M/Ph<VdZddlZddlmZ d dZ ddZ ddZd Zd Z dd Z dS)z5 Created on Wed May 30 15:11:09 2018 @author: josef N)statscn||||f\}}}}tj|} ||} | |} |+|)|||} n|.| || j} n-|||j} | tj| | } t j| | }| || fS)ageneral formula for score/LM test generalized score or lagrange multiplier test for implicit constraints `r(params) = 0`, with gradient `R = d r / d params` linear constraints are given by `R params - q = 0` It is assumed that all arrays are evaluated at the constrained estimates. Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model constraint_matrix R : ndarray Linear restriction matrix or Jacobian of nonlinear constraints score_deriv_inv, Ainv : ndarray, symmetric, square inverse of second derivative of objective function TODO: could be inverse of OPG or any other estimator if information matrix equality holds cov_score B : ndarray, symmetric, square covariance matrix of the score. This is the inner part of a sandwich estimator. cov_params V : ndarray, symmetric, square covariance of full parameter vector evaluated at constrained parameter estimate. This can be specified instead of cov_score B. Returns ------- lm_stat : float score/lagrange multiplier statistic p-value : float p-value of the LM test based on chisquare distribution Notes ----- ) nplinalg matrix_rankdotTsolverchi2sf)scoreconstraint_matrixscore_deriv_inv cov_score cov_paramsRAinvBV k_constraintstmpwscorelm_statinnerpvals e/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/base/_parameter_inference.py _lm_robustr sV& :MMAtQI))!,,M %%++C WWU^^FyQY))DHHUOO,, 9GGAJJNN35))EEEE!HHLL%%E**RY__UF;;<< :==- 0 0D D- ''jointTc L t|dr|j}|j} | jjd} ||j}||n|j}| durddi} ni} |t|drBt|jtr|jd}n |jj }|jd}n|td| d|i} || d<ni} | j |fi| }| j |fi| }| j|fi| }n|d krtd t|drtd t|tr/t!||g|Rd | i}|\}}}}|d}nDt%j|}d}t%j| j|f}||jd | jjd z z }t%jt/|j|z| d}| |}|jd kr|dddf|z}n3|}t%j|dddd f|z|ddd dff}|d}| j|fi| }ddlm}t| |r|dz}t%j|j|z|}|dkr| }n|dkrRt$j !| }| t%j"|jz}tG||||d}|S|d kr{t$j !| }| t%j"|jz}|j$}tG|||||}tJj&'||}||fSd}t||dkrb|t$j (||dddf}tJj&'||}|||fS|dkre|}t%j)t%j*|} || z }!tJj+'t%j,|!dz}|!|fStd)ascore test for restrictions or for omitted variables Null Hypothesis : constraints are satisfied Alternative Hypothesis : at least one of the constraints does not hold This allows to specify restricted and unrestricted model properties in three different ways - fit_constrained result: model contains score and hessian function for the full, unrestricted model, but the parameter estimate in the results instance is for the restricted model. This is the case if the model was estimated with fit_constrained. - restricted model with variable addition: If exog_extra is not None, then it is assumed that the current model is a model with zero restrictions and the unrestricted model is given by adding exog_extra as additional explanatory variables. - unrestricted model with restricted parameters explicitly provided. If params_constrained is not None, then the model is assumed to be for the unrestricted model, but the provided parameters are for the restricted model. TODO: This case will currently only work for `nonrobust` cov_type, otherwise we will also need the restriction matrix provided by the user. Parameters ---------- exog_extra : None or array_like Explanatory variables that are jointly tested for inclusion in the model, i.e. omitted variables. params_constrained : array_like estimated parameter of the restricted model. This can be the parameter estimate for the current when testing for omitted variables. hypothesis : str, 'joint' (default) or 'separate' If hypothesis is 'joint', then the chisquare test results for the joint hypothesis that all constraints hold is returned. If hypothesis is 'joint', then z-test results for each constraint is returned. This is currently only implemented for cov_type="nonrobust". cov_type : str Warning: only partially implemented so far, currently only "nonrobust" and "HC0" are supported. If cov_type is None, then the cov_type specified in fit for the Wald tests is used. If the cov_type argument is not None, then it will be used instead of the Wald cov_type given in fit. 