M/PhdZddlmZddlZddlZddlmZddlm cm Z ddl m cm Z ddlmZddlmZddlm cmZddlmZmZmZddlmcmZddlmcmZ ddl!m"Z"m#Z#m$Z$dd l%m&Z&dd l'm(Z(m)Z)m*Z*dd l+m,Z,d d l-m.Z.ddgZ/dZ0GddZ1e1Z2e2j3Z4Gdde j5Z6e&ej7jZ8e89dGdde j:Z;Gdde j<Z=e j>e=e;e?dkrkddl@mAZAeAjBZCe6eCjDeCjEFZGeGHdZIeGHdZJdSdS)a Generalized linear models currently supports estimation using the one-parameter exponential families References ---------- Gill, Jeff. 2000. Generalized Linear Models: A Unified Approach. SAGE QASS Series. Green, PJ. 1984. "Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives." Journal of the Royal Statistical Society, Series B, 46, 149-192. Hardin, J.W. and Hilbe, J.M. 2007. "Generalized Linear Models and Extensions." 2nd ed. Stata Press, College Station, TX. McCullagh, P. and Nelder, J.A. 1989. "Generalized Linear Models." 2nd ed. Chapman & Hall, Boca Rotan. )AppenderN) LinAlgError)_prediction_inference)PredictionResultsMean)_plot_added_variable_doc_plot_ceres_residuals_doc_plot_partial_residuals_doc)cache_readonly cached_data cached_value) Docstring) DomainWarningHessianInversionWarningPerfectSeparationWarning) float_like)familiesGLMrcPtj||||dz||S)Nr)atolrtol)npallclose) criterion iterationrrs k/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/genmod/generalized_linear_model.py_check_convergencer=s2 ;y+Yy1}-E t - - --c.eZdZdZedZdZdS)_ModuleVariableNc|jSN)_valueselfs r use_bic_llfz_ModuleVariable.use_bic_llfFs {rc\|dvrtd|t|n||_dS)N)TFNzMust be True, False or None) ValueErrorboolr#r%vals rset_use_bic_llfz_ModuleVariable.set_use_bic_llfJs6 ) ) ):;; ;#&?d3iii r)__name__ __module__ __qualname__r#propertyr&r,rrr r CsA F X<<<<d!Z d?d#Z d@d$Zd%Z dAd,Z! dBfd. Z" dCd/Z# dDd3Z$d4Z%d8d5Z&xZ'S)Era' Generalized Linear Models GLM inherits from statsmodels.base.model.LikelihoodModel Parameters ---------- endog : array_like 1d array of endogenous response variable. This array can be 1d or 2d. Binomial family models accept a 2d array with two columns. If supplied, each observation is expected to be [success, failure]. 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 (models specified using a formula include an intercept by default). See `statsmodels.tools.add_constant`. family : family class instance The default is Gaussian. To specify the binomial distribution family = sm.family.Binomial() Each family can take a link instance as an argument. See statsmodels.family.family for more information. offset : array_like or None An offset to be included in the model. If provided, must be an array whose length is the number of rows in exog. exposure : array_like or None Log(exposure) will be added to the linear prediction in the model. Exposure is only valid if the log link is used. If provided, it must be an array with the same length as endog. freq_weights : array_like 1d array of frequency weights. The default is None. If None is selected or a blank value, then the algorithm will replace with an array of 1's with length equal to the endog. WARNING: Using weights is not verified yet for all possible options and results, see Notes. var_weights : array_like 1d array of variance (analytic) weights. The default is None. If None is selected or a blank value, then the algorithm will replace with an array of 1's with length equal to the endog. WARNING: Using weights is not verified yet for all possible options and results, see Notes. {extra_params} Attributes ---------- df_model : float Model degrees of freedom is equal to p - 1, where p is the number of regressors. Note that the intercept is not reported as a degree of freedom. df_resid : float Residual degrees of freedom is equal to the number of observation n minus the number of regressors p. endog : ndarray See Notes. Note that `endog` is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. exposure : array_like Include ln(exposure) in model with coefficient constrained to 1. Can only be used if the link is the logarithm function. exog : ndarray See Notes. Note that `exog` is a reference to the data so that if data is already an array and it is changed, then `exog` changes as well. freq_weights : ndarray See Notes. Note that `freq_weights` is a reference to the data so that if data is already an array and it is changed, then `freq_weights` changes as well. var_weights : ndarray See Notes. Note that `var_weights` is a reference to the data so that if data is already an array and it is changed, then `var_weights` changes as well. iteration : int The number of iterations that fit has run. Initialized at 0. family : family class instance The distribution family of the model. Can be any family in statsmodels.families. Default is Gaussian. mu : ndarray The mean response of the transformed variable. `mu` is the value of the inverse of the link function at lin_pred, where lin_pred is the linear predicted value of the WLS fit of the transformed variable. `mu` is only available after fit is called. See statsmodels.families.family.fitted of the distribution family for more information. n_trials : ndarray See Notes. Note that `n_trials` is a reference to the data so that if data is already an array and it is changed, then `n_trials` changes as well. `n_trials` is the number of binomial trials and only available with that distribution. See statsmodels.families.Binomial for more information. normalized_cov_params : ndarray The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1) offset : array_like Include offset in model with coefficient constrained to 1. scale : float The estimate of the scale / dispersion of the model fit. Only available after fit is called. See GLM.fit and GLM.estimate_scale for more information. scaletype : str The scaling used for fitting the model. This is only available after fit is called. The default is None. See GLM.fit for more information. weights : ndarray The value of the weights after the last iteration of fit. Only available after fit is called. See statsmodels.families.family for the specific distribution weighting functions. