M/Ph dZddlZddlZddlZddlmZddlm Z ddl m Z dZ GddZ Gd d Zd Zd ZGd dZGddeZdS)a# Overview -------- This module implements the Multiple Imputation through Chained Equations (MICE) approach to handling missing data in statistical data analyses. The approach has the following steps: 0. Impute each missing value with the mean of the observed values of the same variable. 1. For each variable in the data set with missing values (termed the 'focus variable'), do the following: 1a. Fit an 'imputation model', which is a regression model for the focus variable, regressed on the observed and (current) imputed values of some or all of the other variables. 1b. Impute the missing values for the focus variable. Currently this imputation must use the 'predictive mean matching' (pmm) procedure. 2. Once all variables have been imputed, fit the 'analysis model' to the data set. 3. Repeat steps 1-2 multiple times and combine the results using a 'combining rule' to produce point estimates of all parameters in the analysis model and standard errors for them. The imputations for each variable are based on an imputation model that is specified via a model class and a formula for the regression relationship. The default model is OLS, with a formula specifying main effects for all other variables. The MICE procedure can be used in one of two ways: * If the goal is only to produce imputed data sets, the MICEData class can be used to wrap a data frame, providing facilities for doing the imputation. Summary plots are available for assessing the performance of the imputation. * If the imputed data sets are to be used to fit an additional 'analysis model', a MICE instance can be used. After specifying the MICE instance and running it, the results are combined using the `combine` method. Results and various summary plots are then available. Terminology ----------- The primary goal of the analysis is usually to fit and perform inference using an 'analysis model'. If an analysis model is not specified, then imputed datasets are produced for later use. The MICE procedure involves a family of imputation models. There is one imputation model for each variable with missing values. An imputation model may be conditioned on all or a subset of the remaining variables, using main effects, transformations, interactions, etc. as desired. A 'perturbation method' is a method for setting the parameter estimate in an imputation model. The 'gaussian' perturbation method first fits the model (usually using maximum likelihood, but it could use any statsmodels fit procedure), then sets the parameter vector equal to a draw from the Gaussian approximation to the sampling distribution for the fit. The 'bootstrap' perturbation method sets the parameter vector equal to a fitted parameter vector obtained when fitting the conditional model to a bootstrapped version of the data set. Class structure --------------- There are two main classes in the module: * 'MICEData' wraps a Pandas dataframe, incorporating information about the imputation model for each variable with missing values. It can be used to produce multiply imputed data sets that are to be further processed or distributed to other researchers. A number of plotting procedures are provided to visualize the imputation results and missing