M/Ph dZgdZddlmZddlZddlZddlmZm Z ddl m Z m Z ddl mZmZmZmZddlmZdd lmZdd lmZddlmcmZddlmcmZdd lmZddl mcm!Z"dd l#m$Z%dd l&m'Z'ddl(m)cm*Z+ddl,m-Z.m/Z/ddl0m1Z1ddl2m3Z3ddl4m5Z5m6Z6m7Z7 ddl8Z8dZ9n #e:$rdZ9YnwxYwej;e<j=Z>ej?ej;ej@jAdz ZBdZCdZDdZEdZFdZGdZHdZIdZJGddejKZLGdd eLZMGd!d"eMZNGd#d$eLZOGd%d&eOZPGd'd(eOZQGd)d*eMZRGd+d,eMZSGd-d.eNZTGd/d0eOZUGd1d2eOZVGd3d4ejWZXGd5d6eXZYGd7d8eYZZGd9d:eZZ[Gd;deXZ]Gd?d@eYZ^GdAdBe]e^Z_GdCdDe]eZZ`GdEdFe]e\ZaGdGdHeXZbGdIdJeXZcGdKdLecZdGdMdNecZeGdOdPecZfGdQdReXZgGdSdTegZhGdUdVe+jiZjejkejebGdWdXe+jiZlejkeleYGdYdZe+jiZmejkemeZGd[d\e+jiZnejkene[Gd]d^e+jiZoejkeoe\Gd_d`e+jiZpejkepe^Gdadbe+jiZqGdcdde+jiZrejkere_Gdedfe+jiZsejkese`Gdgdhe+jiZtejketeaGdidje+jiZuejkeuecGdkdle+jiZvejkevefGdmdne+jiZwejkewegGdodpe+jiZxejkexehdS)qa Limited dependent variable and qualitative variables. Includes binary outcomes, count data, (ordered) ordinal data and limited dependent variables. General References -------------------- A.C. Cameron and P.K. Trivedi. `Regression Analysis of Count Data`. Cambridge, 1998 G.S. Madalla. `Limited-Dependent and Qualitative Variables in Econometrics`. Cambridge, 1983. W. Greene. `Econometric Analysis`. Prentice Hall, 5th. edition. 2003. )PoissonLogitProbitMNLogitNegativeBinomialGeneralizedPoissonNegativeBinomialP CountModel)AppenderN) MultiIndex get_dummies)specialstats)digammagammalnloggamma polygamma)nbinom) handle_data) fit_l1_slsqpfit_constrained_wrap)_prediction_inference) genpoisson_p)datatools)cache_readonly)approx_fprime_cs)PerfectSeparationErrorPerfectSeparationWarningSpecificationWarningTF? a %(one_line_description)s Parameters ---------- model : A DiscreteModel instance params : array_like The parameters of a fitted model. hessian : array_like The hessian of the fitted model. scale : float A scale parameter for the covariance matrix. Attributes ---------- df_resid : float See model definition. df_model : float See model definition. llf : float Value of the loglikelihood %(extra_attr)sa nnz_params : int The number of nonzero parameters in the model. Train with trim_params == True or else numerical error will distort this. trimmed : bool array trimmed[i] == True if the ith parameter was trimmed from the model.z Compute one-step moment estimator for null (constant-only) model This is a preliminary estimator used as start_params. Returns ------- params : ndarray parameter estimate based one one-step moment matching z check_rank : bool Check exog rank to determine model degrees of freedom. Default is True. Setting to False reduces model initialization time when exog.shape[1] is large. c$|jdkr+|jjdvr|}t|jd}nVt |dfdtjdD}t jt}||fS||fS)N)SOF) drop_firstc,i|]}|j|S)columns).0idummiess c/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/discrete/discrete_model.py z%_numpy_to_dummies..~s"IIIA!W_Q'IIIdtype) ndimr4kindrangeshaper npasarrayfloat)endog endog_dummiesynamesr/s @r0_numpy_to_dummiesr?xs zQ5;+:== u{1~&&e666IIIIw}Q7G1H1HIII 7%888 f$$ &  r2c |jdkrB|jddkr,|jd}t|jdddf}nd}|}n|j}|d}t|}|j}|||fS)Nr%r(r y)r5r8r,r ilocnametolist)r<ynamer=r>s r0_pandas_to_dummiesrFs zQ ;q>Q  M!$E' 111a4(899MME!MM  =E#E**  " ) ) + +F &% ''r2cT|dvr#td|dS)a  As of 0.10.0, the supported values for `method` in `fit_regularized` are "l1" and "l1_cvxopt_cp". If an invalid value is passed, raise with a helpful error message Parameters ---------- method : str Raises ------ ValueError )l1 l1_cvxopt_cpzG`method` = {method} is not supported, use either "l1" or "l1_cvxopt_cp"methodN) ValueErrorformatrJs r0_validate_l1_methodrNsA+++228&&2G2GII I,+r2ceZdZdZdfd ZdZdZdZdZe e j j j dfd Z dfd Z dZddZ ddZdZxZS) DiscreteModelz Abstract class for discrete choice models. This class does not do anything itself but lays out the methods and call signature expected of child classes in addition to those of statsmodels.model.LikelihoodModel. Tc h||_tj||fi|d|_d|_dS)NFr ) _check_ranksuper__init__raise_on_perfect_predictionk_extra)selfr<exog check_rankkwargs __class__s r0rTzDiscreteModel.__init__s?%/////+0( r2c|jrtj|jd}n|jjd}t |dz |_t |jjd|z |_dS)z Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model. qrrJr(r N)rRr matrix_rankrXr8r;df_modeldf_resid)rWranks r0 initializezDiscreteModel.initializesj   &$TYt<<))  .  W6^33 C C C C C C.>ON + + \\^^~ - -VWW W  /HH ',$*%,)4"&&.-<-<'' &'' sA A*)A*c||}|d}tj|d}|}|dkr5||dddf|f}tj| } ntjd} tjtj|j z} | | |dddf|f<| S)a Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit. Returns a full cov_params matrix, with entries corresponding to zero'd values set to np.nan. trimmedr N) hessianr9nonzerosumlinalginvzerosnanonesr8) rWlikelihood_modelxoptretvalsHrnz_idx nnz_params H_restrictedH_restricted_inv cov_paramss r0rz DiscreteModel.cov_params_func_l1s  $ $T * *)$WH%%a(h^^%% >>VAAAtG_f45L!y}}l];;  !x{{ Vbgag... .> 6!!!T'?F*+r2meanct)zQ Predict response variable of a model given exogenous variables. rd)rWrrrXwhichlinears r0rnzDiscreteModel.predictrir2ct)zQ This should implement the derivative of the non-linear function rd)rWrrrX dummy_idx count_idxs r0_derivative_exogzDiscreteModel._derivative_exogs "!r2c^ddlm}m}||||||||}||||||||}|S)zK Helper for _derivative_exog to wrap results appropriately r()_get_count_effects_get_dummy_effects)discrete_marginsrr) rWmargeffrrrXrr transformrrs r0_derivative_exog_helperz%DiscreteModel._derivative_exog_helpersn MLLLLLLL  (($ 9)-v77G  (($ 9)-v77Gr2TNrwrxr(r(N) NrHrr(TNr rrrrFNrNNNN)__name__ __module__ __qualname____doc__rTrbrhrkrvr baseLikelihoodModelrrrrnrr __classcell__r[s@r0rPrPsO 9 9 9""" """ F F FXd"&.//>@,00/.9=IM:@GK#( ______B2"""" =A#'""""r2rPceZdZdZdfd Z ddZeejj  dfd ZddZ e j e _ ddZ ddZ dZddZxZS) BinaryModelFNTc ||tj||f||d|t|jt s8t j|jdk|jdkzstd|Zt|d|j sEt j |jt j |jkrtddSdSdS)N)offsetrYr r(z#endog must be in the unit interval.rz#endog must be binary, either 0 or 1) _check_kwargsrSrT issubclassr[MultinomialModelr9allr<rLdelattr_continuous_okanyround)rWr<rXrrYrZr[s r0rTzBinaryModel.__init__s  6""" #V  # #! # # #$.*:;; H64:?tzQ?@@ H !FGGG > D( # # #' HF4:$*)=)==>> H !FGGG > H H H Hr2rcz|"d}tj|t|durd}||t|dr|j}n|d}||j}t j|||z}|dkr||S|dkr|S|dkr||}|d |z z} | Std ) a Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like Fitted parameters of the model. exog : array_like 1d or 2d array of exogenous values. If not supplied, the whole exog attribute of the model is used. which : {'mean', 'linear', 'var', 'prob'}, optional Statistic to predict. Default is 'mean'. - 'mean' returns the conditional expectation of endog E(y | x), i.e. exp of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var' returns the estimated variance of endog implied by the model. .. versionadded: 0.14 ``which`` replaces and extends the deprecated ``linear`` argument. linear : bool If True, returns the linear predicted values. If False or None, then the statistic specified by ``which`` will be returned. .. deprecated: 0.14 The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. Returns ------- array Fitted values at exog. N0linear keyword is deprecated, use which="linear"Trrrvarr(z8Only `which` is "mean", "linear" or "var" are available.) rprq FutureWarninghasattrrrXr9dotrhrL) rWrrrXrrrrulinpredmuvar_s r0rnzBinaryModel.predictsP  DC M#} - - -~~  >dlwtX/F/Fl[FF ^F <9D&v&&/ F??88G$$ $ h  N E>>'""BR=DK+,, ,r2rHrr(r rrrrc  t|tjd||||||||| | | d | } t|| }t |SN r{rKr|r}r~rrrrrrr+)rNrSrL1BinaryResultsL1BinaryResultsWrapper)rWr{rKr|r}r~rrrrrrrZbnryfit discretefitr[s r0rzBinaryModel.fit_regularized-s~ F###)%'') 4|17296A/33;054=8E8E17 4 4-3 4 4&dG44 %k222r2c &t||fddi|}|S)Nr{r)rW constraintsr{fit_kwdsress r0fit_constrainedzBinaryModel.fit_constrainedEs."4//4/%-// r2dydxc||j}||||d}||dddf|z}d|vr%|||||dddfz}|S)} For computing marginal effects standard errors. This is used only in the case of discrete and count regressors to get the variance-covariance of the marginal effects. It returns [d F / d params] where F is the predict. Transform can be 'dydx' or 'eydx'. Checking is done in margeff computations for appropriate transform. Nrrreyr)rXrnrk)rWrrrXrrrdFs r0_derivative_predictzBinaryModel._derivative_predictMs <9D,,vtF(,KK XXg  qqqv & - 9   $,,vtF,;;AAAdFC CB r2cR||j}||||d}tj||dddf|dddf}d|vr||z}d|vr#||||dddfz}|||||||S)a; For computing marginal effects returns dF(XB) / dX where F(.) is the predicted probabilities transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. Nrrexr)rXrnr9rrkr) rWrrrXrrrrrrs r0rzBinaryModel._derivative_exogas <9D,,vtF(,KK&'**111T62QQQ)) 9   tOG 9   t||FD11!!!T': :G++GVT,5y)MM Mr2c|j}||d}||}|j|dddfz}|S)M Derivative of the expected endog with respect to the parameters. Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. rrN)linkrn inverse_derivrX)rWrrrlin_predidldmats r0_deriv_mean_dparamszBinaryModel._deriv_mean_dparams}sPy<<h<77  **y3qqq$w<' r2c^||||}tj|}|S)a4Get frozen instance of distribution based on predicted parameters. Parameters ---------- params : array_like The parameters of the model. exog : ndarray, optional Explanatory variables for the main count model. If ``exog`` is None, then the data from the model will be used. offset : ndarray, optional Offset is added to the linear predictor of the mean function with coefficient equal to 1. Default is zero if exog is not None, and the model offset if exog is None. exposure : ndarray, optional Log(exposure) is added to the linear predictor of the mean function with coefficient equal to 1. If exposure is specified, then it will be logged by the method. The user does not need to log it first. Default is one if exog is is not None, and it is the model exposure if exog is None. Returns ------- Instance of frozen scipy distribution. )rXr)rnr bernoulli)rWrrrXrrdistrs r0get_distributionzBinaryModel.get_distributions/6\\&tF\ ; ;## r2NT)NrNN NrHrr(r(Nr rrrrN)NrN)NrNNNNN)rrrrrTrnr rPrrrrrrrrrrs@r0rrs0NHHHHHH ?CC,C,C,C,JXm+3448wxYw| S)NrAr() design_infoformula) data_tools_is_using_ndarray_typer?_is_using_pandasrFr9r: isinstancerzipr7r8 _ynames_maprr> orig_endogr<wendogsetattr__dict__popKeyError) rWr<rXmissinghasconstrZr=r>rErkeys r0 _handle_datazMultinomialModel._handle_datasd  ,UD 9 9 $5e$<$< !M6EE  ( 5 5 +=e+D+D (M655Ju%%E$5e$<$< !M6E&$'' F#eM$7$:;;VDDEEF!=$LLVLL j   C000 c4=#4#4S#9#9::::     s)D++ D87D8cft|jd|_|jjd|_|jjd|_|xj |jdz zc_ |jjd|j z |jdz z |_ dS)z4 Preprocesses the data for MNLogit. r(r N) rSrbr<argmaxrr8JrXKr_r`)rWr[s r0rbzMultinomialModel.initializes Z&&q)) "1%# $&(#  *T]:dfQhG r2NrcF|"d}tj|t|durd}||j}|jdkr|d}t |||}|dkr5tjtj t||f}|S)ag Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like 2d array of fitted parameters of the model. Should be in the order returned from the model. exog : array_like 1d or 2d array of exogenous values. If not supplied, the whole exog attribute of the model is used. If a 1d array is given it assumed to be 1 row of exogenous variables. If you only have one regressor and would like to do prediction, you must provide a 2d array with shape[1] == 1. which : {'mean', 'linear', 'var', 'prob'}, optional Statistic to predict. Default is 'mean'. - 'mean' returns the conditional expectation of endog E(y | x), i.e. exp of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var' returns the estimated variance of endog implied by the model. .. versionadded: 0.14 ``which`` replaces and extends the deprecated ``linear`` argument. linear : bool If True, returns the linear predicted values. If False or None, then the statistic specified by ``which`` will be returned. .. deprecated: 0.14 The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. Notes ----- Column 0 is the base case, the rest conform to the rows of params shifted up one for the base case. NrTrr(r) rprqrrXr5rSrnr9 column_stackrlen)rWrrrXrrrupredr[s r0rnzMultinomialModel.predictsV  DC M#} - - -~~  <9D 9>>:Dwwvt599 H  ?BHSYY$7$7#>??D r2rwrxr(c J|%tj|j|jdz z}ntj|}|d}t jj|f||||||d|}|j |jdd|_t||}t|S)Nr(cdSrr+)xrss r0z&MultinomialModel.fit..#sr2rzForder) r9rrrr:rrrrrreshapeMultinomialResultsMultinomialResultsWrapper) rWr{rKr|r}r~rrZmnfits r0rzMultinomialModel.fits  8DFdfQh$788LL:l33L  --H$(8lwKH880688|++DFBc+BB "4//(///r2rHrr rrrrc  @|%tj|j|jdz z}ntj|}t j|f||||||||| | | d | } | j|jdd| _t|| } t| S)Nr(rr(r)r*) r9rrrr:rPrrrr,L1MultinomialResultsL1MultinomialResultsWrapper)rWr{rKr|r}r~rrrrrrrZr/s r0rz MultinomialModel.fit_regularized,s  8DFdfQh$788LL:l33L-F#/'dXy +F FF?E FF |++DFBc+BB $T511*5111r2rc||j}|jdkr%||j|jdz d}t jt j||}d|dzdddf}t|j}t|j}t j ||d}t j ||dz } | | z|dzz } |j dddddf| z||z z|dzz } | d} t jt j|dz t j|t$} |j dddddf | z|z|dzz ddd| f| dd| f<t j| dddddf| fd} d|vr&| |||dddddfz} | S) a For computing marginal effects standard errors. This is used only in the case of discrete and count regressors to get the variance-covariance of the marginal effects. It returns [d F / d params] where F is the predicted probabilities for each choice. dFdparams is of shape nobs x (J*K) x (J-1)*K. The zero derivatives for the base category are not included. Transform can be 'dydx' or 'eydx'. Checking is done in margeff computations for appropriate transform. Nr(r)r*axisr%)r(r r%r)rXr5r,rrr9exprrintrepeattileT transposekroneyerastypebool concatenatern)rWrrrXreXBsum_eXBrr repeat_eXBrgF0F1 other_idxdFdXs r0rz$MultinomialModel._derivative_predict>s <9D ;!  ^^DFDF1HC^@@FfRVD&))**swwqzz>111T6* KK KKYsAA... GD!A#  [1_w!| +U111QQQt8_Q 'J"6 77A: F \\' " "WRVAaC[["'!**55<@,0000)(0$Xm+3448 D( # # #   D* % % % dj. ; ;Z B//  diorz : :Jty"-- r2c|+|jd|jdkrtd|+|jd|jdkrtddSdS)Nr z&offset is not the same length as endogz(exposure is not the same length as endog)r8rL)rWrrXr<s r0rZzCountModel._check_inputssg  &,q/U[^"C"CEFF F  HN1$5Q$G$GGHH H $G$Gr2ct}d|vr%|dtj|d|d<|S)NrX)rS_get_init_kwdsr9r6rWkwdsr[s r0r`zCountModel._get_init_kwdssMww%%''   $z"2">!vd:&677D  r2c |&tjtj|}|tj|}|.|j}|t |dd}|t |dd}ntj|}|d}|d}|||fS)NrXr r)r9rYr:rXgetattr)rWrXrrXs r0_get_predict_arrayszCountModel._get_predict_arrayss  vbj2233H  Z''F <9D"4Q77~ x33:d##D~VX%%r2rc|"d}tj|t|durd}||t|dr|j}n|d}||t|dr|j}n|d}nt j|}||j}t j ||d|j d}||z|z} |d krt j | S| d r| Std ) ah Predict response variable of a count model given exogenous variables Parameters ---------- params : array_like Model parameters exog : array_like, optional Design / exogenous data. Is exog is None, model exog is used. exposure : array_like, optional Log(exposure) is added to the linear prediction with coefficient equal to 1. If exposure is not provided and exog is None, uses the model's exposure if present. If not, uses 0 as the default value. offset : array_like, optional Offset is added to the linear prediction with coefficient equal to 1. If offset is not provided and exog is None, uses the model's offset if present. If not, uses 0 as the default value. which : 'mean', 'linear', 'var', 'prob' (optional) Statitistic to predict. Default is 'mean'. - 'mean' returns the conditional expectation of endog E(y | x), i.e. exp of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var' variance of endog implied by the likelihood model - 'prob' predicted probabilities for counts. .. versionadded: 0.14 ``which`` replaces and extends the deprecated ``linear`` argument. linear : bool If True, returns the linear predicted values. If False or None, then the statistic specified by ``which`` will be returned. .. deprecated: 0.14 The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. Notes ----- If exposure is specified, then it will be logged by the method. The user does not need to log it first. NrTrrrrXr(rlin+keyword which has to be "mean" and "linear")rprqrrrrXr9rYrXrr8r6 startswithrL) rWrrrXrXrrrrufittedrs r0rnzCountModel.predictsd  DC M#} - - -~~  >dlwtX/F/Fl[FF ^F   z1J1J }HH  HHvh''H <9Df^djm^4558#f, F??6'?? "   e $ $ LNJKK Kr2rc||j}|||dddf|z}d|vr#||||dddfz}|S)rNr)rXrn)rWrrrXrrs r0rzCountModel._derivative_predict8sj <9D \\&$ ' '$ /$ 6 9   $,,vt,,QQQtV4 4B r2cJ||j}t|dd}|dkr|n |d| }|||dddf|dddfz}d|vr||z}d|vr#||||dddfz}|||||||S)a For computing marginal effects. These are the marginal effects d F(XB) / dX For the Poisson model F(XB) is the predicted counts rather than the probabilities. transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. NrVr rr)rXrdrnr) rWrrrXrrrrV params_exogrs r0rzCountModel._derivative_exogKs <9D$ 1-- '1 ff&7(2C ,,vt,,QQQtV4{467JJ 9   tOG 9   t||FD11!!!D&9 9G++GVT,5y)MM Mr2cHddlm}|}||d}||}|j|dddfz}|jdkr@,0 0 0 0 0 0)( 0Xm+3448#>>L040K0K0M0Ma0PL, - ::j ! ! -%zz*55D %zz*b99D ,z4((,7,4:5<9D266> 77 06 77%T6::T:: $[111r2rHrr rrrrc  t|tt|jd||||||||| | | d | } t || }t |Sr)rNrSr rL1PoissonResultsL1PoissonResultsWrapperr|s r0rzPoisson.fit_regularizedVs F###8z4((8F)&''dXy +F FF?E FF 'tV44 &{333r2c 6ddlm}ddlm}m}||j|}|j|j} }|||| ||\} } } | dddd} | j dtj | j d<| j d tj | j d <| j d | j d <| | j_| | j_| d d }|d kr | | j_n d | j_t%| }| jxj|z c_| jxj|zc_||| j_|| j_| | j_| S)aefit the model subject to linear equality constraints The constraints are of the form `R params = q` where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters ---------- constraints : formula expression or tuple If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance r ) DesignInfo)rLinearConstraints)r{rnmF)r|rKr~warn_convergencefcall iterations convergedr nonrobustN)patsyrstatsmodels.base._constraintsrr exog_nameslinear_constraintcoefs constantsr mle_retvalsrr9r_resultsrrcov_params_defaultnormalized_cov_paramsr"r`r_ from_patsyrk_constrresults_constrained)rWrr{rrrrlcRqrrcov res_constrrrrs r0rzPoisson.fit_constrainedgsD %$$$$$ F F F F F F F FZ ( ( : :; G Gx1#2/$1?K;C#E#E#EZhhqA(-//#-#9#=#=grv#N#N (2(>(B(B8Dbf)N)N %'1'=k'J $$ *- '<< K88 { " "14CL . .15CL .q66 ) )#4#?