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.scotland.load() >>> data.exog = sm.add_constant(data.exog) Instantiate a gamma family model with the default link function. >>> gamma_model = sm.GLM(data.endog, data.exog, ... family=sm.families.Gamma()) >>> gamma_results = gamma_model.fit() >>> gamma_results.params array([-0.01776527, 0.00004962, 0.00203442, -0.00007181, 0.00011185, -0.00000015, -0.00051868, -0.00000243]) >>> gamma_results.scale 0.0035842831734919055 >>> gamma_results.deviance 0.087388516416999198 >>> gamma_results.pearson_chi2 0.086022796163805704 >>> gamma_results.llf -83.017202161073527 See Also -------- statsmodels.genmod.families.family.Family :ref:`families` :ref:`links` Notes ----- Note: PerfectSeparationError exception has been converted to a PerfectSeparationWarning and perfect separation or perfect prediction will not raise an exception by default. (changed in version 0.14) Only the following combinations make sense for family and link: ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Family ident log logit probit cloglog pow opow nbinom loglog logc ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Gaussian x x x x x x x x x inv Gaussian x x x binomial x x x x x x x x x Poisson x x x neg binomial x x x x gamma x x x Tweedie x x x ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Not all of these link functions are currently available. Endog and exog are references so that if the data they refer to are already arrays and these arrays are changed, endog and exog will change. statsmodels supports two separate definitions of weights: frequency weights and variance weights. Frequency weights produce the same results as repeating observations by the frequencies (if those are integers). Frequency weights will keep the number of observations consistent, but the degrees of freedom will change to reflect the new weights. Variance weights (referred to in other packages as analytic weights) are used when ``endog`` represents an an average or mean. This relies on the assumption that that the inverse variance scales proportionally to the weight--an observation that is deemed more credible should have less variance and therefore have more weight. For the ``Poisson`` family--which assumes that occurrences scale proportionally with time--a natural practice would be to use the amount of time as the variance weight and set ``endog`` to be a rate (occurrences per period of time). Similarly, using a compound Poisson family, namely ``Tweedie``, makes a similar assumption about the rate (or frequency) of occurrences having variance proportional to time. Both frequency and variance weights are verified for all basic results with nonrobust or heteroscedasticity robust ``cov_type``. Other robust covariance types have not yet been verified, and at least the small sample correction is currently not based on the correct total frequency count. Currently, all residuals are not weighted by frequency, although they may incorporate ``n_trials`` for ``Binomial`` and ``var_weights`` +---------------+----------------------------------+ | Residual Type | Applicable weights | +===============+==================================+ | Anscombe | ``var_weights`` | +---------------+----------------------------------+ | Deviance | ``var_weights`` | +---------------+----------------------------------+ | Pearson | ``var_weights`` and ``n_trials`` | +---------------+----------------------------------+ | Reponse | ``n_trials`` | +---------------+----------------------------------+ | Working | ``n_trials`` | +---------------+----------------------------------+ WARNING: Loglikelihood and deviance are not valid in models where scale is equal to 1 (i.e., ``Binomial``, ``NegativeBinomial``, and ``Poisson``). If variance weights are specified, then results such as ``loglike`` and ``deviance`` are based on a quasi-likelihood interpretation. The loglikelihood is not correctly specified in this case, and statistics based on it, such AIC or likelihood ratio tests, are not appropriate. ) extra_paramsNnonec jt|tur|| dg|qt|jt |jsJtjdt|jj dt|j dt|tj |}|tj |}|tj |}|tj |}||_||_t!j||f|||||d| |||j|j|j|j|j|t-|d|t-|d|jjd|_|jgd |jd |d| vr | d|_d } t?|dr|j} t?|dr | |jz} | |_ d|_!dS) Nn_trialszThe z2 link function does not respect the domain of the z family.)missingoffsetexposure freq_weights var_weightsr9r:r)weightsmur;r<iweights_offset_exposurer7family)"typer _check_kwargs isinstancelinktuple safe_linkswarningswarnr-rrlogasarrayr;r<super__init__ _check_inputsr9r:endogdelattrshapenobs _data_attrextend _init_keysappend_setup_binomialr7hasattrr@ scaletype) r%rPexogrAr9r:r;r<r8kwargsoffset_exposure __class__s rrNz GLM.__init__*s ::     v | 4 4 4   6;389J3K3K)M)M  M>$v{"3"3"<>>"6ll3>>>( ) ) )  vh''H  Z''F  #:l33L  "*[11K(& Eg)/(/;.9 E E>D E E E 64; tz,d.> @ @ @ > D( # # #   D* % % %J$Q'   , , , - - - x(((    ":.DM 4 " " *"kO 4 $ $ >- =O /rctj|jdz |_|j]|jjd|jjdkr7|j|_ |j |jz dz |_ dS|jjd|_ |jjd|jz dz |_ dS)z8 Initialize a generalized linear model. rNr) rlinalg matrix_rankr[df_modelr;rRrPsumwnobsdf_residr$s r initializezGLM.initializejs --di881<   )   #A &$**:1*= = =*..00DJ J6:DMMM+DJ IOA.>BDMMMrcv|tj}||_|ct|jjtjjstd|jd|jdkrtd|+|jd|jdkrtd|R|jd|jdkrtdt|jdkrtd|j du|_ |j $tj |jd|_ tj|j dkr7|j dkr,|j tj |jdz|_ |R|jd|jdkrtd t|jdkrtd |du|_|$tj |jd|_tj|j |jz|_dS) N4exposure can only be used with the log link functionrz(exposure is not the same length as endogz&offset is not the same length as endogz)freq weights not the same length as endogrz$freq weights has too many dimensionsr1z(var weights not the same length as endogz#var weights has too many dimensions)rGaussianrArErFlinksLogr(rRlenr;_has_freq_weightsrones_has_var_weightsr<rLr?)r%rAr9r:rPr;r<s rrOzGLM._check_inputsxs >&((F  dk.0BCC M "1222"ek!n44 !KLLL  |A%+a.00 !IJJJ  #!!