data patterns. The `history_func` hook allows any features of interest of the imputed data sets to be saved for further analysis. * 'MICE' takes both a 'MICEData' object and an analysis model specification. It runs the multiple imputation, fits the analysis models, and combines the results to produce a `MICEResults` object. The summary method of this results object can be used to see the key estimands and inferential quantities. Notes ----- By default, to conserve memory 'MICEData' saves very little information from one iteration to the next. The data set passed by the user is copied on entry, but then is over-written each time new imputations are produced. If using 'MICE', the fitted analysis models and results are saved. MICEData includes a `history_callback` hook that allows arbitrary information from the intermediate datasets to be saved for future use. References ---------- JL Schafer: 'Multiple Imputation: A Primer', Stat Methods Med Res, 1999. TE Raghunathan et al.: 'A Multivariate Technique for Multiply Imputing Missing Values Using a Sequence of Regression Models', Survey Methodology, 2001. SAS Institute: 'Predictive Mean Matching Method for Monotone Missing Data', SAS 9.2 User's Guide, 2014. A Gelman et al.: 'Multiple Imputation with Diagnostics (mi) in R: Opening Windows into the Black Box', Journal of Statistical Software, 2009. N)LikelihoodModelResults)OLS) defaultdictz >>> imp = mice.MICEData(data) >>> imp.set_imputer('x1', formula='x2 + np.square(x2) + x3') >>> for j in range(20): ... imp.update_all() ... imp.data.to_csv('data%02d.csv' % j)ceZdZdZdZdS) PatsyFormulazM A simple wrapper for a string to be interpreted as a Patsy formula. cd|z|_dS)Nz0 + )formula)selfr s [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/imputation/mice.py__init__zPatsyFormula.__init__s' N)__name__ __module__ __qualname____doc__r r r rrs-(((((r rceZdZdeZ d!dZdZdZd Z d"d Z d Z d#dZ dZ dZdZ d$dZ d%dZ d%dZ d&dZdZdZdZdZdZdZdZd ZdS)'MICEDataa Wrap a data set to allow missing data handling with MICE. Parameters ---------- data : Pandas data frame The data set, which is copied internally. perturbation_method : str The default perturbation method k_pmm : int The number of nearest neighbors to use during predictive mean matching. Can also be specified in `fit`. history_callback : function A function that is called after each complete imputation cycle. The return value is appended to `history`. The MICEData object is passed as the sole argument to `history_callback`. Notes ----- Allowed perturbation methods are 'gaussian' (the model parameters are set to a draw from the Gaussian approximation to the posterior distribution), and 'boot' (the model parameters are set to the estimated values obtained when fitting a bootstrapped version of the data set). `history_callback` can be implemented to have side effects such as saving the current imputed data set to disk. Examples -------- Draw 20 imputations from a data set called `data` and save them in separate files with filename pattern `dataXX.csv`. The variables other than `x1` are imputed using linear models fit with OLS, with mean structures containing main effects of all other variables in `data`. The variable named `x1` has a conditional mean structure that includes an additional term for x2^2. {_mice_data_example_1} )_mice_data_example_1gaussianNc |jjtjdkrd}t|t _|dd_|_ g_ i_ tfd_ i_i_jjD]9}j|\}}|j|<|j|<:i_i_i_tt_tt_i_i_|jD]} | t3|j fd D} tj| } tj| } | t9| d kd} fd | D_|_dS) NOz0MICEData data column names should be string typeall)howT)dropcSNr)perturbation_methodsr z#MICEData.