#?#C#C  ( +5 ( r2ct|dd}t|dd}|j}tjtj|||z|z}tj|j|z |S)a\ Poisson model score (gradient) vector of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` Notes ----- .. math:: \frac{\partial\ln L}{\partial\beta}=\sum_{i=1}^{n}\left(y_{i}-\lambda_{i}\right)x_{i} where the loglinear model is assumed .. math:: \ln\lambda_{i}=x_{i}\beta rr rXrdrXr9r6rr<rWrrrrXrgLs r0scorez Poisson.scoresj.x++4Q// I F26!F##f,x7 8 8vdj1na(((r2ct|dd}t|dd}|j}tjtj|||z|z}|j|z dddf|zS)aK Poisson model Jacobian of the log-likelihood for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- score : array_like The score vector (nobs, k_vars) of the model evaluated at `params` Notes ----- .. math:: \frac{\partial\ln L_{i}}{\partial\beta}=\left(y_{i}-\lambda_{i}\right)x_{i} for observations :math:`i=1,...,n` where the loglinear model is assumed .. math:: \ln\lambda_{i}=x_{i}\beta rr rXNrrs r0 score_obszPoisson.score_obssp0x++4Q// I F26!F##f,x7 8 8 Q$'!++r2ct|dd}t|dd}|j}tjtj|||z|z}|j|z S)a. Poisson model score_factor for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- score : array_like The score factor (nobs, ) of the model evaluated at `params` Notes ----- .. math:: \frac{\partial\ln L_{i}}{\partial\beta}=\left(y_{i}-\lambda_{i}\right) for observations :math:`i=1,...,n` where the loglinear model is assumed .. math:: \ln\lambda_{i}=x_{i}\beta rr rXrrs r0 score_factorzPoisson.score_factors^0x++4Q// I F26!F##f,x7 8 8 Qr2ct|dd}t|dd}|j}tjtj|||z|z}tj||jz| S)aV Poisson model Hessian matrix of the loglikelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- .. math:: \frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\sum_{i=1}^{n}\lambda_{i}x_{i}x_{i}^{\prime} where the loglinear model is assumed .. math:: \ln\lambda_{i}=x_{i}\beta rr rX)rdrXr9r6rr:rs r0rzPoisson.hessiansm.x++4Q// I F26!F##h.7 8 8qua    r2ct|dd}t|dd}|j}tjtj|||z|z}| S)aP Poisson model Hessian factor Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (nobs,) The Hessian factor, second derivative of loglikelihood function with respect to the linear predictor evaluated at `params` Notes ----- .. math:: \frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\sum_{i=1}^{n}\lambda_{i} where the loglinear model is assumed .. math:: \ln\lambda_{i}=x_{i}\beta rr rX)rdrXr9r6rrs r0hessian_factorzPoisson.hessian_factor"sY.x++4Q// I F26!F##h.7 8 8r r2c|jS)aderivative of score_obs w.r.t. endog Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- derivative : ndarray_2d The derivative of the score_obs with respect to endog. This can is given by `score_factor0[:, None] * exog` where `score_factor0` is the score_factor without the residual. rX)rWrrscales r0_deriv_score_obs_dendogzPoisson._deriv_score_obs_dendog?s &yr2rcr|"d}tj|t|durd}|drd}|dvr't ||||||S|dkr||||| } | S|d kr|t j|}nAt jt jd t j |j d z}||||| dddf} tj || Std )a@ Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like 2d array of fitted parameters of the model. Should be in the order returned from the model. exog : array_like, optional 1d or 2d array of exogenous values. If not supplied, then the exog attribute of the model is used. If a 1d array is given it assumed to be 1 row of exogenous variables. If you only have one regressor and would like to do prediction, you must provide a 2d array with shape[1] == 1. offset : array_like, optional Offset is added to the linear predictor with coefficient equal to 1. Default is zero if exog is not None, and the model offset if exog is None. exposure : array_like, optional Log(exposure) is added to the linear prediction with coefficient equal to 1. Default is one if exog is is not None, and is the model exposure if exog is None. which : 'mean', 'linear', 'var', 'prob' (optional) Statitistic to predict. Default is 'mean'. - 'mean' returns the conditional expectation of endog E(y | x), i.e. exp of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var' returns the estimated variance of endog implied by the model. - 'prob' return probabilities for counts from 0 to max(endog) or for y_values if those are provided. .. versionadded: 0.14 ``which`` replaces and extends the deprecated ``linear`` argument. linear : bool The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. If True, returns the linear predicted values. If False or None, then the statistic specified by ``which`` will be returned. .. deprecated: 0.14 The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. y_values : array_like Values of the random variable endog at which pmf is evaluated. Only used if ``which="prob"`` NrTrrg)rr)rXrXrrrrrXrXrprobr r(z-Value of the `which` option is not recognized)rprqrrirSrnr9 atleast_2darangemaxr<rr_pmfrL) rWrrrXrXrrry_valuesrurr[s r0rnzPoisson.predictTscv  DC M#} - - -~~    E " " E & & &77??6x*0).v#?? ?e^^f4'/  BI f__#=22=Ia !3!3a!788::f4'/  !4)B=%%h33 3LMM Mr2c2tj|  }|S)rProbability that count is not zero internal use in Censored model, will be refactored or removed )r9expm1)rWrrrprob_nzs r0 _prob_nonzerozPoisson._prob_nonzeros HbSMM/r2c|S)bvariance implied by the distribution internal use, will be refactored or removed r+)rWrrrs r0_varz Poisson._vars  r2c`|||||}tj|}|S)a=Get frozen instance of distribution based on predicted parameters. Parameters ---------- params : array_like The parameters of the model. exog : ndarray, optional Explanatory variables for the main count model. If ``exog`` is None, then the data from the model will be used. offset : ndarray, optional Offset is added to the linear predictor of the mean function with coefficient equal to 1. Default is zero if exog is not None, and the model offset if exog is None. exposure : ndarray, optional Log(exposure) is added to the linear predictor of the mean function with coefficient equal to 1. If exposure is specified, then it will be logged by the method. The user does not need to log it first. Default is one if exog is is not None, and it is the model exposure if exog is None. Returns ------- Instance of frozen scipy distribution subclass. r)rnrr)rWrrrXrXrrrs r0rzPoisson.get_distributions16\\&thv\ N N b!! r2rrrNNNrNNr) rrrr_model_params_doc_missing_param_doc_check_rank_docrrrrhrkrrr _get_start_params_null_docsrrPrrrrrrrrrrnrrrrrs@r0rrsH + %  & )8  8 9 99G*""^"///8:::<   ::::8X)**+*Xm'((>@,022222)(20Xm+3448 > @ @8 Kr2o use_transparams : bool This parameter enable internal transformation to impose non-negativity. True to enable. Default is False. use_transparams=True imposes the no underdispersion (alpha > 0) constraint. 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Jqqqv  \\& ! !!!!D& )xA   %$," " VBF2JJ27A|a"f/D"E$&Fb=27#:#;<== r2c |jrtj|d}n|d}|dd}|j}|j}|jdddf}||dddf}tj||}d||zz}|||z|zz} ||z||dz zz} | |z} |||dz zz} ||z} |jd}tj |dz|dzf}t|D]}t|dzD]}tj ||dd|dfz|dd|dfz|| | z|dzz d| dzz| z|dzz z d| z| dzz|dzz z| |z||zz z | |z| z||dzzz z|dz | z|dz z| |zz z|dz d| zdzz| dzz z | |dz z||zz z z|dz d| zz| z d| z|z z zzd}tj ||||f<tj |d}|j|||<tj d| z|z|dzz d| z|z| z|dzz z ||z|dz zd| zz| dzz z |d| zz|dzz z| |z|dz z| z zd| z|z|z z | | z|dzz z| zd}||dddf<||dddf<|dzd|z|dzz || z d z|dz zz d| z|dzz z z}| |d <|S) al Generalized Poisson model Hessian matrix of the loglikelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` r(Nr(r%r r4k@r(r()rr9r6rrXr<rnrr8emptyr7rsqueeze triu_indicesr:)rWrrrrrXrArrrrr2r3a5r4dimhess_arrr.rMhess_valtri_idxdldpdadldadas r0rzGeneralizedPoisson.hessian)sK   F6":&&EE2JE  !y Jqqqv  \\& ! !!!!D& )xA   %$," " QYA & !V A T jm8SU3q5M**s 6 6A1q5\\ 6 66"tAAAaH~"5QQQqX"F27RU?r1u9r>BE12r6R!V,r1u456R"W-.6B;"r1u*5 6 ER<1q51R"W= > Ea"fq[02q58 9Q<273451uR(2-2vm$ % #&-. / / /"$H!5!5A 6/#+++$Jw/R$Q.R$+b!e34QU+q2v6Q>?R2q501a1q5)B. / R!b ) b2q5 ) -2 2   "CRC!"RqAEBEMVbLAE23FRUN+,!