$ A66 !LMMM<%&&** !GHHH#'"34"?   $ " A 7 7D  8D% & &" , ,1BQ1F1F!%!2!#Q!8!8"9D   " #u{1~55 !KLLL;$%%)) !FGGG"-D!8  !wu{1~66D  4#4t7G#GHH rct}d|vr%|dtj|d|d<|S)Nr:)rM_get_init_kwdsrexp)r%kwdsr^s rrqzGLM._get_init_kwdssMww%%''   $z"2">!vd:&677D  r?c|t|d}|j|j||j|j|S)M Evaluate the log-likelihood for a generalized linear model. scale)rrAloglikerPr<r;)r%r>rws r loglike_muzGLM.loglike_mus@5'**{""4:r43C#'#4e== =rc4t|dd}tj|j||jz}|jj|}|||}|j |j ||j |j |}|S)rvrwToptional) rrdotr[r@rArFinverseestimate_scalerxrPr<r;)r%paramsrwlin_predexpvalllfs rrxz GLM.loglikes5'D9996$)V,,t/DD!))(33 =''//Ek!!$*fd6F"&"3U<< rc|t|dd}|||}|dddf|jzS)agscore first derivative of the loglikelihood for each observation. 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 ------- score_obs : ndarray, 2d The first derivative of the loglikelihood function evaluated at params for each observation. rwTr{rwN)r score_factorr[r%rrwrs r score_obsz GLM.score_obssJ$5'D999((u(== AAAtG$ty00rct|dd}|||}tj||jS)aQscore, first derivative of the loglikelihood function 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 ------- score : ndarray_1d The first derivative of the loglikelihood function calculated as the sum of `score_obs` rwTr{r)rrrr}r[rs rscorez GLM.scoresD$5'D999((u(== vlDI...rcJt|dd}||}|||}|j|z |jj|z }||j|z}||j|j zz}|dks||z}|S)aweights for score for each observation This can be considered as score residuals. Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- score_factor : ndarray_1d A 1d weight vector used in the calculation of the score_obs. The score_obs are obtained by `score_factor[:, None] * exog` rwTr{Nr) rpredictrrPrArFderivvariancer?r7r%rrwr>rs rrzGLM.score_factors(5'D999 \\& ! ! =''++E R4;+;+A+A"+E+EE  ,,R000   55 zz E !LrTc||}|||}d|jj|dz|j|zz }||j|jzz}|s |dks||z}|S||d}|j dks |j dkrtd|j||jj |z}||jj||jj|zz }||z}||j|jzz}|d|zz}|j dkrtd|dks||z}|S)aWeights for calculating Hessian Parameters ---------- params : ndarray parameter at which Hessian is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- hessian_factor : ndarray, 1d A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)` Nrr4rtrzsomething wrong) rrrArFrrr?r7rndim RuntimeErrorderiv2) r%rrwobservedr> eim_factorrtmp oim_factors rhessian_factorzGLM.hessian_factors.\\& ! ! =''++E$+*0044a7+..r2234 dmdm33  A::e#  ((r(:: ?Q  ,"3a"7"7011 1k""2&&)9)@)@)D)DD t{#))"-- 0@0F0Fr0J0JJJS  t}t},,1s7+ 8a<<011 1zz % Jrcx|t|dddkrd}nd}t|dd}t|dtj|jt }|||| }tj|jj||j |j |j S) aHessian, second derivative of loglikelihood function Parameters ---------- params : ndarray parameter at which Hessian 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. observed : bool If True, then the observed Hessian is returned (default). If False, then the expected information matrix is returned. Returns ------- hessian : ndarray Hessian, i.e. observed information, or expected information matrix. N_optim_hessianeimFTrwr{_tmp_like_exogdtyperwr)out) getattrrr empty_liker[floatrmultiplyTr})r%rrwrrfactors rhessianz GLM.hessianMs(  t-t44== 5'D999d,bmDIU.S.S.STT$$V58$LL DIKSU3333 $)$$$$rcVt|dd}|||dS)z, Fisher information matrix. rwTr{Fr)rr)r%rrws r informationzGLM.informationms05'D999||F%%|@@@rdydxc||j}||td|||d||}t|dd} | dkr|n |d| } |jj|dddf| z} d|vr| |z} d|vr.|jj|} | | dddfz} || |||||S) zS Derivative of mean, expected endog with respect to the parameters N!offset and exposure not supportedlinear)whichr9r:k_extrarexey) r[NotImplementedErrorrrrArF inverse_derivr~_derivative_exog_helper) r%rr[ transform dummy_idx count_idxr9r:rr params_exogmargeffmeans r_derivative_exogzGLM._derivative_exogts  <9D  H$8%&IJJ J<<H'- BB$ 1-- '1 ff&7(2C ;#11(;;AAAtGD 9   tOG 9  ;#++H55D tAAAdF| #G++GVT,5y)MM Mrc^ddlm}m}||||||||}||||||||}|S)zK Helper for _derivative_exog to wrap results appropriately r)_get_count_effects_get_dummy_effects)%statsmodels.discrete.discrete_marginsrr) r%rrr[rrrrrs rrzGLM._derivative_exog_helpers}           (($ 9)-v77G  (($ 9)-v77GrcP||j}||t|ddtd|||d}|jj|}||dddfz}d|vr.|jj|} || dddfz}|S)a( Derivative of the expected endog with respect to the parameters. Parameters ---------- params : ndarray parameter at which score is evaluated exog : ndarray or None Explanatory variables at which derivative are computed. If None, then the estimation exog is used. offset, exposure : None Not yet implemented. Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. Nr9rr)r[rr)r[rrrrArFrr~) r%rr[rr9r:ridldmatrs r_derivative_predictzGLM._derivative_predicts, <9D  H$8h--9%&IJJ J<<T<BBk,,X66c!!!T'l" 9  ;#++H55D DDM !D rc||d}|jj|}|j|dddfz}|S)aM Derivative of the expected endog with respect to the parameters. Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. rrN)rrArFrr[)r%rrrrs r_deriv_mean_dparamszGLM._deriv_mean_dparamssN<<h<77k,,X66y3qqq$w<' rc^t|dd}||}|||}d|jj|z }||j|z}||j|jzz}|dks||z}|dddf|j zS)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. rwTr{Nr) rrrrArFrrr?r7r[rs r_deriv_score_obs_dendogzGLM._deriv_score_obs_dendogs&5'D999 \\& ! ! =''++E4;+11"555  ,,R000   55 zz E !LAAAtG$ty00rc|>|td||}|||}n|d}tj|j|f}||jd|jjdz z }||}|dddf|zd}| ||} tj |j | z| }ddl m } | tj||dddf } | j| |} | | |fS)aWscore test for restrictions or for omitted variables The covariance matrix for the score is based on the Hessian, i.e. observed information matrix or optionally on the expected information matrix.. Parameters ---------- params_constrained : array_like estimated parameter of the restricted model. This can be the parameter estimate for the current when testing for omitted variables. k_constraints : int or None Number of constraints that were used in the estimation of params restricted relative to the number of exog in the model. This must be provided if no exog_extra are given. If exog_extra is not None, then k_constraints is assumed to be zero if it is None. exog_extra : None or array_like Explanatory variables that are jointly tested for inclusion in the model, i.e. omitted variables. observed : bool If True, then the observed Hessian is used in calculating the covariance matrix of the score. If false then the expected information matrix is used. Returns ------- chi2_stat : float chisquare statistic for the score test p-value : float P-value of the score test based on the chisquare distribution. df : int Degrees of freedom used in the p-value calculation. This is equal to the number of constraints. Notes ----- not yet verified for case with scale not equal to 1. Nz:if exog_extra is None, then k_constraintsneeds to be givenrrr)stats)r(rrr column_stackr[rRrrcrr}rscipyrr`solvechi2sf) r%params_constrained k_constraints exog_extrarrrrrrrchi2statpvals r score_testzGLM.score_testsqT  $ "5666JJ122Ell#5lIIGG$ ! $)Z!899B RXa[49?1+== =M,,-?