. Assumed that it is (intercept, slope) ax : axes, optional Matplotlib axes instance kwargs Options passed to matplotlib.pyplot.plt Returns ------- fig : Figure The figure given by `ax.figure` or a new instance. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> np.random.seed(12345) >>> X = sm.add_constant(np.random.normal(0, 20, size=30)) >>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) >>> mod = sm.OLS(y,X).fit() >>> fig = sm.graphics.abline_plot(model_results=mod) >>> ax = fig.axes[0] >>> ax.scatter(X[:,1], y) >>> ax.margins(.1) >>> import matplotlib.pyplot as plt >>> plt.show() Nrz-specify slope and intercepty or model_resultsr)Line2Dcs:eZdZfddZfddZfddZZS)zabline_plot..ABLine2Dcs"t|j||d|_d|_dS)N)super__init__id_xlim_callbackid_ylim_callback)selfargsrH)ABLine2D __class__r'r(rsz&abline_plot..ABLine2D.__init__cs@|j}|jr|j|j|jr.|j|jt|dS)N)Zaxesr callbacksZ disconnectrrremove)rr0)rrr'r(rs z$abline_plot..ABLine2D.removecsp|d|}fdd|D}|d}|}|d|dg}||||jjdS)NFcsg|]}|kr|qSr'r').0Zchild)rr'r( sz@abline_plot..ABLine2D.update_datalim..rr)Zset_autoscale_onZ get_childrenget_xlimset_datar/ZcanvasZdraw)rr0ZchildrenZablinesZablinernrK) interceptslope)rr(update_datalims   z,abline_plot..ABLine2D.update_datalim)__name__ __module__ __qualname__rrr __classcell__r')rrr)rr(rsrZ xlim_changedZ ylim_changed)rr r;r|rr>minmaxrZset_xlimZmatplotlib.linesrZadd_linerZconnectrrrZhlineZvline) rrZhorizZvertZ model_resultsr0rHrnrIZdata_yrliner')rrrr(rws4)        皙?cooks0?c Kst|\}}|} |dr0| jd} n,|drPt| jd} n t d|t | } |dd} | | | | d} | j } |r| j }n| j}ddlm}|jd|d|j}t||k}| t|k}t||}|j| || |d |jjj}|d krtt|}tt|d|t| |t| dd  | dd d |}d dd}|jd||j d||j!d||S)ad Plot of influence in regression. Plots studentized resids vs. leverage. Parameters ---------- results : results instance A fitted model. external : bool Whether to use externally or internally studentized residuals. It is recommended to leave external as True. alpha : float The alpha value to identify large studentized residuals. Large means abs(resid_studentized) > t.ppf(1-alpha/2, dof=results.df_resid) criterion : str {'DFFITS', 'Cooks'} Which criterion to base the size of the points on. Options are DFFITS or Cook's D. size : float The range of `criterion` is mapped to 10**2 - size**2 in points. plot_alpha : float The `alpha` of the plotted points. ax : matplotlib Axes instance An instance of a matplotlib Axes. Returns ------- fig : matplotlib figure The matplotlib figure that contains the Axes. Notes ----- Row labels for the observations in which the leverage, measured by the diagonal of the hat matrix, is high or the residuals are large, as the combination of large residuals and a high influence value indicates an influence point. The value of large residuals can be controlled using the `alpha` parameter. Large leverage points are identified as hat_i > 2 * (df_model + 1)/nobs. ZcoorZdffzCriterion %s not understoodrQ@)statsg?)sr8Ng?zx-largerV)rUr5Studentized Residuals H LeverageInfluence Plot)r)r)r)"r r; get_influencelower startswithZcooks_distancer?absZdffitsrZptprhat_matrix_diagZresid_studentized_externalZresid_studentized_internalZscipyrtppfZdf_residr) logical_orZscatterrrdrerr~rwhererrErDrC)r&Zexternalr8Z criterionrxZ plot_alphar0rHrIinflZpsizeZ old_rangeZ new_rangeleverageZresidsrcutoff large_residlarge_leverageZ large_pointslabelsZfontr'r'r(rs@'              c Ks ddlm}m}t|\}}|}|j}||j} |j| d|df|| d| d| d|t |k} | d|d} t| | k} |jjj} | d krtt|j} tt| | d}tj|| t| d|d gt|jd |d d d}|dd|S)a Plots leverage statistics vs. normalized residuals squared Parameters ---------- results : results instance A regression results instance alpha : float Specifies the cut-off for large-standardized residuals. Residuals are assumed to be distributed N(0, 1) with alpha=alpha. ax : Axes instance Matplotlib Axes instance Returns ------- fig : matplotlib Figure A matplotlib figure instance. r)zscorenormrQrRzNormalized residuals**2ZLeveragez)Leverage vs. Normalized residuals squaredg?N)rrtrTrprq)r0rrrsg333333?)Z scipy.statsrrr r;rrrWr.rDrErCr)rr?rrrdrerrr%rrrrZmargins)r&r8r0rHrrrIrrrWrrrrr[r'r'r(r8s*        c Cs|j}t|\}}t|||||d\}} |j| |ddd|jdddt|tkr\|} n |j|} |j | dd |j |j d dd |S) N) resid_typeuse_glm_weights fit_kwargsrRg333333?)r8zAdded variable plotrT)rU)rxz residuals) rr r;rr.rCtypestrrrDrEr@) r& focus_exogrrrr0rrI endog_residfocus_exog_residxnamer'r'r(r"es   Zextra_params_docz6results: object Results for a fitted regression modelc Cs|j}t||\}}t||}|jjdd|f}t|\}}|j||ddd|jdddt|t krt|}n |j |}|j |dd|j d dd|S) NrRg333333?)r8zPartial residuals plotrT)rUr)rxzComponent plus residual) rr r<r r>r;r.rCrrrrDrE) r&rr0r focus_colZprfocus_exog_valsrIrr'r'r(r#s   