**,,r2chtj|}|jrtj|d}n|d}|dd}|j}|j}||}tj||}d||zz}|||z|zz}||z||dz zz} | |z} |||dz zz} |} ||| | z|dzz d| dzz|z|dzz z d| z| dzz|dzz z| |z||zz z | |z|z||dzzz z| ||zz z| |z||dzzz z |dz | z|dz z||zz z|dz d| zdzz|dzz z | |dz z||zz z d|dzz z z| |z | |z|dzz z|dz d| zz|z zd| z|z z d|z zzz} d| z|z|dzz d| z|z|z|dzz z ||z|dz zd| zz|dzz z |d| zz|dzz z| |z|dz z|z zd| z|z|z z | |z|dzz z| z}|dzd|z|dzz ||z dz|dz zz d|z|dzz z z}| ||fS)a Generalized Poisson model Hessian matrix of the loglikelihood Parameters ---------- params : array-like The parameters of the model Returns ------- hess : ndarray, (nobs, 3) The Hessian factor, second derivative of loglikelihood function with respect to linear predictor and dispersion parameter evaluated at `params` The first column contains the second derivative w.r.t. linpred, the second column contains the cross derivative, and the third column contains the second derivative w.r.t. the dispersion parameter. r(Nr(r%r@rCr;)rWrrrrrArrrrr2r3rHr4dbbdbadaas r0rz!GeneralizedPoisson.hessian_factorus*F##   F6":&&EE2JE  ! J \\& ! !xA   %$," " QYA & !V A  27RU?r1u9r>BE)*r6R!V$r1u,-6R"W%&6B;"r1u*- . b> " 7b2q5j) *ER<1q5)R"W56Ea"fq[(2q501Q<27+ ,r1u9  cBh2gAo1uR 2%&2vm"f &B A%R$+b!e34QU+q2v6Q>?R2q501a1q5)B. / R!b ) b2q5 ) -2 2AgQQVbLAE23FRUN+,C}r2rc||j}|t|dd}n|dkrtj|}|t|dd}tj||d|jd}||z|z}|dkrtj|S|dkr|S|dkr6tj|} |d} |j} | d| | | zzzd zz} | S|d kr|Atjtj dtj |j dz}| |||| dddf} tj|| |d|jdzStd ) NrXr rr(rrrr(r%rrzkeyword 'which' not recognized)rXrdr9rYrr8r6rrrrr<rnrpmfrL)rWrrrXrXrrrrjrrrpm1rrs r0rnzGeneralizedPoisson.predicts <9D  tZ33HH ]]vh''H >T8Q//Ff^djm^4558#f, F??6'?? " h  N e^^6'??D2JE'C1utSy00144DK f__=1bfTZ6H6H6J)K)KLLf4(%+---.QQW6B#Hb&*$($9A$=?? ??@@ @r2cddlm}fd}|jdddf|}|ddddfjz}|ddddf}t j||fS)#derivative of score_obs w.r.t. endog Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- derivative : ndarray_2d The derivative of the score_obs with respect to endog. r _approx_fprime_cs_scalarc|jdkr|jddkr |dddf}|}tj|SNr%r(r )r<r5r8rr9r!rAsfrrrWs r0fz5GeneralizedPoisson._deriv_score_obs_dendog..fUv{{qwqzQaaadG""6"33B?2&& &r2Nr(r%statsmodels.tools.numdiffrYr<rXr9r!rWrrrYr_dsfd1d2s`` r0rz*GeneralizedPoisson._deriv_score_obs_dendogs GFFFFF ' ' ' ' ' ' '&tz!!!T'':A>> BQBZ$) # AaC[Bx(((r2cF|d}|j}|d|||zzzdzz}|S)rr(r(r%r)rWrrrrrUrs r0rzGeneralizedPoisson._var s6 r #QS(1,, r2cp|d}|j}tj| d|||zzzz }d|z }|Srr(r()rr9r6)rWrrrrrU prob_zerors r0rz GeneralizedPoisson._prob_nonzero sF r #FR41ur3w#6788 i-r2cz|||||}|jdz}t||d|}|S)rQrr(r()rnrr)rWrrrXrXrrrrs r0rz#GeneralizedPoisson.get_distribution sD\\&thv\ N N  !A %RQ// r2)r(NNrVTr Nrrxr(r(NFrNNNrr}r)!rrrrrrrrrTr`rrrr rrrrPrrrrrr>rrrrnrrrrrrs@r0rrs +014CC D DDG015;? " " " " " " !!!///0&;&;&;PX)**   +*  X   Xm'((<>BGOS66666)(  6pXm+3448JJJXGGGRXgo%&&?C'+#A#A#A'&#AJ))):   Xg&.//0/r2rceZdZdejejezZdZ e dZ dZ dZ e dZdZd Zd Zd Zd Zd ZdZeejj dfd ZdZxZS)raG Logit Model {params} offset : array_like Offset is added to the linear prediction with coefficient equal to 1. {extra_params} Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. rTc:ddlm}|}|SNr ro)rqrprrWrprs r0rz Logit.link5 s&555555{{}} r2c`tj|}ddtj| zz S)a The logistic cumulative distribution function Parameters ---------- X : array_like `X` is the linear predictor of the logit model. See notes. Returns ------- 1/(1 + exp(-X)) Notes ----- In the logit model, .. math:: \Lambda\left(x^{\prime}\beta\right)= \text{Prob}\left(Y=1|x\right)= \frac{e^{x^{\prime}\beta}}{1+e^{x^{\prime}\beta}} r(r9r:r6rfs r0rhz Logit.cdf; s** JqMM!BFA2JJ,r2ctj|}tj| dtj| zdzz S)a2 The logistic probability density function Parameters ---------- X : array_like `X` is the linear predictor of the logit model. See notes. Returns ------- pdf : ndarray The value of the Logit probability mass function, PMF, for each point of X. ``np.exp(-x)/(1+np.exp(-X))**2`` Notes ----- In the logit model, .. math:: \lambda\left(x^{\prime}\beta\right)=\frac{e^{-x^{\prime}\beta}}{\left(1+e^{-x^{\prime}\beta}\right)^{2}} r(r%rsrfs r0rkz Logit.pdfS s9* JqMMvqbzz1RVQBZZ||}| d|z zS)ak Logit model Hessian factor Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (nobs,) The Hessian factor, second derivative of loglikelihood function with respect to the linear predictor evaluated at `params` r()rn)rWrrrs r0rzLogit.hessian_factor s% LL rQU|r2Nrwrxr(c tjd||||||d|}t||} t| Sru)rSr LogitResultsBinaryResultsWrapper rWr{rKr|r}r~rrZrrr[s r0rz Logit.fit& s`%''+(<%+&-*5#''/ (( !' ((#411 #K000r2c|jS)derivative of score_obs w.r.t. endog Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- derivative : ndarray_2d The derivative of the score_obs with respect to endog. This can is given by `score_factor0[:, None] * exog` where `score_factor0` is the score_factor without the residual. rrs r0rzLogit._deriv_score_obs_dendog4 s yr2r)rrrrMrrrrrrrrrhrkrrrrrrrrr rPrrrrs@r0rr! sc d,//A  C C "N^    0,,,0##^#555:--->%%%2(((6:&&&.$Xm'((>@,0 1 1 1 1 1)( 1r2rceZdZdejejezZe dZ dZ dZ dZ dZdZd Zd Zd Zd Zeejj dfd ZdZxZS)raH Probit Model {params} offset : array_like Offset is added to the linear prediction with coefficient equal to 1. {extra_params} Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. rc:ddlm}|}|Srp)rqrprrqs r0rz Probit.linkX s&555555||~~ r2c@tj|S)an Probit (Normal) cumulative distribution function Parameters ---------- X : array_like The linear predictor of the model (XB). Returns ------- cdf : ndarray The cdf evaluated at `X`. Notes ----- This function is just an alias for scipy.stats.norm.cdf )rnorm_cdfrfs r0rhz Probit.cdf^ s$zq!!!r2chtj|}tj|S)a Probit (Normal) probability density function Parameters ---------- X : array_like The linear predictor of the model (XB). Returns ------- pdf : ndarray The value of the normal density function for each point of X. Notes ----- This function is just an alias for scipy.stats.norm.pdf )r9r:rr_pdfrfs r0rkz Probit.pdfr s%$ JqMMzq!!!r2c d|jzdz }||d}tjtjtj|||ztdS)a= Log-likelihood of probit model (i.e., the normal distribution). Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes ----- .. math:: \ln L=\sum_{i}\ln\Phi\left(q_{i}x_{i}^{\prime}\beta\right) Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. r%r(rr)r<rnr9rrYrrh FLOAT_EPSrxs r0rzProbit.loglike sa. djL1 ,,vX,66vbfRWTXXa'k%:%:IqIIJJKKKr2cd|jzdz }||d}tjtj|||zt dS)ai Log-likelihood of probit model for each observation Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : array_like The log likelihood for each observation of the model evaluated at `params`. See Notes Notes ----- .. math:: \ln L_{i}=\ln\Phi\left(q_{i}x_{i}^{\prime}\beta\right) for observations :math:`i=1,...,n` where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. r%r(rr)r<rnr9rYrrhrrxs r0rzProbit.loglikeobs sW2 djL1 ,,vX,66vbgdhhqy119a@@AAAr2c0|j}|j}||d}d|zdz }||||zzt j|||ztdtz z }t j||S)a Probit model score (gradient) vector Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` Notes ----- .. math:: \frac{\partial\ln L}{\partial\beta}=\sum_{i=1}^{n}\left[\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}\right]x_{i} Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. rrr%r() r<rXrnrkr9rrhrrrWrrrArgrrrs r0rz Probit.score s, J I \\&\ 1 1 aC!G dhhqtnn RWTXXad^^YI NN Nva{{r2c$|j}|j}||d}d|zdz }||||zzt j|||ztdtz z }|dddf|zS)a Probit model Jacobian for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- jac : array_like The derivative of the loglikelihood for each observation evaluated at `params`. Notes ----- .. math:: \frac{\partial\ln L_{i}}{\partial\beta}=\left[\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}\right]x_{i} for observations :math:`i=1,...,n` Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. rrr%r(N)r<rXrnrkr9rrhrrs r0rzProbit.score_obs s0 J I \\&\ 1 1 aC!G dhhqtnn RWTXXad^^YI NN N4y1}r2c|j}||d}d|zdz }||||zztj|||zt dt z z }|S)a Probit model Jacobian for each observation Parameters ---------- params : array-like The parameters of the model Returns ------- score_factor : array_like (nobs,) The derivative of the loglikelihood function for each observation with respect to linear predictor evaluated at `params` Notes ----- .. math:: \frac{\partial\ln L_{i}}{\partial\beta}=\left[\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}\right]x_{i} for observations :math:`i=1,...,n` Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. rrr%r()r<rnrkr9rrhr)rWrrrArrrs r0rzProbit.score_factor so0 J \\&\ 1 1 aC!G dhhqtnn RWTXXad^^YI NN Nr2c|j}||d}d|jzdz }||||zz|||zz }t j| ||zz|jz|S)a Probit model Hessian matrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- .. math:: \frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\lambda_{i}\left(\lambda_{i}+x_{i}^{\prime}\beta\right)x_{i}x_{i}^{\prime} where .. math:: \lambda_{i}=\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)} and :math:`q=2y-1` rrr%r()rXrnr<rkrhr9rr:)rWrrrgrrrs r0rzProbit.hessian s}2 I \\&\ 1 1 djL1  dhhqtnn TXXad^^ +vqb!B$imA&&&r2c||d}d|jzdz }||||zz|||zz }| ||zzS)a Probit model Hessian factor of the log-likelihood Parameters ---------- params : array-like The parameters of the model Returns ------- hess : ndarray, (nobs,) The Hessian factor, second derivative of loglikelihood function with respect to linear predictor evaluated at `params` Notes ----- .. math:: \frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\lambda_{i}\left(\lambda_{i}+x_{i}^{\prime}\beta\right)x_{i}x_{i}^{\prime} where .. math:: \lambda_{i}=\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)} and :math:`q=2y-1` rrr%r()rnr<rkrh)rWrrrrrs r0rzProbit.hessian_factor> sh2\\&\ 1 1  NQ  R  488AF#3#3 3rQV}r2Nrwrxr(c tjd||||||d|}t||} t| Sru)rSr ProbitResultsrrs r0rz Probit.fit\ s`%''+(<%+&-*5#''/ (( !' (($D'22 #K000r2c||d}||}tj||t dt z }||z d|z z }|dddf|jzS)rrrr(N)rnrkr9rrhrrX)rWrrrpdf_cdf_derivs r0rzProbit._deriv_score_obs_dendogi sx ,,vX,66xx  wtxx(()Q]CCt q4x(QQQW~ ))r2r)rrrrMrrrrrrrrhrkrrrrrrrr rPrrrrs@r0rrF sK d,//A  C C "^ """(""",LLL6BBB<<@@'''><Xm'((>@,0 1 1 1 1 1)( 1*******r2rceZdZdejezZd fd ZdZ dZ dZ dZ d Z d Zd Zd ZxZS)ra Multinomial Logit Model Parameters ---------- endog : array_like `endog` is an 1-d vector of the endogenous response. `endog` can contain strings, ints, or floats or may be a pandas Categorical Series. Note that if it contains strings, every distinct string will be a category. No stripping of whitespace is done. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See `statsmodels.tools.add_constant`. {extra_params} Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. J : float The number of choices for the endogenous variable. Note that this is zero-indexed. K : float The actual number of parameters for the exogenous design. Includes the constant if the design has one. names : dict A dictionary mapping the column number in `wendog` to the variables in `endog`. wendog : ndarray An n x j array where j is the number of unique categories in `endog`. Each column of j is a dummy variable indicating the category of each observation. See `names` for a dictionary mapping each column to its category. Notes ----- See developer notes for further information on `MNLogit` internals. )rTc ^tj||fd|i||j}|jtfdt t|jDtj dd|j j f|df}||j _ dS)NrYc g|] }| Sr+r+r-rr>s r0rKz$MNLogit.__init__.. s<<<#&+<<r[s @r0rTzMNLogit.__init__ sFFFvFFF !#==fEE<<<<s46{{););<<<%vabbz493C&D-2DM;;;! r2ct)z NotImplemented rd)rWrAs r0rkz MNLogit.pdf rir2ctjtjt|tj|f}||ddddfz S)a Multinomial logit cumulative distribution function. Parameters ---------- X : ndarray The linear predictor of the model XB. Returns ------- cdf : ndarray The cdf evaluated at `X`. Notes ----- In the multinomial logit model. .. math:: \frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)} r(N)r9r!rr"r6r)rWrgrAs r0rhz MNLogit.cdf sP&orws1vvq :;;3771::aaaf%%%r2c||jdd}|j}tj|tj|j|}tj||zS)a Log-likelihood of the multinomial logit model. Parameters ---------- params : array_like The parameters of the multinomial logit model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes ----- .. math:: \ln L=\sum_{i=1}^{n}\sum_{j=0}^{J}d_{ij}\ln \left(\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)} {\sum_{k=0}^{J} \exp\left(\beta_{k}^{\prime}x_{i}\right)}\right) where :math:`d_{ij}=1` if individual `i` chose alternative `j` and 0 if not. r(r)r*) r,rrr9rYrhrrXrrWrrdlogprobs r0rzMNLogit.loglike sa6#66 K&"&6":":;;<<va'k"""r2c||jdd}|j}tj|tj|j|}||zS)a Log-likelihood of the multinomial logit model for each observation. Parameters ---------- params : array_like The parameters of the multinomial logit model. Returns ------- loglike : array_like The log likelihood for each observation of the model evaluated at `params`. See Notes Notes ----- .. math:: \ln L_{i}=\sum_{j=0}^{J}d_{ij}\ln \left(\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)} {\sum_{k=0}^{J} \exp\left(\beta_{k}^{\prime}x_{i}\right)}\right) for observations :math:`i=1,...,n` where :math:`d_{ij}=1` if individual `i` chose alternative `j` and 0 if not. r(r)r*)r,rrr9rYrhrrXrs r0rzMNLogit.loglikeobs sW:#66 K&"&6":":;;<<7{r2c8||jdd}|jddddf|t j|j|ddddfz }t j|j|jS)a8 Score matrix for multinomial logit model log-likelihood Parameters ---------- params : ndarray The parameters of the multinomial logit model. Returns ------- score : ndarray, (K * (J-1),) The 2-d score vector, i.e. the first derivative of the loglikelihood function, of the multinomial logit model evaluated at `params`. Notes ----- .. math:: \frac{\partial\ln L}{\partial\beta_{j}}=\sum_{i}\left(d_{ij}-\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right)x_{i} for :math:`j=1,...,J` In the multinomial model the score matrix is K x J-1 but is returned as a flattened array to work with the solvers. r(r)r*Nr() r,rrrhr9rrXr:flattenrWrr firstterms r0rz MNLogit.score s2#66K!""% 282:2:););;<11QRR4)AA vik49--55777r2c||jdd}|tj|j|}tj|jtj|z}|jddddf|ddddfz }tj|j |j }||fS)z Returns log likelihood and score, efficiently reusing calculations. Note that both of these returned quantities will need to be negated before being minimized by the maximum likelihood fitting machinery. r(r)r*Nr() r,rrhr9rrXrrrYr:r)rWrrcdf_dot_exog_params loglike_valuer score_arrays r0loglike_and_scorezMNLogit.loglike_and_score7 s#66"hhrvdi'@'@AAt{RV4G-H-HHII K122&)> k))r2cf||jdd}|jddddf|t j|j|ddddfz }|dddddf|jdddddfz|jjddS)a\ Jacobian matrix for multinomial logit model log-likelihood Parameters ---------- params : ndarray The parameters of the multinomial logit model. Returns ------- jac : array_like The derivative of the loglikelihood for each observation evaluated at `params` . Notes ----- .. math:: \frac{\partial\ln L_{i}}{\partial\beta_{j}}=\left(d_{ij}-\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right)x_{i} for :math:`j=1,...,J`, for observations :math:`i=1,...,n` In the multinomial model the score vector is K x (J-1) but is returned as a flattened array. The Jacobian has the observations in rows and the flattened array of derivatives in columns. r(r)r*Nr(r )r,rrrhr9rrXr8rs r0rzMNLogit.score_obsE s2#66K!""% 282:2:););;<11QRR4)AA !!!AAAd(#di$qqq&99BB49?STCUWYZZZr2c R||jdd}|j}|t j||}g}|j}|j}t|dz D]}t|dz D]}||kr\|t j|dd|dzfd|dd|dzfz zdddf|zj | d|t j|dd|dzf|dd|dzf zdddf|zj | t j |} t j | |dz |dz ||d|dz |z|dz |z} | S)a Multinomial logit Hessian matrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (J*K, J*K) The Hessian, second derivative of loglikelihood function with respect to the flattened parameters, evaluated at `params` Notes ----- .. math:: \frac{\partial^{2}\ln L}{\partial\beta_{j}\partial\beta_{l}}=-\sum_{i=1}^{n}\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\left[\boldsymbol{1}\left(j=l\right)-\frac{\exp\left(\beta_{l}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right]x_{i}x_{l}^{\prime} where :math:`\boldsymbol{1}\left(j=l\right)` equals 1 if `j` = `l` and 0 otherwise. The actual Hessian matrix has J**2 * K x K elements. Our Hessian is reshaped to be square (J*K, J*K) so that the solvers can use it. This implementation does not take advantage of the symmetry of the Hessian and could probably be refactored for speed. r(r)r*r(N)r r%r(r@) r,rrXrhr9rrr7rr:rr;) rWrrrgprpartialsrrr.rMrs r0rzMNLogit.hessiand s:#66 I XXbfQv&& ' ' F Fqs U UA1Q3ZZ U U66OO"QQQqsU)Qr!!!AaC%y["9111T6!B1!D GJJJLLLLOORVb1Q3iAAAacE .BAAAdF-KA-M,PQR%S%S$STTTT  U HX   L1Q3!Q22L A A I I1Q3PQ'TUVWTWYZSZ [ [r2r)rrrrMrrrrrTrkrhrrrrrrrrs@r0rr s(P D3oEFFQ T " " " " " """" &&&,###@   D888> * * *[[[>-------r2rceZdZdejdejzezdzZ d*fd Zd Z d Z d Z d+d Z dZ dZdZdZdZd+dZdZdZdZdZdZeejj d,dZeedZd-dZ d.fd! Z d/fd( Zeej jd0d)Z xZ!S)1ra Negative Binomial Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. References ---------- Greene, W. 2008. "Functional forms for the negative binomial model for count data". Economics Letters. Volume 99, Number 3, pp.585-590. Hilbe, J.M. 2011. "Negative binomial regression". Cambridge University Press. a>loglike_method : str Log-likelihood type. 