__init__..s /Br cDg|]}tj|Sr)lenix_miss).0vr s r z%MICEData.__init__..s'666!T\!_%%666r rc g|] }| Srr)r$ivnamess r r&z%MICEData.__init__..s3331VAY333r ) columnsdtypenp ValueErrordict regularizeddropna reset_indexdatahistory_callbackhistory predict_kwdsrrix_obsr#_split_indicesmodelsresultsconditional_formula init_kwdsfit_kwds model_classparams set_imputerlistasarrayargsortsum _cycle_order_initial_imputationk_pmm) r r2rrFr3msgcolr6r#vnamenmissiir)s ` ` @r r zMICEData.__init__s < # . .DCS// !66KKEK**66D6AA 0 $/0C0C0C0C$D$D   9$ ( (C"11$)C.AAOFG%DK  'DL    $& %T**#D))  \ $ $E   U # # # #dl##6666v666 5!! Z   EQJ  !3333333   """ r c:|d|jS)a Returns the next imputed dataset in the imputation process. Returns ------- data : array_like An imputed dataset from the MICE chain. Notes ----- `MICEData` does not have a `skip` parameter. Consecutive values returned by `next_sample` are immediately consecutive in the imputation chain. The returned value is a reference to the data attribute of the class and should be copied before making any changes. ) update_allr2)r s r next_samplezMICEData.next_samples& yr c@i}|jjD]r}|j||j|z }tj|}|}|j|j|||<s|j|ddS)z Use a PMM-like procedure for initial imputed values. For each variable, missing values are imputed as the observed value that is closest to the mean over all observed values. T)inplaceN)r2r*meanr,absidxminlocfillna)r imp_valuesrHdiixs r rEzMICEData._initial_imputations 9$ 5 5C3$)C."5"5"7"77BBB"in04JsOO T22222r ctj|}tj|}tj|}t |dkrt d||fS)Nrz-variable to be imputed has no observed values)pdisnullr, flatnonzeror"r-)r vecnullr6r#s r r7zMICEData._split_indices!sYy~~&&.&& v;;!  LMM Mwr Fc f|>fd|jjD} dzd| z} | |j<ndz|z} | |j<|t|j<n ||j<| ||j<| ||j<| ||j<| ||j <||_ | |j <dS)a Specify the imputation process for a single variable. Parameters ---------- endog_name : str Name of the variable to be imputed. formula : str Conditional formula for imputation. Defaults to a formula with main effects for all other variables in dataset. The formula should only include an expression for the mean structure, e.g. use 'x1 + x2' not 'x4 ~ x1 + x2'. model_class : statsmodels model Conditional model for imputation. Defaults to OLS. See below for more information. init_kwds : dit-like Keyword arguments passed to the model init method. fit_kwds : dict-like Keyword arguments passed to the model fit method. predict_kwds : dict-like Keyword arguments passed to the model predict method. k_pmm : int Determines number of neighboring observations from which to randomly sample when using predictive mean matching. perturbation_method : str Either 'gaussian' or 'bootstrap'. Determines the method for perturbing parameters in the imputation model. If None, uses the default specified at class initialization. regularized : dict If regularized[name]=True, `fit_regularized` rather than `fit` is called when fitting imputation models for this variable. When regularized[name]=True for any variable, perturbation_method must be set to boot. Notes ----- The model class