@@L!!!!T'*R/44Q77E!001C:B1DDNvbd^3R888GIIbiooguQQQW~FFGGGz}}X}55},,rc |d|j|d|j|j||j|j|j|S)zG Helper method to update history during iterative fit. rdeviance)rWrrArrPr<r;rw)r% tmp_resultr>historys r_update_historyzGLM._update_historyDst   !2333 ""4;#7#7 B8<8H8<8I8< $D$D E E Erc|jsMt|jtjtjtjfrdS||St|jtrtj |jSt|jtr|j dkr||S|j dkr5|j |j||j|jd|jz St%d|jdt'|jdt%d|jdt'|jd)a2 Estimate the dispersion/scale. Type of scale can be chose in the fit method. Parameters ---------- mu : ndarray mu is the mean response estimate Returns ------- Estimate of scale Notes ----- The default scale for Binomial, Poisson and Negative Binomial families is 1. The default for the other families is Pearson's Chi-Square estimate. See Also -------- statsmodels.genmod.generalized_linear_model.GLM.fit rtx2devzScale z with type z not understood)rZrErArBinomialPoissonNegativeBinomial_estimate_x2_scalerrarraystrlowerrrPr<r;rer(rC)r%r>s rrzGLM.estimate_scaleOs2~ 3$+(98;K(0(A(CDD 3r..r222 dne , , ,8DN++ + dnc * * E~##%%--..r222%%''500 ,,TZT=M-1->DD()!j"&...$t~2F2F2F2F"HIII*"nnnd4>.B.B.B.BDEE Erctj|j|z d|jz}tj||j|z |jz SNr4)rpowerrPr?rcrArre)r%r>resids rrzGLM._estimate_x2_scalesLb!,,t}<vedk22266677$-GGrbrentq)\(?@ch|dkrddlm}fd}|||||}ntd|S)a3 Tweedie specific function to estimate scale and the variance parameter. The variance parameter is also referred to as p, xi, or shape. Parameters ---------- mu : array_like Fitted mean response variable method : str, defaults to 'brentq' Scipy optimizer used to solve the Pearson equation. Only brentq currently supported. low : float, optional Low end of the bracketing interval [a,b] to be used in the search for the power. Defaults to 1.01. high : float, optional High end of the bracketing interval [a,b] to be used in the search for the power. Defaults to 5. Returns ------- power : float The estimated shape or power. rr)rc2jj|z dzz||zz jz }t jjj|z dz|||zzz dz zt j|zjz S)Nr4r)r?rPrcrerrKr;)rr>rwr%s rpsi_pz)GLM.estimate_tweedie_power..psi_ps-4:?q*@@;(),?t}bQ0F %u 5179:1; <!vbzz *++-1->-B-B-D-DEFr)argsz!Only brentq can currently be used)scipy.optimizerr)r%r>methodlowhighrrrs` restimate_tweedie_powerzGLM.estimate_tweedie_powersp0 X   - - - - - - F F F F F F5#t2777EE%&IJJ J rrc|"d}tj|t|durd}||t|dr|j}n|d}|8t |jjtj j std||t|dr|j }n+|d}n&tjtj|}||j}tj|||z|z}|d kr|j|S|dkr|S|d kr6|j|} |j| } | Std |d ) a Return predicted values for a design matrix Parameters ---------- params : array_like Parameters / coefficients of a GLM. exog : array_like, optional Design / exogenous data. Is exog is None, model exog is used. exposure : array_like, optional Exposure time values, only can be used with the log link function. See notes for details. offset : array_like, optional Offset values. See notes for details. which : 'mean', 'linear', 'var'(optional) Statitistic to predict. Default is 'mean'. - 'mean' returns the conditional expectation of endog E(y | x), i.e. inverse of the model's link function of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var_unscaled' variance of endog implied by the likelihood model. This does not include scale or var_weights. 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. Returns ------- An array of fitted values Notes ----- Any `exposure` and `offset` provided here take precedence over the `exposure` and `offset` used in the model fit. If `exog` is passed as an argument here, then any `exposure` and `offset` values in the fit will be ignored. Exposure values must be strictly positive. Nz0linear keyword is deprecated, use which="linear"Trr9rBrhr:r var_unscaledzThe which value "z" is not recognized)rIrJ FutureWarningrYr9rErArFrrjrkr(r:rrKrLr[r}fittedr) r%rr[r:r9rrmsglinpredrvar_s rrz GLM.predictsZ  DC M#} - - -~~  >dlwtX/F/Fl[FF ^F   4;3C3;>3E)G)G ()) )   z1J1J }HH  HHvbj2233H <9D&v&&/(: F??;%%g.. . h  N n $ $;%%g..D;''--DKKKKKLL Lrcvt|dd}t|jtjtjtjfrd}|||||d}i} tj |dkr$t|jtjr|| d<|jj ||fd |i| } | S) a  Return a instance of the predictive distribution. Parameters ---------- params : array_like The model parameters. scale : scalar The scale parameter. exog : array_like The predictor variable matrix. offset : array_like or None Offset variable for predicted mean. exposure : array_like or None Log(exposure) will be added to the linear prediction. var_weights : array_like 1d array of variance (analytic) weights. The default is None. n_trials : int Number of trials for the binomial distribution. The default is 1 which corresponds to a Bernoulli random variable. Returns ------- gen Instance of a scipy frozen distribution based on estimated parameters. Use the ``rvs`` method to generate random values. Notes ----- Due to the behavior of ``scipy.stats.distributions objects``, the returned random number generator must be called with ``gen.rvs(n)`` where ``n`` is the number of observations in the data set used to fit the model. If any other value is used for ``n``, misleading results will be produced. rwTr{rtrrrr7r<) rrErArrrrrranyget_distribution) r%rrwr[r:r9r<r7r>rsdistrs rrzGLM.get_distributionsL5'D999 dkH$5x7G$,$=$? @ @ E \\&$&\ G G F8q= ! ! (4;(9:: ( (D , ,RNN9DNHLNN rcLtj|jjd|_t |jtjr[|j |j|j }|d|_|d|_|j ddSdS)Nrrr7) rrnrPrRr7rErArrrfr;rVrW)r%rs rrXzGLM._setup_binomial9s 0 344 dk8#4 5 5 /+((T5FGGCQDJFDM O " ": . . . . .  / /rdIRLS:0yE> nonrobustFc  bt|tr(|}|dvrtdn=|; t |}n*#t $r} t | dd} ~ wwxYw||_|dkr/|dkrd}|jd |||||||d| S| d |_ |j | d =tj |j t |_|jd |||||| | |||| d | }|` |`|S) a Fits a generalized linear model for a given family. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is family-specific and is given by the ``family.starting_mu(endog)``. If start_params is given then the initial mean will be calculated as ``np.dot(exog, start_params)``. maxiter : int, optional Default is 100. method : str Default is 'IRLS' for iteratively reweighted least squares. Otherwise gradient optimization is used. tol : float Convergence tolerance. Default is 1e-8. scale : str or float, optional `scale` can be 'X2', 'dev', or a float The default value is None, which uses `X2` for Gamma, Gaussian, and Inverse Gaussian. `X2` is Pearson's chi-square divided by `df_resid`. The default is 1 for the Binomial and Poisson families. `dev` is the deviance divided by df_resid cov_type : str The type of parameter estimate covariance matrix to compute. cov_kwds : dict-like Extra arguments for calculating the covariance of the parameter estimates. use_t : bool If True, the Student t-distribution is used for inference. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. Not used if methhod is IRLS. disp : bool, optional Set to True to print convergence messages. Not used if method is IRLS. max_start_irls : int The number of IRLS iterations used to obtain starting values for gradient optimization. Only relevant if `method` is set to something other than 'IRLS'. atol : float, optional (available with IRLS fits) The absolute tolerance criterion that must be satisfied. Defaults to ``tol``. Convergence is attained when: :math:`rtol * prior + atol > abs(current - prior)` rtol : float, optional (available with IRLS fits) The relative tolerance criterion that must be satisfied. Defaults to 0 which means ``rtol`` is not used. Convergence is attained when: :math:`rtol * prior + atol > abs(current - prior)` tol_criterion : str, optional (available with IRLS fits) Defaults to ``'deviance'``. Can optionally be ``'params'``. wls_method : str, optional (available with IRLS fits) options are 'lstsq', 'pinv' and 'qr' specifies which linear algebra function to use for the irls optimization. Default is `lstsq` which uses the same underlying svd based approach as 'pinv', but is faster during iterations. 'lstsq' and 'pinv' regularize the estimate in singular and near-singular cases by truncating small singular values based on `rcond` of the respective numpy.linalg function. 'qr' is only valid for cases that are not singular nor near-singular. optim_hessian : {'eim', 'oim'}, optional (available with scipy optimizer fits) When 'oim'--the default--the observed Hessian is used in fitting. 'eim' is the expected Hessian. This may provide more stable fits, but adds assumption that the Hessian is correctly specified. Notes ----- If method is 'IRLS', then an additional keyword 'attach_wls' is available. This is currently for internal use only and might change in future versions. If attach_wls' is true, then the final WLS instance of the IRLS iteration is attached to the results instance as `results_wls` attribute. )rrz-scale must be either X2 or dev when a string.Nz/scale must be a float if given and no a string.irlsrr start_paramsmaxitertolrwcov_typecov_kwdsuse_t optim_hessianr) r rr r rw full_outputdispr rrmax_start_irlsr1)rErrr(r ExceptionrCrZ _fit_irlsgetrrrr[r _fit_gradient)r%r r rr rwr rrrrrr\excfit_s rfitzGLM.fitDsb eS ! ! KKMMEM)) C*  e    d3iiE  <<>>V # #~~5((&!4>L|W&)+35LLDJLL L#)**_"="=D ".?+"$- "G"G"GD %4%0<-3.5*-U2=+/(/7u5C00)/00D##KsA A8A33A8newtonc ^|j} d|_| dkr||jd|| |ddddd| }|j}~tjd|||||d| }| |_||j}||}|jd}n |j|z }|dkrd}d}nd } tj | |j|  |z }n,#t$rtjd t d}YnwxYwt#|d t$}t#|d t&}|||j|||| | }ddi}|r%|j|_d|jvr|jd|d<||_||_||S)z} Fits a generalized linear model for a given family iteratively using the scipy gradient optimizers. rtrNrr )r r rrrrFTrz8Inverting hessian failed, no bse or cov_params available_results_class_results_class_wrapperr rrr iterationsr1)rZrrrMrrrnormalized_cov_paramsrrr`invrrrIrJrr GLMResultsGLMResultsWrapper mle_retvalsr fit_history)r%r rr r rrrwr rrrr\rZ irls_rsltrsltr>cov_poim results_classresults_class_wrapper glm_resultsrr^s rrzGLM._fit_gradients>N  Q  \%9&1L/=+.b;04D11*0 11I %+Luww{H ,3+1HH@FHH # \\$+ & &##B''  % -EE.6E >>  u $ $C"HHC IMM4<< c<#J#J"JKKeSEE    M&'> @ @ @EEE   &6 CC '.FHY Z Z#mD$+$)$)-5*/ 111 "  F&*&6K #t///'+'7 'E $# ") $$[111s>=C<<&D%$D%c |dd} |d} |dd} |dd} |dd } | |n| } |j}|j}|^t j|jjd }|j|j}|j |}n7t j |||j z}|j |}| ||_|j|j||j|j|j}t j|rt'd t)tj|gtj|g }d}|| }|dkrL|j |}| ||_t-j||d }d}t1|D]z}|j|jz|j|z|_||jj||j|z zz|j z }t=j|||jdd}| | }t j |j|j!}||j z }|j |}|"|||}| ||_|#j$d kr5t j%||z drd}tMj'|tPtS||d z| | }|rn|||_*|dkr;| d krdn| }t-j+|||j}| |}tY||j!|j-|j|||}d|_.i|_/| |j/d<|j.|j/d<|dkr | dur||_0|d z|d<||_1||_2tg|S)z Fits a generalized linear model for a given family using iteratively reweighted least squares (IRLS). attach_wlsFrrrB tol_criterionr wls_methodlstsqNrzsThe first guess on the deviance function returned a nan. This could be a boundary problem and should be reported.)rrrT) check_endog check_weights)rzJPerfect separation or prediction detected, parameter may not be identified)categorypinvrr optimizerr)4poprrPr[rzerosrRrA starting_murr}r@rrrwrr<r;isnanr(dictinflmRegressionResultsranger?r7r=rFr reg_tools _MinimalWLSrrrsqueezerrrIrJrrr>WLSr#r!r mle_settings results_wlsr& convergedr$)r%r r r rwr rrr\r/rrr0r1rPwlsexogr>rrrrGr wls_resultsrwlsendogwls_modr wls_method2 wls_modelr-s rrz GLM._fit_irlssYZZ e44 zz&!!zz&"%% ?J?? ZZ g66 lss )  8DIOA$677L((44B{**2..HHvg|44t7LLH##H--B((,, k""4:r43C#'#4djBB 8C== A@AA A rv|4}MMM M*  a<<##H--B,,R00DJ.t\4HHKIw  I MDM9 K//334DL 4;#3#9#9"#=#=B#OO/0H+Hg,0Ld:>@@@G"++Z+88Kvdi);<rrwrGrIrJ) r%rrYr rZ opt_methodr\rRdefaultsllkwsckwhekwresults rfit_regularizedzGLM.fit_regularized[s|z ::gq ! !Q & &??5, CC C?????? ] " "MNN N!AE %''zz."