'nb2','nb1', or 'geometric'. Fitted value :math:`\mu` Heterogeneity parameter :math:`\alpha` - nb2: Variance equal to :math:`\mu + \alpha\mu^2` (most common) - nb1: Variance equal to :math:`\mu + \alpha\mu` - geometric: Variance equal to :math:`\mu + \mu^2` offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1. rnb2NrVTc tj||f||||d|||_||dvr"|jdd|_nd|_|jddS)Nr)rnb1rr(r loglike_method)rSrTr _initializerrrV _init_keys) rWr<rXrrrXrrYrZr[s r0rTzNegativeBinomial.__init__ s # &"*!($.  # # "  # # #-  ^ + + O " "7 + + +DLLDL /00000r2cb|jdkr-|j|_|j|_|j|_d|_dS|jdkr-|j|_|j |_|j |_d|_dS|jdkr&|j |_|j |_|j |_dStd)NrTr geometricz0Likelihood type must "nb1", "nb2" or "geometric")r _hessian_nb2r _score_nbinr_ll_nb2rr _hessian_nb1 _score_nb1_ll_nb1 _hessian_geom _score_geom _ll_geometricrLrs r0rzNegativeBinomial._initialize s  % ' ',DL)DJ"lDO $D     E ) ),DLDJ"lDO $D     K / /-DL)DJ"0DOOO.// /r2cJ|j}|d=|d=|d=|S)Nrrr)rcopy)rWodicts r0 __getstate__zNegativeBinomial.__getstate__ s1 ""$$ )  'N ,  r2cb|j||dSr)rrr)rWindicts r0 __setstate__zNegativeBinomial.__setstate__$ s0 V$$$ r2r ctjtj|stj|rt}nt}|j}||}d|z ||zz}|||zz }|||z||dzz ||z } | |tj|zz|tjd|z zz} | S)Nr()r9r iscomplexrrr<rnrY) rWrrrQgamma_lnr<rrrcoeffllfs r0_ll_nbinzNegativeBinomial._ll_nbin( s 6",v&& ' ' 2<+>+> HHH  \\& ! !wQT"W~$u*%%q(9(99$ d26$<<''%qv*>> r2c|jrtj|d}n|d}||dd|dS)Nr(r rrr9r6rrWrrrs r0rzNegativeBinomial._ll_nb26 K   F6":&&EE2JE}}VCRC[%1}555r2c|jrtj|d}n|d}||dd|dS)Nr(r(rrrs r0rzNegativeBinomial._ll_nb1= rr2c0||ddSNr(r )rrs r0rzNegativeBinomial._ll_geometricD s}}VQ***r2cTtj||}|S)a Loglikelihood for negative binomial model Parameters ---------- params : array_like The parameters of the model. If `loglike_method` is nb1 or nb2, then the ancillary parameter is expected to be the last element. Returns ------- llf : float The loglikelihood value at `params` Notes ----- Following notation in Greene (2008), with negative binomial heterogeneity parameter :math:`\alpha`: .. math:: \lambda_i &= exp(X\beta) \\ \theta &= 1 / \alpha \\ g_i &= \theta \lambda_i^Q \\ w_i &= g_i/(g_i + \lambda_i) \\ r_i &= \theta / (\theta+\lambda_i) \\ ln \mathcal{L}_i &= ln \Gamma(y_i+g_i) - ln \Gamma(1+y_i) + g_iln (r_i) + y_i ln(1-r_i) where :math`Q=0` for NB2 and geometric and :math:`Q=1` for NB1. For the geometric, :math:`\alpha=0` as well. r)rWrrrs r0rzNegativeBinomial.loglikeH s%BfT__V,,-- r2c|j}|jdddf}||dddf}|||z z|dzz }|dSr)rXr<rnr)rWrrrXrArr6s r0rzNegativeBinomial._score_geoml say Jqqq$w  \\& ! !!!!T' *!B$-A&{{1~~r2c|jrtj|d}n|d}|dd}|j}|jdddf}||dddf}d|z ||zz}|||zz }|dkrt ||zt |z } ||ztj|| zz} |||tj|zz || dzzz z|tj|| zzz |dz|dzzz } n|dkrt ||zt |z } ||z||z z||zz } |dz } | tj|ztj||zz ||z ||zz z | z} |jr*tj | d| |zfStj | d| fS)z, Score vector for NB2 model r(Nr(r%r ) rr9r6rXr<rnrrYrr_) rWrrrrrXrArrrdgpartr6r5da1s r0rzNegativeBinomial._score_nbins s'   F6":&&EE2JEy Jqqqv  \\& ! !!!!D& ) uWr1u_R"W~ 66QV__wr{{2FRi26$<<$GB$5 5 &1*o!./RVD\\!"##q%!), .03suu F !VVQV__wr{{2F2g2&2.G"9*Crvbzz)&B--(+,R4"R%.9:=#%%#FF   15Q56 65Q/0 0r2c0||dS)Nr(r)rrs r0rzNegativeBinomial._score_nb1 s!,,,r2c |j}|jdddf}||dddf}|jd}t j||f}|d|zz|dzdzz }t |D]e}t |D]S} | |kr t jt j|dd|df |dd| dfz|zd||| f<Tft j |d} |j | || <|S)Nr(r%r r4rA) rXr<rnr8r9rEr7rFrrGr:) rWrrrXrArrIrJ const_arrr.rMrLs r0rzNegativeBinomial._hessian_geom s8y Jqqqv  \\& ! !!!!D& )jm8S#J''!HbdQY& s  A3ZZ  q55 " FD1TN?T!!!Ad(^;iG !!!1  /#+++$Jw/r2c |jrtj|d}n|d}|dd}|j}|jdddf}||dddf}||z }t ||zt |z }dd|zz }|jd} tj| dz| dzf} ||z tj ||zz} ||z} ||z} tj d||ztj d|z }t| D]}t| D]n}||kr tj tj| dd|df| dd|dfz| dd|df| dd|dfz|zzd| ||f<otj| d}| j|| |<tj| | z||z| |z|dzz |z zzd}|| dddf<|| dddf<tj |}|dz}|dz}|dz}||zd|zd|zzdzzd|z|zz d |z|z||zzz|d|z|z zzd|z|z|zz||zz||z|zzd|z|z||zzz|d z|d|zzdzzz }|| d <| S) z' Hessian of NB1 model. r(Nr(r r4rAr%r@rD)rr9r6rXr<rnrr8rErYrrr7rFrrGr:)rWrrrrXrArrrrrIrJr6r4 xmu_alphatrigammar.rMrLrM log_alphaalpha3alpha2mu2dadas r0rzNegativeBinomial._hessian_nb1 s   F6":&&EE2JEy Jqqqv  \\& ! !!!!D& ) XR72;;.AIjm8SU3q5M**,"&,,"(#)*R2I %aa00%a,,-s  A3ZZ  q55 " F!D)E!!!Ad(O;!!!!Ad(+i!D.AAHLM!!1  /#+++$Jw/g r "2eQh.5)77=>@@@"CRC!"RF4LL !eAiK!F(2Q676!6"i&0121R4!8$%5X% &),h 7:@#9P Q 5Y/0 1 1Hfqw.23 5((**r2c |jrtj|d}n|d}d|z }|dd}|j}|jdddf}||dddf}|||zz }t ||zt |z }|jd} tj| dz| dzf} ||z||zz||zdzz } t| D]e} t| D]S} | | kr tj |dd| df |dd| dfz| zd | | | f<Tftj | d}| j || |<|dz }tj ||z||z z|dzz||zdzz d }|| dddf<|| dddf<d|d zz}||tj|z||z ||zz z z}||z|z |dztjd||ztjd|z d|z zd||zz z ||z ||zdzz zzz }|| d <| S) z' Hessian of NB2 model. r(r(Nr%r r4rArrD)rr9r6rXr<rnrr8rEr7rrFrGr:rYrr)rWrrrrrXrArrrrIrJrr.rMrLrrMda2r5rs r0rzNegativeBinomial._hessian_nb2 s   F6":&&EE2JE uWy Jqqqv  \\& ! !!!!D& )R"W~a72;;.jm8SU3q5M**rE2a4L"R%!+ s D DA3ZZ D Dq55 "QQQqXaaa$h'G'0(178!:!:!::A'))1  D /#+++$Jw/byj&D!B$A-r"uqj8BBBB!CRC!"Rr kF4LL!$%FRU#345f S 36W->q"Q$-G-G%a,,.-/0t.467bk.BVb2g\).*$++,/CEE r2c0t||j}|Sr)rr)rWrrscs r0rzNegativeBinomial.score_obs's fdo 6 6 r2rcR|"d}tj|t|durd}|dkr|||||} |0t jdt j|jdz}nt j|}|j dksJ|d}| |j S| ||| \}}}t j ||d|jd} | |z|z} |d krt j| S|d r| S|d kr^t j| } |jd kr | d| zz} n4|jdkrd}n |jdkrd}|d}| d|| |dz zzzz} | St%d)NrTrrrr r().N)rXrrXrrgrrrr%rr(rh)rprqrrr9rrr<r:r5rTr:rerr8r6rirrL)rWrrrXrXrrrrrurrjrrrrrs r0rnzNegativeBinomial.predict+s  DC M#} - - -~~  F??))! *E 9Qtz(:(:Q(>??:h//=A%%%% *H99X&&( (!%!9!9":""fh f^djm^4558#f, F??6'?? 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" " " " " " !!!///"!!!F*&*&*&X,****XIIIV; ; ; zX)**   +*  Xm'((<>BG7;"99999)(9vXm+3448tj||||||||}|S)N) exog_extraparams_constrained hypothesisrr k_constraintsobserved)r\ score_test) rWrfrgrhrrrirjrs r0rkzDiscreteResults.score_test5s73E+5)1H.;)1 333  r2rFc \|durd}| } ||| d<tj|||||||| } | S)a7 Compute prediction results when endpoint transformation is valid. Parameters ---------- exog : array_like, optional The values for which you want to predict. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. which : str Which statistic is to be predicted. Default is "mean". The available statistics and options depend on the model. see the model.predict docstring linear : bool Linear has been replaced by the `which` keyword and will be deprecated. If linear is True, then `which` is ignored and the linear prediction is returned. row_labels : list of str or None If row_lables are provided, then they will replace the generated labels. average : bool If average is True, then the mean prediction is computed, that is, predictions are computed for individual exog and then the average over observation is used. If average is False, then the results are the predictions for all observations, i.e. same length as ``exog``. agg_weights : ndarray, optional Aggregation weights, only used if average is True. The weights are not normalized. y_values : None or nd_array Some predictive statistics like which="prob" are computed at values of the response variable. If y_values is not None, then it will be used instead of the default set of y_values. **Warning:** ``which="prob"`` for count models currently computes the pmf for all y=k up to max(endog). This can be a large array if the observed endog values are large. This will likely change so that the set of y_values will be chosen to limit the array size. **kwargs : Some models can take additional keyword arguments, such as offset, exposure or additional exog in multi-part models like zero inflated models. See the predict method of the model for the details. Returns ------- prediction_results : PredictionResults The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary dataframe for the prediction. Notes ----- Status: new in 0.14, experimental TrNr)rXrr row_labelsaverage agg_weights pred_kwds)r#get_prediction) rWrXrrrrmrnrorrZrprs r0rqzDiscreteResults.get_predictionCs^H T>>E  $,Ij !! !#    r2c |||\}}|tj|}|jj|jfd|i|}|S)N)rrX)_transform_predict_exogr9r:r6rrr)rWrXrrZ_rs r0rz DiscreteResults.get_distributionsi..ty.IIa  :d##D+ +DK..15..4.. r2cB| |jj}| |jj}||fSr)r6r)rWrE yname_lists r0_get_endog_namezDiscreteResults._get_endog_names, =J*E  /Jj  r2overallrczt|jddtdddlm}|||||||fS)a Get marginal effects of the fitted model. Parameters ---------- at : str, optional Options are: - 'overall', The average of the marginal effects at each observation. - 'mean', The marginal effects at the mean of each regressor. - 'median', The marginal effects at the median of each regressor. - 'zero', The marginal effects at zero for each regressor. - 'all', The marginal effects at each observation. If `at` is all only margeff will be available from the returned object. Note that if `exog` is specified, then marginal effects for all variables not specified by `exog` are calculated using the `at` option. method : str, optional Options are: - 'dydx' - dy/dx - No transformation is made and marginal effects are returned. This is the default. - 'eyex' - estimate elasticities of variables in `exog` -- d(lny)/d(lnx) - 'dyex' - estimate semi-elasticity -- dy/d(lnx) - 'eydx' - estimate semi-elasticity -- d(lny)/dx Note that tranformations are done after each observation is calculated. Semi-elasticities for binary variables are computed using the midpoint method. 