must meet the following conditions: * A model must have a 'fit' method that returns an object. * The object returned from `fit` must have a `params` attribute that is an array-like object. * The object returned from `fit` must have a cov_params method that returns a square array-like object. * The model must have a `predict` method. Nc g|] }|k| Srr)r$x endog_names r r&z(MICEData.set_imputer..Zs)000! J.r z ~ z + ) r2r*joinr:rr=r;r<r5rrFr/) r rcr r=r;r<r5rFrr/ main_effectsfmls ` r r?zMICEData.set_imputer)s` ?0000ty'8000Lu$uzz,'?'??C36D $Z 0 0u$w.C36D $Z 0  +.D Z ( (+6D Z (  )2DN: &  (0DM* %  #,8D j )  *3FD $Z 0 '2$$$r c|j|}t|dkrBtj||jj||jj|f<dSdS)z Fill in dataset with imputed values. Parameters ---------- col : str Name of variable to be filled in. vals : ndarray Array of imputed values to use for filling-in missing values. rN)r#r"r, atleast_1dr2ilocr*get_loc)r rHvalsrYs r _store_changeszMICEData._store_changesvs\\#  r77Q;;ACtATATDIN2ty088=== > > > ;r rMct|D]!}|jD]}||"|j1||}|j|dSdS)aU Perform a specified number of MICE iterations. Parameters ---------- n_iter : int The number of updates to perform. Only the result of the final update will be available. Notes ----- The imputed values are stored in the class attribute `self.data`. N)rangerDupdater3r4append)r n_iterkrIhvs r rNzMICEData.update_allsv # #A* # # E"""" #  ,&&t,,B L   # # # # # - ,r c*|j|}tj||jd\}}|j|}t j|j|d}t j|j|ddfd}|j|}t j|j|ddfd} i} ||j vr#|j |} | | |} i} ||j vr#|j |} | | |} ||| | | fS)aJ Return endog and exog for imputation of a given variable. Parameters ---------- vname : str The variable for which the split data is returned. Returns ------- endog_obs : DataFrame Observed values of the variable to be imputed. exog_obs : DataFrame Current values of the predictors where the variable to be imputed is observed. exog_miss : DataFrame Current values of the predictors where the variable to be Imputed is missing. init_kwds : dict-like The init keyword arguments for `vname`, processed through Patsy as required. fit_kwds : dict-like The fit keyword arguments for `vname`, processed through Patsy as required. dataframe return_typeW requirementsN) r:patsy dmatricesr2r6r,requirerir#r5 _process_kwds) r rIr endogexogixo endog_obsexog_obsixm exog_misspredict_obs_kwdskwdspredict_miss_kwdss r get_split_datazMICEData.get_split_datas56*51ogty2=??? tk% Juz#SAAA :diQQQ/cBBBl5!Jtyaaa0sCCC  D% % %$U+D#11$<<  D% % %$U+D $ 2 24 = = 8Y0@!# #r c8|}|D]}||}t|trctj|j|jd}tj|d|ddf}|j ddkr |dddf}|||<|S)NrurvrxryrMr) copy isinstancerr{dmatrixr r2r,r}shape)r rrYrrr%mats r r~zMICEData._process_kwdssyy{{  AQA!\** mAIty0;===j3777AAA>9Q<1$$aaad)CQ r c|j|}|j|}tj||jd\}}t j|j|dfd}t j|j|ddfd}||j ||}||j ||}||||fS)a Return the data needed to fit a model for imputation. The data is used to impute variable `vname`, and therefore only includes cases for which `vname` is observed. Values of type `PatsyFormula` in `init_kwds` or `fit_kwds` are processed through Patsy and subset to align with the model's endog and exog. Parameters ---------- vname : str The variable for which the fitting data is returned. Returns ------- endog : DataFrame Observed values of `vname`. exog : DataFrame Regression design matrix for imputing `vname`. init_kwds : dict-like The init keyword arguments for `vname`, processed through Patsy