Q?c Cs|j}t||\}}t||||d}|jdd|f}t|\} }|j||ddd|jddd|j|dd |j d dd | S) N)r+ cond_meansrRg333333?)r8zCERES residuals plotrT)rUr)rxzComponent plus residual) rr r<r!r>r;r.rCrDrE) r&rr+rr0rrpresidrrIr'r'r(r$scCs|j}t|tttfs&td|jjt ||\}}t t |j }t |}||t |}|dkr,|jdd|f}||d8}tj|d\} } } t| dk} | dd| f}|jdd|f} tt | |jdf}xFt |jdD]4}|dd|f}t|| |dd}||dd|f<qWtj|jdd|f|fdd}|j}|}||j|f|}|}|j|j}t|ttfr||jj|j9}|jd|kr|t |dd|df|j |d7}|S) a Calculate the CERES residuals (Conditional Expectation Partial Residuals) for a fitted model. Parameters ---------- results : model results instance The fitted model for which the CERES residuals are calculated. focus_exog : int The column of results.model.exog used as the 'focus variable'. frac : float, optional Lowess smoothing parameter for estimating the conditional means. Not used if `cond_means` is provided. cond_means : array-like, optional If provided, the columns of this array are the conditional means E[exog | focus exog], where exog ranges over some or all of the columns of exog other than focus exog. If this is an empty nx0 array, the conditional means are treated as being zero. If None, the conditional means are estimated. Returns ------- An array containing the CERES residuals. Notes ----- If `cond_means` is not provided, it is obtained by smoothing each column of exog (except the focus column) against the focus column. Currently only supports GLM, GEE, and OLS models. z$ceres residuals not available for %sNrgư>rF)r+Z return_sorted)Zaxis)!rrur r rrrrr r<rr~r|rvrr>Zmeanr?ZlinalgZsvdZ flatnonzeror{rarZ concatenate_get_init_kwdsr=rjrAfamilylinkderivdot)r&rr+rrrZix_nfZnnfZpexogurZvtiiZfcoljr1ZcfZnew_exogklassZ init_kwargs new_model new_resultrr'r'r(r!s@"     *cCs|j}|j|}t|ttfr8||jj|j 9}n"t|t t t frJnt dt|t|tkrt|j|}n|}|j||jdd|f}||S)a: Returns partial residuals for a fitted model with respect to a 'focus predictor'. Parameters ---------- results : results instance A fitted regression model. focus col : int The column index of model.exog with respect to which the partial residuals are calculated. Returns ------- An array of partial residuals. References ---------- RD Cook and R Croos-Dabrera (1998). Partial residual plots in generalized linear models. Journal of the American Statistical Association, 93:442. z+Partial residuals for '%s' not implemented.N)rr=Zpredictrur r rrrrArrr rrrrr[r|r>)r&rrrWrZ focus_valr'r'r(r s  cCs|j}t|tttfs&td|jj|j}|j }t ||\}}|dd|f} |dkrrt|ttfrnd}nd}t |j d} t| } | ||dd| f} |j| } |j} |}| || f|}d| i}|dk r|||jf|}|jstdyt||}Wn"tk r,td|YnXd dlmm}t|ttfr|r|j|j}t|d rz||j}|| | |}n|| | }|j }||fS) aY Residualize the endog variable and a 'focus' exog variable in a regression model with respect to the other exog variables. Parameters ---------- results : regression results instance A fitted model including the focus exog and all other predictors of interest. focus_exog : integer or string The column of results.model.exog or a variable name that is to be residualized against the other predictors. resid_type : string The type of residuals to use for the dependent variable. If None, uses `resid_deviance` for GLM/GEE and `resid` otherwise. use_glm_weights : bool Only used if the model is a GLM or GEE. If True, the residuals for the focus predictor are computed using WLS, with the weights obtained from the IRLS calculations for fitting the GLM. If False, unweighted regression is used. fit_kwargs : dict, optional Keyword arguments to be passed to fit when refitting the model. Returns ------- endog_resid : array-like The residuals for the original exog focus_exog_resid : array-like The residuals for the focus predictor Notes ----- The 'focus variable' residuals are always obtained using linear regression. Currently only GLM, GEE, and OLS models are supported. z8model type %s not supported for added variable residualsNZresid_deviancerWr start_paramsz>fit did not converge when calculating added variable residualsz '%s' residual type not availabler data_weights)!rrur r rrrrr>r=r r<rrarvrr|rrrjZ convergedgetattrAttributeError#statsmodels.regression.linear_modelZ regressionZ linear_modelrweightsrAr}rr rW)r&rrrrrr>r=rrrZ reduced_exogrrrHrrrrZlmrZ lm_resultsrr'r'r(rAsN)       )rr*)NN)N)NNN)N)NNN)NNNNNN)TrrrrN)rN)NTNN)N)rNN)rN)NTN)5__doc__Zstatsmodels.compat.pythonrrrrZnumpyr?rcryZpatsyrrrrr Z+statsmodels.genmod.generalized_linear_modelr Z3statsmodels.genmod.generalized_estimating_equationsr Z&statsmodels.sandbox.regression.predstdr Zstatsmodels.graphicsr Z*statsmodels.nonparametric.smoothers_lowessrrrZstatsmodels.baserZ_regressionplots_docrrr__all__r)rrrrlrrrrrrrr"r#r$r!r rr'r'r'r( sf          Z L U ? K e Z -       Y0