'dyex' and 'eyex' do not make sense for discrete variables. For interpretations of these methods see notes below. atexog : array_like, optional Optionally, you can provide the exogenous variables over which to get the marginal effects. This should be a dictionary with the key as the zero-indexed column number and the value of the dictionary. Default is None for all independent variables less the constant. dummy : bool, optional If False, treats binary variables (if present) as continuous. This is the default. Else if True, treats binary variables as changing from 0 to 1. Note that any variable that is either 0 or 1 is treated as binary. Each binary variable is treated separately for now. count : bool, optional If False, treats count variables (if present) as continuous. This is the default. Else if True, the marginal effect is the change in probabilities when each observation is increased by one. Returns ------- DiscreteMargins : marginal effects instance Returns an object that holds the marginal effects, standard errors, confidence intervals, etc. See `statsmodels.discrete.discrete_margins.DiscreteMargins` for more information. Notes ----- Interpretations of methods: - 'dydx' - change in `endog` for a change in `exog`. - 'eyex' - proportional change in `endog` for a proportional change in `exog`. - 'dyex' - change in `endog` for a proportional change in `exog`. - 'eydx' - proportional change in `endog` for a change in `exog`. When using after Poisson, returns the expected number of events per period, assuming that the model is loglinear. rNz&Margins with offset are not available.r )DiscreteMargins)rdr6re%statsmodels.discrete.discrete_marginsrz)rWatrKatexogdummycountrzs r0 get_margeffzDiscreteResults.get_margeffsWP 4:x . . :%&NOO OIIIIIItb&&%%GHHHr2c$ddlm}||Sam Get an instance of MLEInfluence with influence and outlier measures Returns ------- infl : MLEInfluence instance The instance has methods to calculate the main influence and outlier measures as attributes. See Also -------- statsmodels.stats.outliers_influence.MLEInfluence r ) MLEInfluence$statsmodels.stats.outliers_influencerrWrs r0 get_influencezDiscreteResults.get_influence' FEEEEE|D!!!r2rc ^dd|jjjgfd|jgfdddd|jdzgfg}d d d d d |jzgfddd|jzgfdd |jzgfg}t|dr| d|j gf||jjjdzdz}ddl m }|} | ||\}}| ||||||| |||||jt|dr| dg| S)am Summarize the Regression Results. Parameters ---------- yname : str, optional The name of the endog variable in the tables. The default is `y`. xname : list[str], optional The names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model. title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. Returns ------- Summary Class that holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : Class that hold summary results. )zDep. Variable:NzModel:zMethod:)zDate:N)zTime:Nz converged:z%sr)zNo. Observations:N)z Df Residuals:N)z Df Model:NzPseudo R-squ.:z%#6.4g)zLog-Likelihood:NzLL-Null:z%#8.5gz LLR p-value:rzCovariance Type:N zRegression Resultsr )Summary)gleftgrightrExnametitle)rErrrr@Model has been estimated subject to linear equality constraints.)r6r[rrKrr=r<rCrrrstatsmodels.iolib.summaryrrwadd_table_2colsadd_table_paramsr add_extra_txt) rWrErrrrvtop_left top_rightrsmrys r0summaryzDiscreteResults.summary s:-!5!> ?@$+/$$"TD,<[,I%I$JK 1,(&DN)B(CD. 8dk#9":;$x$/'A&BC   4 $ $ C OO/$-A B B B =J(1C7:NNE 655555wyy 00 CCz T)#(U  D D D d*E$(J  0 0 0 4 ' ' :   !8 9 : : : r2%.4fcddlm}|}|||||||t |dr|d|S)a Experimental function to summarize regression results. Parameters ---------- yname : str Name of the dependent variable (optional). xname : list[str], optional List of strings of length equal to the number of parameters Names of the independent variables (optional). title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. float_format : str The print format for floats in parameters summary. Returns ------- Summary Instance that contains the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : Class that holds summary results. r summary2)resultsr float_formatrrErrr)statsmodels.iolibrradd_baseradd_text)rWrErrrrrrs r0rzDiscreteResults.summary2Ss< /.....!! d%l!e  = = = 4 ' ' 3 MM2 3 3 3 r2)rNNrr )NNrdNNNT)NTrNNFNN)rxrNFFNNNrN)NNNrr)rrr_discrete_results_docsrrTrrr=r?rCrIr<rtrSrUrXrZr]rcrkr\rqrrwrrrrr+r2r0r-r-Bs$E((GFJ7777>((^( ++^+ DD^D''''''''R++^+ZOO^O 11^133^3==^=MM^M%%^%'N'N'N'NR>B?C04     *2J"&<@0526WWWWr    !!!?C$KIKIKIKIZ""""ADEEEENBE$''''''r2r-c<eZdZedddzZedZddZdS)rvzA results class for count datar.r/cD|jj|z S)z Residuals Notes ----- The residuals for Count models are defined as .. math:: y - p where :math:`p = \exp(X\beta)`. Any exposure and offset variables are also handled. rRrs r0rzCountResults.residsz$,,..00r2Nc(ddlm}|||S)a Get instance of class with specification and diagnostic methods. experimental, API of Diagnostic classes will change Returns ------- CountDiagnostic instance The instance has methods to perform specification and diagnostic tesst and plots See Also -------- statsmodels.statsmodels.discrete.diagnostic.CountDiagnostic r )CountDiagnosticy_max)statsmodels.discrete.diagnosticr)rWrrs r0get_diagnosticzCountResults.get_diagnostics, DCCCCCt51111r2r)rrrrrrrrr+r2r0rvrv}s]$ @((G 1 1^ 1222222r2rvcveZdZedddzZedZedZedZedZ dS) rz,A results class for NegativeBinomial 1 and 2r.r/c@tj|jdS)zNatural log of alphar()r9rYrrrs r0lnalphazNegativeBinomialResults.lnalphasvdk"o&&&r2c8|jd|jdz S)z!Natural log of standardized errorr()bserrrs r0lnalpha_std_errz'NegativeBinomialResults.lnalpha_std_errsx|dk"o--r2cht|jdd}d|j|j|jz|zz zSNrVr r)rdr6rr_ k_constantrWs r0rXzNegativeBinomialResults.aics7$*i3348t}t>HIJJr2ct|jdd}d|jztj|j|j|jz|zzzSr)rdr6rr9rYr8r_rrWs r0rZzNegativeBinomialResults.bicsX$*i33$({RVDI.. 041@BI1JKK Kr2N) rrrrrrrrrXrZr+r2r0rrs$ N((G''^'..^.KK^K KK^KKKr2rceZdZedddzZdS)r!z%A results class for NegativeBinomialPr.r/Nrrrrrr+r2r0r!r!s($ G((GGGr2r!c4eZdZedddzZedZdS)rz'A results class for Generalized Poissonr.r/ct|jdd}|}d|jd||zzzdzS)Nrr r(r(r%)rdr6rnrr)rWrrs r0_dispersion_factorz,GeneralizedPoissonResults._dispersion_factorsB DJ 2A 6 6 \\^^DKOb!e++a//r2N)rrrrrrrr+r2r0rrsI$ I((G00^000r2rc.eZdZededzZfdZxZS)rzz7A results class for count data fit by l1 regularizationr/cft|||jd|_|j|_t |jdd}|jdz |z |_t|jj j d|jz |z|_ dS)NrrVr r() rSrTrrrrrdr6r_r;r<r8r`)rWr6rxrVr[s r0rTzL1CountResults.__init__s '''))4  L=--// $*i33!+g5 dj.4Q7$/IJJWT r2rrrr_l1_results_attrrrTrrs@r0rzrzs[$ E+(-(--G U U U U U U U U Ur2rzc>eZdZ ddZedZdZddZdS) rNTcD|tj|}nFtjtjdtj|jjdz}|||||ddddf}tj ||S)am Return predicted probability of each count level for each observation Parameters ---------- n : array_like or int The counts for which you want the probabilities. If n is None then the probabilities for each count from 0 to max(y) are given. Returns ------- ndarray A nobs x n array where len(`n`) columns are indexed by the count n. If n is None, then column 0 is the probability that each observation is 0, column 1 is the probability that each observation is 1, etc. Nr r(r)rXrXrrr) r9rrrr6r<rnrrrT)rWnrXrXrrcountsrs r0 predict_probzPoissonResults.predict_probs( =]1%%FF]29Qtz7G0H0H0J#K#KLLF \\thv$-V===>QQtVE}  ,,,r2cr|}|jj|z tj|z S)l Pearson residuals Notes ----- Pearson residuals are defined to be .. math:: r_j = \frac{(y - M_jp_j)}{\sqrt{M_jp_j(1-p_j)}} where :math:`p_j=cdf(X\beta)` and :math:`M_j` is the total number of observations sharing the covariate pattern :math:`j`. For now :math:`M_j` is always set to 1. )rnr6r<r9r)rWrs r0rUzPoissonResults.resid_pearson s." LLNN  1$bgajj00r2c$ddlm}||Srrrs r0rzPoissonResults.get_influencerr2c(ddlm}|||S)a Get instance of class with specification and diagnostic methods experimental, API of Diagnostic classes will change Returns ------- PoissonDiagnostic instance The instance has methods to perform specification