--zz,++zz+r**W W W #' !% $,V&+-9&+,,#+ ,, ,,v}--((11  B M@ A A A rc|$tjjjd}fd}fd}ddlm}ddlm}m}|||||} | j } | j sGtj tj | j dz} d | z} tj| || } || } | S) Nrc||jz tj|dzzdz z Sr)rxrSrrcxrYr%s rfunzGLM._fit_ridge..funs9\\!__ty026%!Q$,3G3G!3KKL LrcL|jz |zz Sr")rrSrgs rgradzGLM._fit_ridge..grads&ZZ]]TY.:; ;rr)minimize)RegularizedResultsRegularizedResultsWrapper)jacrr4z1GLM ridge optimization may have failed, |grad|=%f)rr9r[rRrrlr\rmrnrhsuccesssqrtrcrorIrJ)r%rYr rrirkrlrmrnmrrngradrresultss`` rr[zGLM._fit_ridges+  8DIOA$677L M M M M M M < < < < < < ,+++++        Xc %$$$$$        Z ( ( : :; G Gx1#2/$1?K;C#E#E#EZhhFAh66$ *- '<< K88 { " "14z7G1GCL . .15CL .'- q66 ) )#4#?#?#C#C  ( +5 ( r)NNNNNr5)rtr")NT)NN)NrNNNN)NrNN)NNT)rrr)NNNrN)NNNNrtrt) NrrrNrNNTFr) NrrrTTNrNNr)NrrNrNN)rNrBNFrO)(r-r.r/formatbase_missing_param_doc__doc___formula_max_endogrNrfrOrqryrxrrrrrrrrrrrrrrrrrrrXrrrrdr[rx __classcell__r^s@rrrTsQQb D344c f8>>>>>@ C C C.I.I.I`====    1111,////,    D8888t%%%%@AAAA=C37/3MMMM8&@F26####J&1111B<@-1F-F-F-F-P   /E/E/EbHHH$$$$L@D%)UMUMUMUMnHL?A6666p / / /FJCG9:wwwwr7?9=6A@AC2C2C2C2C2C2J=A=AW.W.W.W.r;=16#)____B>????????r pred_kwdsc`eZdZdZ d4fd ZedZedZedZedZ ed Z ed Z ed Z e d Zed ZedZedZedZedZedZd5dZe dZd6dZe dZedZe dZe dZd7dZ d8dZe e!j"j d9d!Z"d:d"Z#d:d#Z$ d;d%Z% dd/Z/d?d1Z0 d@d3Z1xZ2S)Ar#av Class to contain GLM results. GLMResults inherits from statsmodels.LikelihoodModelResults Attributes ---------- df_model : float See GLM.df_model df_resid : float See GLM.df_resid fit_history : dict Contains information about the iterations. Its keys are `iterations`, `deviance` and `params`. model : class instance Pointer to GLM model instance that called fit. nobs : float The number of observations n. normalized_cov_params : ndarray See GLM docstring params : ndarray The coefficients of the fitted model. Note that interpretation of the coefficients often depends on the distribution family and the data. pvalues : ndarray The two-tailed p-values for the parameters. scale : float The estimate of the scale / dispersion for the model fit. See GLM.fit and GLM.estimate_scale for more information. stand_errors : ndarray The standard errors of the fitted GLM. #TODO still named bse See Also -------- statsmodels.base.model.LikelihoodModelResults rNct|||||j|_|j|_|jjd|_|j|_|j |_ |j |_ t|jtjr|jj|_nd|_|j|_|j|_i|_|jgd|jddgt3|dg|_|jdddlm}|d |_n||_|d kp&| d } |jj!r| sdd l"m#} tIj%d | |jj&r| sdd l"m#} tIj%d| |d krd |_'ddi|_(dS|i}||f|d|d|dS)N)r!rwrr)r _freq_weights _var_weights _iweightsnullr>_data_attr_model)get_robustcov_resultsFrHC)SpecificationWarningz.cov_type not fully supported with freq_weightsz-cov_type not fully supported with var_weights descriptionzWStandard Errors assume that the covariance matrix of the errors is correctly specified.T)r use_selfr))rMrNrArP_endogrRrSr;rr<rr?rrErrmodelr7 _n_trialsrerb_cacherTrU_data_in_cacherrrWstatsmodels.base.covtyperrupper startswithrmstatsmodels.tools.sm_exceptionsrrIrJror r) r%rrr!rwr rrrctrr^s rrNzGLMResults.__init__Gsp &;     l k K%a( "/!- dk8#4 5 5 !Z0DNNDN    = = = > > > ""FD>222 '.@" E E $$T*** CBBBBB =DJJDJ+% M8>>+;+;+F+Ft+L+L : ' 0 0 L L L L L L MJ. 0 0 0 : & 0r 0 L L L L L L MI. 0 0 0 { " "'DM*-*+DMMM  ! !$ ;D(- ; ;19 ; ; ; ; ;rc0|j|j|jz zS)zm Response residuals. The response residuals are defined as `endog` - `fittedvalues` )rrr>r$s rresid_responsezGLMResults.resid_responses ~TW!455rctj|j|j|jz ztj|jztj|j|jz S)a Pearson residuals. The Pearson residuals are defined as (`endog` - `mu`)/sqrt(VAR(`mu`)) where VAR is the distribution specific variance function. See statsmodels.families.family and statsmodels.families.varfuncs for more information. )rrqrrr>rrArr$s r resid_pearsonzGLMResults.resid_pearsons_''4;tw+>?)**+ ,,TW55667 8rcr|j|jj|jz}||jz}|S)z Working residuals. The working residuals are defined as `resid_response`/link'(`mu`). See statsmodels.family.links for the derivatives of the link functions. They are defined analytically. )rrArFrr>rr*s r resid_workingzGLMResults.resid_workings7"T[%5%;%;DG%D%DD t~ rc|jS)z Anscombe residuals. See statsmodels.families.family for distribution- specific Anscombe residuals. Currently, the unscaled residuals are provided. In a future version, the scaled residuals will be provided. )resid_anscombe_scaledr$s rresid_anscombezGLMResults.resid_anscombes ))rcf|j|j|j|j|jS)z Scaled Anscombe residuals. See statsmodels.families.family for distribution-specific Anscombe residuals. r<rw)rArr fittedvaluesrrwr$s rrz GLMResults.resid_anscombe_scaleds7 {))$+t7H6:6G04 *<< rArrrrrc)r%chisqchisqsums r pearson_chi2zGLMResults.pearson_chi2sS tw&*T[-A-A$'-J-JJ $.006%==rc|jS)a The estimated mean response. This is the value of the inverse of the link function at lin_pred, where lin_pred is the linear predicted value obtained by multiplying the design matrix by the coefficient vector. )r>r$s rrzGLMResults.fittedvaluess wrc@|j|jS)z$ See GLM docstring. )rrrr$s rr>z GLMResults.mus z!!$+...rcB|j}|j}tjt |df}|}|dt|dgD]}||=tj |j | }|jj }tj|dkr|dksvtj5tjdt$t'||fd|j i|}||j} dddn #1swxYwYn=t-j|||j|jz} | j} | S) z1 Fitted values of the null model rrA_null_drop_keysrignore)r N)r=)rrrrnrlrqcopyr8r atleast_1drArFrr@sizerIcatch_warnings simplefilterrrrrr>rDrr) r%rPrr[r\keyr oemodrrMs rrzGLMResults.nulls   wE A''%%'',,.. 