as required. fit_kwds : dict-like The fit keyword arguments for `vname`, processed through Patsy as required. rurvrrxryN) r6r:r{r|r2r,r}rir~r;r<)r rIrYr rrr;r<s r get_fitting_datazMICEData.get_fitting_datas>[ *51ogty2=??? t 5:b!e,3???z$)BE*===&&t~e'.?s$$$AQ$$$r z) is not an allowed value for `row_order`.c g|] }| Srrrs r r&z1MICEData.plot_missing_pattern..Vs(((DG(((r utils)LinearSegmentedColormapT)return_inverseautonearest gist_ncar_r)aspect interpolationcmap_whitedarkgreyCasesZ)rotation) r,zerosr2rr* enumerater#rBrRcovTlinalgsvdaranger"r-dotr]anystatsmodels.graphicsrmatplotlib.colorsr create_mpl_ax get_figureuniqueimshow from_list set_ylabel set_xticksrnset_xticklabels)r ax row_order column_orderhide_complete_rowshide_complete_columnscolor_row_patternsmissjrHrYcvusvtrbrkygutilsrfigrrcolrrs @r plot_missing_patternzMICEData.plot_missing_pattern s@x ((y oo  FAsc"BDQKK < ' 'DIIaLL))BB Y & &By}}R++HAq"Bqqq!tH%%BB U " "3t99%%BBMMOO OAAArE{$$$$$$$  $ $DIIaLL))BB ) # #29TZ]+++A&q//CCBB %  4:a=))BBGGII IBE{   2 233BAAA;D  ) 2 233B2;D((((R(((D888888====== :**2..GC--//C  !29TZ]+++A&q//CiD999GAt AQQQW % %D IId6(  * * * *+44S6=z5JLLD IId6  ! ! ! g eCII&&''' 4"--- r (c ddlm}ddlm} |i}|||\} }n|} |gd|j|} |j|} |j|} |j|}tj | | }tj | |}tj | | }tj | |}tj |j |d}tj |j |d}|tj |r||f}||dtjt!|zz }||d tjt!|zz }gd }d d d }||||d}ddddd}|rZ|D]W}||}||ddz||d z}|||||d|||dX|D]}||}t!||kr||vr ||}ni}||}| ||||fi|}|r6||dddf|ddd fd||dd||ddz||d z}||dddf|ddd fd||dd||\}}|rdnd}| ||dd |} | d ||||| S)!a Plot observed and imputed values for two variables. Displays a scatterplot of one variable against another. The points are colored according to whether the values are observed or imputed. Parameters ---------- col1_name : str The variable to be plotted on the horizontal axis. col2_name : str The variable to be plotted on the vertical axis. lowess_args : dictionary A dictionary of dictionaries, keys are 'ii', 'io', 'oi' and 'oo', where 'o' denotes 'observed' and 'i' denotes imputed. See Notes for details. lowess_min_n : int Minimum sample size to plot a lowess fit jitter : float or tuple Standard deviation for jittering points in the plot. Either a single scalar applied to both axes, or a tuple containing x-axis jitter and y-axis jitter, respectively. plot_points : bool If True, the data points are plotted. ax : AxesSubplot Axes on which to plot, created if not provided. Returns ------- The matplotlib figure on which the plot id drawn. rrlowessN皙?rgffffff?g?rxrysizerM)ooiooirKimpobs)r(o)rKrrrgreyredorangelime)rrKrr/r333333?colorlabelalpha-)rrlwrrrrg-C6?g? center right)rU numpoints handletextpadF)rr*statsmodels.nonparametric.smoothers_lowessrrr set_positionr#r6r, intersect1dr}r2isscalarrandomnormalr"plotget_legend_handles_labelslegend draw_frame set_xlabelr)!r col1_name col2_name lowess_args lowess_min_njitter plot_pointsrrrrix1iix1oix2iix2oix_iiix_ioix_oiix_oovec1vec2keyslakixsrkyrYlablalfithapadlegs! r plot_bivariatezMICEData.plot_bivariatessH 988888EEEEEE  K :**2..GC--//C ,,,---|I&{9%|I&{9%tT**tT**tT**tT**z$)I.SAAAz$)I.SAAA  {6"" * &) F1I 0 0c$ii 0 @ @@ @D F1I 0 0c$ii 0 @ @@ @D(''&&%uEBBU(  . . .W"Q%j3&RU3R$r(CuRy!.... 4 4BRB2ww%%[   _RB6$r(DH3333D 4QQQT DAJ59!a))))"Q%j3&RU3QQQT DAJ59!as4444--//B#,ffjjR^q'*,, u i    i    r c ddlm}ddlm}|i}|||\} }n|} |gd|j|} |j|} tj |j |d} |j |} tj| |j d \}}|j|}|| }||}|tj|r||f}| |dtjt+|  zz } ||d tjt+| zz }d dg}| | d}ddd}ddd}|r@|D]=}||}|| |||d ||||d>|D]}||}t+||kr||vr ||}ni}||}|||| |fi|}||dddf|ddd fd||dd|||\}}| ||dd }|d||dz||dz| S)a Plot fitted versus imputed or observed values as a scatterplot. Parameters ---------- col_name : str The variable to be plotted on the horizontal axis. lowess_args : dict-like Keyword arguments passed to lowess fit. A dictionary of dictionaries, keys are 'o' and 'i' denoting 'observed' and 'imputed', respectively. lowess_min_n : int Minimum sample size to plot a lowess fit jitter : float or tuple Standard deviation for jittering points in the plot. Either a single scalar applied to both axes, or a tuple containing x-axis jitter and y-axis jitter, respectively. plot_points : bool If True, the data points are plotted. ax : AxesSubplot Axes on which to plot, created if not provided. Returns ------- The matplotlib figure on which the plot is drawn. rrrNrrxryrurv)rrrMrr()rr(rrrrrrrrrrrUrFz observed or imputedz fitted)rrrrrrrr#r6r,r}r2r:r{r|r9predict_get_predictedrrrr"rrrrrr)r col_namerrrrrrrrixirrr rrr9rr r r rr rYrrrrs r plot_fit_obszMICEData.plot_fit_obssO< 988888EEEEEE  K :**2..GC--//C ,,,---l8$k(#z$)H-C@@@*84ogty2=??? t,x(D))""4((  {6"" * &) F1I 0 0c$ii 0 @ @@ @D F1I 0 0c$ii 0 @ @@ @DSzc""&&V,,  2 2 2WR$r(CuRy!"gS2222 4 4BRB2ww%%[   _RB6$r(DH3333D GGDAJQQQT CuRy!3r7  4 4 4 4--//BjjR^qjAA u h!77888 h*+++ r cddlm}|i}|i}|i}|||\}}n|}|gd|j|}|j|} |j|j|} |j|j| } |||fD] } d| vrd| d< gg}} t| dkrV|j tj | fi|}| |dd| d|j tj | fi|}|j tj |j|fi|}| |dd|ddg|d d g|| |d d }|d|||d|S)aO Display imputed values for one variable as a histogram. Parameters ---------- col_name : str The name of the variable to be plotted. ax : AxesSubplot An axes on which to draw the histograms. If not provided, one is created. imp_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for imputed values. obs_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for observed values. all_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for all values. Returns ------- The matplotlib figure on which the histograms were drawn rrNrhisttypestepImpObsAllrrMrF Frequency)rrrrrr#r6r2rir"histr,rArpextendrrrr)r rr imp_hist_args obs_hist_args all_hist_argsrrrrrrrXrrhh1h2rs r plot_imputed_histzMICEData.plot_imputed_histBs'6 988888  M  M  M :**2..GC--//C ,,,---l8$k(#i!&s+i!&s+ = ( (B##!':RB s88a<< 399=99A IIaeAh    IIe    RWRZ__ 6 6 6 6 RWRZ ( 344 F F F F 2b6!9bfQi())) 5%.!!!jjR^qjAA u h k""" r c.|D]}||}t|tjs%|jdkr)|jdt |kr ||||<|jdkr-|jdt |kr||ddf||<|S)NrMrr)rr,ndarrayndimrr")r rrixrrr%s r _boot_kwdszMICEData._boot_kwdss $ $AQAa,, ! !'!*C"8"8C&Q! !'!*C"8"8CF)Q r c:||\}}}}t|}tjd||}||}||ddf}|||}|||}|j|}|||fi||j|<||jvr.|j|r!|j|j di||j |<n |j|j di||j |<|j |j |j |<dS)zD Perturbs the model's parameters using a bootstrap. rNr) rr"r,rrandintr0r=r8r/fit_regularizedr9fitr>) r rIrrr;r<mr/klasss r _perturb_bootstrapzMICEData._perturb_bootstraps< ,0+@+@+G+G(tY JJi1a((c CF|OOIs33 ??8S11 '"U5$<<)<< E D$ $ $)9%)@ $2 E"2>>X>> L  #9$+e"4"8"D"D8"D"DDL !