and diagnostic tesst and plots See Also -------- statsmodels.statsmodels.discrete.diagnostic.PoissonDiagnostic r )PoissonDiagnosticr)rr)rWrrs r0rzPoissonResults.get_diagnostic.s6         U3333r2)NNNNTr)rrrrpropertyrUrrr+r2r0rrslDH#----:11X1&""""444444r2rceZdZdS)rNrrrr+r2r0rrCDr2rceZdZdS)rNrr+r2r0rrFrr2rceZdZdS)r+Nrr+r2r0r+r+Irr2r+ceZdZedddzZdS)OrderedResultsz*A results class for ordered discrete data.r.r/Nrr+r2r0rrLs0$Am@B(C(CCGDr2rceZdZedddzZd dZeejj d fd Ze d Z e d Z e d Z xZ S) BinaryResultszA results class for binary datar.r/?c|j}|j}tj||kt }tjgd}tj|||dS)a Prediction table Parameters ---------- threshold : scalar Number between 0 and 1. Threshold above which a prediction is considered 1 and below which a prediction is considered 0. Notes ----- pred_table[i,j] refers to the number of times "i" was observed and the model predicted "j". Correct predictions are along the diagonal. r3)r rr(binsr )r6r<r9rrnr; histogram2d)rW thresholdr6actualr#rs r0 pred_tablezBinaryResults.pred_tableSsb x 2%@@@x $$~fd666q99r2Nrc>t|||||}|j|j}t j|jj|z }|dk} | t|z } g} | t|kr,d} | dz } | dz } | dz } | dz } | | n4| dkr.d} | d | zz } | d z } | d z } | d z } | | | r| | |S) Nrz3Complete Separation: The results show that there isz+complete separation or perfect prediction. z3In this case the Maximum Likelihood Estimator does znot exist and the parameters zare not identified.r*z/Possibly complete quasi-separation: A fraction z%4.2f of observations can be z4perfectly predicted. This might indicate that there z0is complete quasi-separation. In this case some z"parameters will not be identified.) rSrr6rhrtr9rr<rr"rr)rWrErrrrvrrt absprederror predclose_sumpredclose_fracetextwstrr[s r0rzBinaryResults.summaryhsRwwueUE2<>>z~~d&788 vdj.=>> %,1133 &\):):: C -- - -HD B BD I ID 4 4D ) )D LL     c ! !DD 4~E ED J JD G GD 8 8D LL     &   u % % % r2c ^|jj}d}|}d|z tjd|ztjtjd|z zz|tjd|ztjtj|zzz}|S)a Deviance residuals Notes ----- Deviance residuals are defined .. math:: d_j = \pm\left(2\left[Y_j\ln\left(\frac{Y_j}{M_jp_j}\right) + (M_j - Y_j\ln\left(\frac{M_j-Y_j}{M_j(1-p_j)} \right) \right] \right)^{1/2} where :math:`p_j = cdf(X\beta)` and :math:`M_j` is the total number of observations sharing the covariate pattern :math:`j`. For now :math:`M_j` is always set to 1. r(r%)r6r<rnr9rrrY)rWr<Mrrs r0 resid_devzBinaryResults.resid_devs(    LLNN%j1RVBF1Q3KK%8%8!8999bgac"&"3"334445 r2c|jj}d}|}|||zz tj||zd|z zz S)rr()r6r<rnr9r)rWr<rrs r0rUzBinaryResults.resid_pearsonsK$    LLNN! RWQqS!A#Y////r2cD|jj|z S)z The response residuals Notes ----- Response residuals are defined to be .. math:: y - p where :math:`p=cdf(X\beta)`. rRrs r0rSzBinaryResults.resid_responsesz$,,..00r2)rr)rrrrrrr r-rrrrUrSrrs@r0rrPs$Absu'v'vvG::::*Xo%-..@C/.:^@00^04 1 1^ 1 1 1 1 1r2rc:eZdZedddzZedZdZdS)rzA results class for Logit Modelr.r/cD|jj|z S)a  Generalized residuals Notes ----- The generalized residuals for the Logit model are defined .. math:: y - p where :math:`p=cdf(X\beta)`. This is the same as the `resid_response` for the Logit model. rRrs r0resid_generalizedzLogitResults.resid_generalizedsz$,,..00r2c$ddlm}||Srrrs r0rzLogitResults.get_influencerr2N)rrrrrrrrr+r2r0rrsX$ A((G11^1 """""r2rc4eZdZedddzZedZdS)rz A results class for Probit Modelr.r/c|j}|j}|d}||}||}||z|z d|z |zd|z z z S)z Generalized residuals Notes ----- The generalized residuals for the Probit model are defined .. math:: y\frac{\phi(X\beta)}{\Phi(X\beta)}-(1-y)\frac{\phi(X\beta)}{1-\Phi(X\beta)} rrr()r6r<rnrkrh)rWr6r<rrkrhs r0rzProbitResults.resid_generalizedsg   \\\ ) )iimmiimms{3!E'3#!666r2N)rrrrrrrr+r2r0rrsI$ B((G77^777r2rc.eZdZededzZfdZxZS)rz9Results instance for binary data fit by l1 regularizationr/c.t|||jd|_|j|_|jdz |_t|jj j d|jz |_ dSNrr(r ) rSrTrrrrr_r;r6r<r8r`)rWr6rr[s r0rTzL1BinaryResults.__init__sz (((*95  L=--//!+ dj.4Q7$/IJJ r2rrs@r0rrs[$?#(%(%%GKKKKKKKKKr2rceZdZedddzZfdZedZddZdZ e d Z e d Z e d Z dfd ZdZdZe dZddZxZS)r-z$A results class for multinomial datar.r/c|t|||j|_|j|_dSr)rSrTrrrWr6rr[s r0rTzMultinomialResults.__init__$s3 '''r2c@d}d}|D]z} ||dzdkr&tt||||<nd}t||||<S#t$rt||||<YwwxYw|rtj|t |S)NFzendog contains values are that not int-like. Uses string representation of value. Use integer-valued endog to suppress this warning.r(r T)strr7rrprqr!)r> issue_warningrur.s r0rz,MultinomialResults._maybe_convert_ynames_int)s ( + +A +!9q=A%% #Cq NN 3 3F1II$(M #F1IF1I + + +q NNq  +  5 M#3 4 4 4 sAA"A?>A?Fc|j}|j|f|j|fdt t |jDfdD|s dd}n}|fS)zE If all is False, the first variable name is dropped Nc g|] }| Sr+r+rs r0rKz6MultinomialResults._get_endog_name..IsAAAcfSkAAAr2c>g|]}d|gS)=)join)r-rCrEs r0rKz6MultinomialResults._get_endog_name..Js)AAA$chht}--AAAr2r()r6rrrr7r7r)rWrErvrr6r>s ` @r0rwz"MultinomialResults._get_endog_name>s  =%E  &F33F;;FAAAAU3uw<<-@-@AAAFAAAA&AAAF $#ABBZ # j  r2c|jjdz }tjdgtjd|dz ||gf}tj|jj|d|dS)z Returns the J x J prediction table. Notes ----- pred_table[i,j] refers to the number of times "i" was observed and the model predicted "j". Correct predictions are along the diagonal. r(r rr) r6rr9r@linspacerr<rnr)rWjurs r0rzMultinomialResults.pred_tableQsZ\A ~sBKR#Xr$B$BRDIJJ~dj. 0E0Ea0H0H#'))))*, ,r2ctjtj|}||jjdS)Nr)r*)r9rdiagrr,rrr8)rWrs r0rzMultinomialResults.bseas@gbgdoo//0011{{4;,C{888r2cFd|j|j|jjzdz z zSNrr()rr_r6rrs r0rXzMultinomialResults.aicfs$48t}TZ\9!;<==r2czd|jztj|j|j|jjzdz zzSr)rr9rYr8r_r6rrs r0rZzMultinomialResults.bicjs4$({RVDI.. djl0J10LMMMr2rNctt|||}|dddS)N)rcolsr%r r()rSr-conf_intr;)rWrrconfintr[s r0rzMultinomialResults.conf_intnsF..77eAE8GG  1Q'''r2ct)z(Not implemented for Multinomial rdrs r0rqz!MultinomialResults.get_predictionsrRr2c td)NzUse get_margeff insteadrdrs r0rzMultinomialResults.margeffxs!";<<r;rs r0resid_misclassifiedz&MultinomialResults.resid_misclassified{sH& !((++ %%a(()*0&-- 8r2rc ddlm}|}||||jjd}||}t|D]}| ||jdd|f|j dd|f|j dd|f|j dd|f||f|}|j jdzt|z} |j|| <|jddgdf}||dd | || |S) a8Experimental function to summarize regression results Parameters ---------- alpha : float significance level for the confidence intervals float_format : str print format for floats in parameters summary Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results r rr(Nrz = )r(r r(r%r@rFT)indexheaderr)r)rrradd_dict summary_modelrrr8rr7summary_paramsrtvaluespvaluesr6rrr rBadd_df add_title) rWrrrreqnrr.r level_strs r0rzMultinomialResults.summary2ss* /.....!! h,,T22333k"--&&s ) )A++T4;qqq!t3D-1Xaaad^-1\!!!Q$-?-1\!!!Q$-?-4QZ -9 38 ,99E/%7#a&&@I${E) Jqqq"8"8"889E KKU4%1  3 3 3 NN4N ( ( ( ( r2)F)rN)rr)rrrrrrT staticmethodrrwrrrrXrZrrqrr rrrs@r0r-r- sQ$ 22(G(GGG \(!!!!&,,, 99^9>>^>NN^N(((((( """ ===88^8*))))))))r2r-c.eZdZededzZfdZxZS)r1z=A results class for multinomial data fit by l1 regularizationr/cHt|||jd|_|j|_|j|jjdz z |_t|jj j d|jz |_ dSr) rSrTrrrrr6rr_r;r<r8r`rs r0rTzL1MultinomialResults.__init__s '''))4  L=--//4:#J#)++KKKr2rceZdZdS)rNrr+r2r0rr$rr2rceZdZddiZejejjeZddiZ ejejj e Z dS)r.r r&rmultivariate_confintN) rrrr'r(r)r*r+r,_methods _wrap_methodsr+r2r0r.r.+sa#V ,F"$"2#>#J#)++K23H$D$R%@%N%-//MMMr2r.ceZdZdS)r2Nrr+r2r0r2r27rr2r2)yr__all__statsmodels.compat.pandasr rpnumpyr9pandasr r scipyrr scipy.specialrrrr scipy.statsrstatsmodels.base.datarstatsmodels.base.l1_slsqprstatsmodels.base.modelrr6statsmodels.base.wrapperwrapperr(rr%statsmodels.base._parameter_inference_parameter_inferencer\statsmodels.baserr#statsmodels.distributionsr#statsmodels.regression.linear_model regression linear_modelr*statsmodels.toolsrr rstatsmodels.tools.decoratorsrrbrstatsmodels.tools.sm_exceptionsrr r!cvxoptr ImportErrorfinfor;epsrrYr\rr_discrete_models_docsrrrrr?rFrNrrPrrr rrrrrrrLikelihoodModelResultsr-rvrr!rrzrrrr+rrrrrr-r1r+rpopulate_wrapperrwrr"rrr{rrr,rrr.r2r+r2r0rPs " D D D/.....******** ????????????------222222%%%%%%%%%'''''''''>>>>>>666666666::::::22222200000000077777777777777666666MMMKKKKK BHUOO  "&"*--122S8 .O  ! ! !((($III,dddddD(dddN ZZZZZ-ZZZzn"n"n"n"n"{n"n"n"b~2~2~2~2~2~2~2~2Htttttjtttn@ @ @ @ @ @ @ @ FbbbbbKbbbJ y*y*y*y*y*[y*y*y*x OOOOOOOO\ lllllzlll^~~~~~ ~~~Fxxxxxd1xxxv&2&2&2&2&2?&2&2&2RKKKKKlKKK:6 0 0 0 0 0 7 0 0 0UUUUU_UUU*V4V4V4V4V4\V4V4V4r     ~~        0G        .2K        _   11111O111D%"%"%"%"%"=%"%"%"P77777M7770 K K K K Km K K KZZZZZZZZz K K K K K- K K K$     B7   +^<<<     "5   )<888     R%@   4-///     b&A   5.000     r'B   6/111     B7   +^<<<     B7        b9   -/?@@@     r'B   6/111     )D   81333+++++26+++*M:::     R8   ,o>>>///// ;////1CDDD     ""=   13GHHHHHsBB)(B)