85"3R88  Cs }T[%5%5ejjll%C%CDD Z ( q  R1WW(** I I%h >>>%DDdkDVDDl;;H I I I I I I I I I I I I I I I ud'+~'FHHHI]]__1F s?A EEEcd|j|j|j|j|jS)zk See statsmodels.families.family for the distribution-specific deviance functions. )rArrr>rrr$s rrzGLMResults.deviance s1 {##DK$:K$($688 8rcd|j|j|j|j|jS)zcThe value of the deviance function for the model fit with a constant as the only regressor.)rArrrrrr$s r null_deviancezGLMResults.null_deviances1{##DKDrrcrrdrwrxrr)r%rw _modelfamilyr+s r llf_scaledzGLMResults.llf_scaled#s{ =4;(9:: #t{/1EFF #[%+r11$+"7;;dnLQQSS)) ""4;/3/@040B).#00 rc*|S)au Value of the loglikelihood function evalued at params. See statsmodels.families.family for distribution-specific loglikelihoods. The result uses the concentrated log-likelihood if the family is Gaussian and the link is linear, otherwise it uses the non-concentrated log-likelihood evaluated at the estimated scale. )rr$s rrzGLMResults.llf=s   rcsc.|}|drd|j|jz z }nX|ds|dvr0dt j|j|jz d|jz zz }ntd|S)a Pseudo R-squared Cox-Snell likelihood ratio pseudo R-squared is valid for both discrete and continuous data. McFadden's pseudo R-squared is only valid for discrete data. Cox & Snell's pseudo-R-squared: 1 - exp((llnull - llf)*(2/nobs)) McFadden's pseudo-R-squared: 1 - (llf / llnull) Parameters ---------- kind : P"cs", "mcf"} Type of pseudo R-square to return Returns ------- float Pseudo R-squared mcfrcox)rlrr4z)only McFadden and Cox-Snell are available)rrrrrrrrSr()r%kindprsqs rpseudo_rsquaredzGLMResults.pseudo_rsquaredIs,zz|| ??5 ! ! Jtx$+--DD __U # # Jt|';';rvt{TX5!di-HIIIDDHII I rc,|dS)zX Akaike Information Criterion -2 * `llf` + 2 * (`df_model` + 1) aic info_criteriar$s rrzGLMResults.aichs !!%(((rctjdvrtjdtt tjr|jS|jS)a Bayes Information Criterion `deviance` - `df_resid` * log(`nobs`) .. warning:: The current definition is based on the deviance rather than the log-likelihood. This is not consistent with the AIC definition, and after 0.13 both will make use of the log-likelihood definition. Notes ----- The log-likelihood version is defined -2 * `llf` + (`df_model` + 1)*log(n) )TFaThe bic value is computed using the deviance formula. After 0.13 this will change to the log-likelihood based formula. This change has no impact on the relative rank of models compared using BIC. You can directly access the log-likelihood version using the `bic_llf` attribute. You can suppress this message by calling statsmodels.genmod.generalized_linear_model.SET_USE_BIC_LLF with True to get the LLF-based version now or False to retainthe deviance version.)_use_bic_helperr&rIrJrr)bic_llf bic_deviancer$s rbiczGLMResults.bicpsV$  &m ; ; M(    + , , <   rc~|j|jj|jz dz t j|jjzz S)z{ Bayes Information Criterion Based on the deviance, `deviance` - `df_resid` * log(`nobs`) r)rrrdrbrrKr$s rrzGLMResults.bic_deviances> !DM1A5tz'(()) *rc,|dS)z Bayes Information Criterion Based on the log-likelihood, -2 * `llf` + log(n) * (`df_model` + 1) rrr$s rrzGLMResults.bic_llfs!!%(((rrc|}|jdz|z}|dkrd|jzd|zzS|dkr6|j|jzdz}d|jz|t j|zz}|S|dkr~|jj}tj tj tj f}t||sd} | dz } tj| |d } d| z|z d|zzSd S) aHReturn an information criterion for the model. Parameters ---------- crit : string One of 'aic', 'bic', or 'qaic'. scale : float The scale parameter estimated using the parent model, used only for qaic. dk_params : int or float Correction to the number of parameters used in the information criterion. By default, only mean parameters are included, the scale parameter is not included in the parameter count. Use ``dk_params=1`` to include scale in the parameter count. Returns ------- Value of information criterion. Notes ----- The quasi-Akaike Information criterion (qaic) is -2 * `llf`/`scale` + 2 * (`df_model` + 1). It may not give meaningful results except for Poisson and related models. The QAIC (ic_type='qaic') must be evaluated with a provided scale parameter. Two QAIC values are only comparable if they are calculated using the same scale parameter. The scale parameter should be estimated using the largest model among all models being compared. References ---------- Burnham KP, Anderson KR (2002). Model Selection and Multimodel Inference; Springer New York. rrr4rqaicz-QAIC is only valid for Binomial, Poisson and zNegative Binomial families.rN)rrbrrerrKrrArrrrrErIrJr) r%critrw dk_paramsk_paramsrSrfflrrs rrzGLMResults.info_criterias Jzz||=1$y0 5===1x</ / U]]=4=014DTX+ 55CJ V^^ !A"H$=#%Ba$$ #E44 c"""///**C8E>AL0 0^rTFc ddlmcm} ||dd} |J| |||| | } d| d<t j|||| | |jjj| } n!||d } t j||||| ||| } | S) a Compute prediction results for GLM compatible models. Options and return class depend on whether "which" is None or not. Parameters ---------- exog : array_like, optional The values for which you want to predict. exposure : array_like, optional Exposure time values, only can be used with the log link function. offset : array_like, optional Offset values. 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 : 'mean', 'linear', 'var'(optional) Statitistic to predict. Default is 'mean'. If which is None, then the deprecated keyword "linear" applies. If which is not None, then a generic Prediction results class will be returned. Some options are only available if which is not None. See notes. - 'mean' returns the conditional expectation of endog E(y | x), i.e. inverse of the model's link function of linear predictor. - 'linear' returns the linear predictor of the mean function. - 'var_unscaled' variance of endog implied by the likelihood model. This does not include scale or var_weights. linear : bool The ``linear` keyword is deprecated and will be removed, use ``which`` keyword instead. If which is None, then the linear keyword is used, otherwise it will be ignored. If True and which is None, the linear predicted values are returned. If False or None, then the statistic specified by ``which`` will be returned. average : bool Keyword is only used if ``which`` is not None. 