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. 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. This currently only applies to GLM where EIM is available. Warning: This option might still change. 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 ----- Status: experimental, several options are not implemented yet or are not verified yet. Currently available ptions might also still change. cov_type is 'nonrobust': The covariance matrix for the score is based on the Hessian, i.e. observed information matrix or optionally on the expected information matrix. cov_type is 'HC0' The covariance matrix of the score is the simple empirical covariance of score_obs without degrees of freedom correction. _resultsrNFobserved constraintsz:if exog_extra is None, then k_constraintsneeds to be givenscalerz4if exog_extra is not None, then cov_type cannot be VzJif exog_extra is not None, then selfshould not be a constrained fit result hess_kwds)GLM nonrobustHC0)rz2Only cov_type "nonrobust" and "HC0" are available.rseparatez$only hypothesis "joint" is available)-hasattrr!modelendogshapeparamscov_type isinstancer#tuplecoefs ValueErrorr score_obshessianNotImplementedError_scorehess_extrasumrasarray column_stackexogeyelen score_factorndimhessian_factor+statsmodels.genmod.generalized_linear_modelr'rr upperrinvcovrcov_params_defaultrr r r sqrtdiagnormabs)"self exog_extraparams_constrained hypothesisr2cov_kwdsrr_matrixr$r"r.nobshess_kwd score_kwdr r7r8shexrAr rCr'cov_score_testhinvrlmrchi2statrmsgdiffbsestats" r score_testr`OsKrtZ  } JE ; Q D!![#/xxT]H5& 4 ' ' 6$*E22 2+A.+1$N1-MM$ "5666   %(I %HW  I .<<)<<#EO$6DD)DD %- 2??h?? s??$%% % 4 ' ' P%'OPP P j% ( ( 8!$(:6Z666,466B:< 7Iw xMM!$$EEJ//JM%*j!9::B RXa[5:+;A+>> >Mvc$+..>  !.1H!--.@AAL A%%)!!!T'2R7 !OR2A2Y^R122Y,GHH MM!$$E1U12D>>4<>>N H G G G G G%%% %"$fRTN2B77G;!   U " " g&&&26)+... xyT J J J   S  g&&&26)+...  #eXtY1MMMz}}X}55~B!#&&&W99RY__^U111d7^LLMMz}}X}55},, z ! !gbgn--..czz}}RVD\\**1,Tz!"HIIIrc|i}|j}||j}|\}}|!tj|jddf}|jd}|jd} |tj||f} n|} |tj||f} n|} | jd} | jd} | |z }| | z }||z}tj|| }tj| | z| | z}tj|t||zf}tj ||d||f<tj |||||z|f<t|dr|j |fddi|\}}n#| |}|j|fi|}|\}}|\}}}|dddf| z}|dddf| z}tj||f}| j|z| }| j|z| }| j|z| } tj||g|j| gg}!||!||fS)zExperimental helper function for variable addition score test. This uses score and hessian factor at the params which should be the params of the restricted model. Nrr&score_hessian_factorreturn_hessianT)r.r1 _get_exogsronesr0r=arangezerosr@r?r-rbrArCr rblock)"rMr1rN exog2_extrar%r.exog_o1exog_o2k_meank_precr>exog2 k_mean_new k_prec_newk_cmk_cpr index_mean index_precrRr hfsf1sf2hf11hf12hf22d1d2r7d11d12d22r8s" rr:r:"s JE ~''))GW'7=+Q/00 ]1 F ]1 F455+ 677AJQJ  D  D4KM6:..J:. Z0GHHJxF m(CDEEH#%&,,HUdUJ .0fTllHT4$;  *+u,--7++F9949.799BB   ' ' !U !& 6 6I 6 6HCD$ QQQW B QQQW BR))I 6D=  d # #C 6D=  e $ $C 7T>  u % %Chc SUCL122G g}h 66rcJt|d|}|j|j}|jdkrO|j|j}|j|z}tj | }||z}n| | z}|S)Nr!r)) getattrr.r8r1r2r7r rrrFr)resultsreshessr7r hessneg_invim_ratios rrrls ':w / /C 9  SZ ( (D |{""I'' 33 K)+ immTE** *>>##u- Orct|dt|}d|jzdtj|zz}|S)zrs  @(@(@(@(F:>;?GKPJPJPJPJf4815G7G7G7G7T   r