\%07 Er cl||\}}}}|j|}|||fi||j|<|j|jdi||j|<|j|}|j|j}tj |||j|<dS)z Gaussian perturbation of model parameters. The normal approximation to the sampling distribution of the parameter estimates is used to define the mean and covariance structure of the perturbation distribution. )rRrNr) rr=r8r4r9 cov_paramsr>r,rmultivariate_normal) r rIrrr;r<r6rmus r _perturb_gaussianzMICEData._perturb_gaussians,0+@+@+G+G(tY '"U5$<<)<< E4dk%04@@x@@ Ul5!,,.. \% 'Y:::LL Er c|j|dkr||dS|j|dkr||dStd)Nrbootzunknown perturbation method)rr<r7r-r rIs r perturb_paramszMICEData.perturb_paramssk  #E *j 8 8  " "5 ) ) ) ) )  %e , 6 6  # #E * * * * *:;; ;r c0||dSr) impute_pmmr?s r imputezMICEData.imputes r cZ||||dS)a. Impute missing values for a single variable. This is a two-step process in which first the parameters are perturbed, then the missing values are re-imputed. Parameters ---------- vname : str The name of the variable to be updated. N)r@rCr?s r rozMICEData.updates0 E""" Er ct|tjr|St|tjr|jSt |dr|jStd|j z)Npredicted_valuesz&cannot obtain predicted values from %s) rr,r-r[SeriesvalueshasattrrFr- __class__)r objs r rzMICEData._get_predictedsu c2: & & JJ RY ' ' J:  S, - - J' '83=HJJ Jr c|j}||\}}}}}|j|}|j|j||fi|} |j|j||fi|} || } || } t j| } || }| | } t j| | } | dddft j | |dddfz} t j | dk| t|dz kz}t j | dt|dz } | dddf| | z }t j |}t j||<t j|dddd|f}t jd|t| }t j |jd}|||f} | || f}t j||}|||dS)z Use predictive mean matching to impute missing values. Notes ----- The `perturb_params` method must be called first to define the model. NrrM)rFrr8rr>rr,rB searchsortedrnonzeror"cliprSinfrr2rarraysqueezerl)r rIrFrrrrrmodel pendog_obs pendog_missrKrYrmskdxdxiirjjiz imputed_misss r rBzMICEData.impute_pmmsU     & & L 8Y(8:K  E""U]4;u#5x77%577 #emDK$6 99&799 ((44 ))+66 Z # #bM ^ _Z 5 5DkBIufe44T111W==j#'cC NNQ,>&>?@@gc1c)nnq011D !JsO 3 VBZZ&3jQ1U7 +Y  q%[)9)9 : :Ysy| $ $ "b] "b]x " ..6688  E<00000r )rrN)NNNNNrNF)rM)NrrFFT)NrNTN)NNNN)rrrformatrrr rOrEr7r?rlrNrr~rrrrr+r0r7r<r@rCrorrBrr r rrs &L $899M P2<,0@@@@D,333"AE@DDIK3K3K3K3ZUUU $$$$.3#3#3#j   +0+0+0Z7@*3053804 eeeeP799=mmmm^26-1*.^^^^@BF<@EEEER&8884MMM&<<< " J J J=1=1=1=1=1r rz >>> imp = mice.MICEData(data) >>> fml = 'y ~ x1 + x2 + x3 + x4' >>> mice = mice.MICE(fml, sm.OLS, imp) >>> results = mice.fit(10, 10) >>> print(results.summary()) .. literalinclude:: ../plots/mice_example_1.txt z >>> imp = mice.MICEData(data) >>> fml = 'y ~ x1 + x2 + x3 + x4' >>> mice = mice.MICE(fml, sm.OLS, imp) >>> results = [] >>> for k in range(10): >>> x = mice.next_sample() >>> results.append(x) c\eZdZdeeZ d dZdZd dZ d Z dS) MICEa Multiple Imputation with Chained Equations. This class can be used to fit most statsmodels models to data sets with missing values using the 'multiple imputation with chained equations' (MICE) approach.. Parameters ---------- model_formula : str The model formula to be fit to the imputed data sets. This formula is for the 'analysis model'. model_class : statsmodels model The model to be fit to the imputed data sets. This model class if for the 'analysis model'. data : MICEData instance MICEData object containing the data set for which missing values will be imputed n_skip : int The number of imputed datasets to skip between consecutive imputed datasets that are used for analysis. init_kwds : dict-like Dictionary of keyword arguments passed to the init method of the analysis model. fit_kwds : dict-like Dictionary of keyword arguments passed to the fit method of the analysis model. Examples -------- Run all MICE steps and obtain results: {mice_example_1} Obtain a sequence of fitted analysis models without combining to obtain summary:: {mice_example_2} )mice_example_1mice_example_2Ncx||_||_||_||_g|_||ni|_||ni|_dSr) model_formular=n_skipr2 results_listr;r<)r rdr=r2rer;r<s r r z MICE.