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 Keyword is only used if ``which`` is not None. Aggregation weights, only used if average is True. row_labels : list of str or None If row_lables are provided, then they will replace the generated labels. Returns ------- prediction_results : instance of a PredictionResults class. The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary tables for the prediction of the mean and of new observations. The Results class of the return depends on the value of ``which``. See Also -------- GLM.predict GLMResults.predict Notes ----- Changes in statsmodels 0.14: The ``which`` keyword has been added. If ``which`` is None, then the behavior is the same as in previous versions, and returns the mean and linear prediction results. If the ``which`` keyword is not None, then a generic prediction results class is returned and is not backwards compatible with the old prediction results class, e.g. column names of summary_frame differs. There are more choices for the returned predicted statistic using ``which``. More choices will be added in the next release. Two additional keyword, average and agg_weights options are now also available if ``which`` is not None. In a future version ``which`` will become not None and the backwards compatible prediction results class will be removed. rNr)r:r9r)r[r row_labelsrrr)r[rrrrFr)r:r9)r[rrraverage agg_weightsr) "statsmodels.regression._prediction regression _predictionget_predictionpredget_prediction_glmrrArF)r%r[r:r9rrrrrrrr res_linpredrs rrzGLMResults.get_predictionst =<<<<<<<rsrs rrzGLMResults.get_distributionsN dj'(*;X=M$,$=*? @ @ EzRJ c;///JE \\$&\ ? ? F8q= ! ! (4:,h.?@@ ( (D 2 !2 88#.82688 roverallrc*t|jddtdtj|jjdks"tj|jjdkrtjdddl m }|||||||fS)a Get marginal effects of the fitted model. Warning: offset, exposure and weights (var_weights and freq_weights) are not supported by margeff. 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. Status : unsupported features offset, exposure and weights. Default handling of freq_weights for average effect "overall" might change. r9Nz&Margins with offset are not available.rz-weights are not taken into account by margeffr)DiscreteMargins) rrrrrr<r;rIrJrr)r%atratexogdummycountrs r get_margeffzGLMResults.get_margeffs^ 4:x . . :%&NOO O F4:)Q. / / Ktz.!344 K MI J J JIIIIIItb&&%%GHHHrc|jd|jjDt|j|d|_d|_d|_d|_ d|_ dS)Ncg|]}d|v| S)z_data.r1).0is r z*GLMResults.remove_data..T s, 6 6 6a#+1#4#4!"#4#4#4r) rTrUrrMr^ remove_datarrrrr)r%r^s rrzGLMResults.remove_dataQ s  6 64:+@ 6 6 6 7 7 7 dnd##//111 ! rextra_params_docc4ddlm}|||||||}|S)Nr)plot_added_variable) resid_typeuse_glm_weights fit_kwargsax)$statsmodels.graphics.regressionplotsr!)r% focus_exogr"r#r$r%r!figs rr!zGLMResults.plot_added_variable_ sG MLLLLL!!$ -72A-7B@@@  rc*ddlm}||||S)Nr)plot_partial_residuals)r%)r&r*)r%r'r%r*s rr*z!GLMResults.plot_partial_residualsm s/ POOOOO%%dJ2>>>>rQ?c.ddlm}||||||S)Nr)plot_ceres_residuals) cond_meansr%)r&r-)r%r'fracr.r%r-s rr-zGLMResults.plot_ceres_residualst s@ NMMMMM##D*d/9bBBB Br皙?c ddd|jjjgfd|jjjjgfd|jgfdddd |jd zgfg} |d }n#t$rtj }YnwxYwd dddd|j zgfddd|j zgfdd|j zgfdd|zgfg}t|dr|d|jgf|d}ddlm}|} | ||||||| |||||jt|d r| d!g| S)"ac Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. 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 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. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results )zDep. Variable:N)zModel:Nz Model Family:zLink Function:zMethod:)zDate:N)zTime:NzNo. Iterations:z%drr)r)zNo. Observations:N)z Df Residuals:N)z Df Model:NzScale:z%#8.5g)zLog-Likelihood:Nz Deviance:z Pearson chi2:z%#6.3gzPseudo R-squ. (CS):z%#6.4gr zCovariance Type:Nz+Generalized Linear Model Regression Resultsr)Summary)gleftgrightynamexnametitle)r5r6rYrr@Model has been estimated subject to linear equality constraints.)rAr^r-rFrr&rr(rnanrwrrrYrWr statsmodels.iolib.summaryr2add_table_2colsadd_table_paramsr add_extra_txt) r%r5r6r7rYtop_left prsquared top_rightr2smrys rsummaryzGLMResults.summary} s:-$$t{'<'E&FG% (8(B(K'LM .##&T-k::;=  ,,$,77II   III 1,(DJ!6 78.!Ht}$<#=>%43D(D'EF+h.B-CD  4 $ $ C OO/$-A B B B =AE 655555wyy T)#(U  D D D d%uE$(J  0 0 0 4 ' ' :   !8 9 : : : sA%%A>=A>%.4fc Rd|_ddlm}|}t j5t jdt|||||||dddn #1swxYwYt|dr| d|S) aExperimental summary for regression Results Parameters ---------- yname : str Name of the dependent variable (optional) xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. 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 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 rr)summary2r)rtrY float_formatr6r5r7Nrr8) rstatsmodels.iolibrEr2rIrrradd_baserYadd_text)r%r5r6r7rYrFrErAs rrEzGLMResults.summary2 s< ......!!  $ & & A A  !(M : : : MM$e, %U%  A A A A A A A A A A A A A A A A A A 4 ' ' 3 MM2 3 3 3 s6A77A;>A;)rNNr")r)Nr) NNNTNNFNN)NNrNNNT)T)NNNrtrt)rrNFF)NTNN)r+NN)NNNr0)NNNr0rC)3r-r.r/rrNr rrrrrrrr rrr>r rrrrrrrrr0rrrrrrrrrrrrrLikelihoodModelResultsrrr!r r*rr-rBrErrs@rr#r#!s##L=A=;=;=;=;=;=;~66[6 8 8[ 8  [ **[*<<[<44[4[\  [ //[/ ^888^888^8 55^54 ! !\ !>))\)!!!!X!!F * *\ *))\)71717171v?C:>26"&BXf'((=A?C04)(8.!!!!F48?A;;;;z?C$UIUIUIUInXd)5=>>    ?> X&*RegressionResultsWrapper _wrap_attrsr1rrr$r$ sJ    F#$"2#>#J#)++KKKrr$__main__)longleytables)returnszTest GLM)r7)Krstatsmodels.compat.pandasrrInumpyr numpy.linalgrstatsmodels.base.modelrrstatsmodels.base.wrapperwrapperrNstatsmodels.baserr&statsmodels.base._prediction_inferencer%statsmodels.base._parameter_inference_parameter_inferencer)statsmodels.graphics._regressionplots_docrrr statsmodels.regression._toolsr_toolsrA#statsmodels.regression.linear_model linear_modelr>statsmodels.tools.decoratorsr r r statsmodels.tools.docstringr rrrrstatsmodels.tools.validationrrr__all__rr rr,SET_USE_BIC_LLFLikelihoodModelrrget_prediction_docremove_parametersrJr#rPr$populate_wrapperr-statsmodels.datasetsrSloaddatarPr[rGLMmodrBGLMTGLMTpr1rrrts&/.....$$$$$$%%%%%%%%%'''''''''::::::HHHHHH666666666 211111111000000000 211111 433333 ) *--- < < < < < < < <"/##!1FFFFF$ FFFR.Yt6>??$$[111OOOOO,OOOd + + + + +3 + + +'444 z,,,,,, 7<>>D STY ' ' + + - -F >>(> + +D NNN , ,E!!r