__init__tsN+&  &/&;$,$8b r cN|j|jdzd}t|jdkr|jdj}|jj|j|jjfi|j }|j d|i|j di|j }|S)a` Perform one complete MICE iteration. A single MICE iteration updates all missing values using their respective imputation models, then fits the analysis model to the imputed data. Returns ------- params : array_like The model parameters for the analysis model. Notes ----- This function fits the analysis model and returns its parameter estimate. The parameter vector is not stored by the class and is not used in any subsequent calls to `combine`. Use `fit` to run all MICE steps together and obtain summary results. The complete cycle of missing value imputation followed by fitting the analysis model is repeated `n_skip + 1` times and the analysis model parameters from the final fit are returned. rMNrr start_paramsr) r2rNrer"rfr>r= from_formulardr;r<ror4)r rhrSresults r rOzMICE.next_samples6 T[1_--- t ! !A % %,R07L. -d.@.2in@@04@@ nl;<<<++T]++ r c"|j|t|D]0}|}|j|1|jj|_|jj|_| S)z Fit a model using MICE. Parameters ---------- n_burnin : int The number of burn-in cycles to skip. n_imputations : int The number of data sets to impute ) r2rNrnrOrfrprS endog_names exog_namescombine)r n_burnin n_imputationsrrjs r r4zMICE.fits X&&&}%% - -A%%''F   $ $V , , , ,!<3 ,1||~~r cg}d}g}|jD]T}|j}||j||z }||jUt j|}t j|}|d}|t|jz}t j |j }ddtt|jz z}|||zz} |t j |zt j | z } t j|} t||| | z }| |_| |_|j|_|j|_|j|_|S)a Pools MICE imputation results. This method can only be used after the `run` method has been called. Returns estimates and standard errors of the analysis model parameters. Returns a MICEResults instance. grrM)rf_resultsrpr>r9scaler,rArRr"rrfloatdiag MICEResultsfrac_miss_infornrmr=) r params_list cov_within scale_listr9 results_uwr> cov_betweenfr9fmirts r roz MICE.combines   ( - -G )J   z0 1 1 1 *//11 1J   gm , , , ,j-- Z ++ !!!$$ c$+,,, f[]++  E#d/00111 1!k/1 "'+&&&)<)<< ##dFJ,>?? !$!_".".r )rbNN)rkrk) rrrr]_mice_example_1_mice_example_2rr rOr4rorr r r_r_Ks$H o)  + +I NAB*. A A A A'''R011111r r_c&eZdZfdZddZxZS)rwcNt|||dSr)superr )r rSr>normalized_cov_paramsrJs r r zMICEResults.__init__s5 *? A A A A Ar N皙?cddlm}|}d}i}d|d<|jj|d<|j|d<d|jjjjdz|d <d |j z|d <dt|jj z|d <| |d || ||}|j|d<|||||||S)a Summarize the results of running MICE. Parameters ---------- title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float Significance level for the confidence intervals Returns ------- smry : Summary instance This holds the summary tables and text, which can be printed or converted to various output formats. r)summary2z%8.3fr_zMethod:zModel:zDependent variable:z%dz Sample size:z%.2fScalezNum. imputationsl)align float_format)rFMI)r)titler9)statsmodels.iolibrSummaryr=rrmrSr2rrtr"rfadd_dictsummary_paramsrxadd_df add_title)r rrrsmryrinfoparams r summaryzMICEResults.summarys& /.....!!  Y)2X&*&6 "##djo&:&@&CC^+W #'#dj.E*F*F#F   d#L AAA''E'::*e  E 555 UD111 r )Nr)rrrr r __classcell__)rJs@r rwrwsQAAAAA ((((((((r rw)rpandasr[numpyr,r{statsmodels.base.modelr#statsmodels.regression.linear_modelr collectionsrrrrrrr_rwrr r rs@ssj 999999333333######3((((((((e1e1e1e1e1e1e1e1PggggggggT/////(/////r