M/PhQdZddlZddlmZmZmZmZmZm Z ddl m Z ddl Z ddlmZddlmZddlmZddlmZd Zd Zdd Z ddZdZeedZGddeZGddZGddZdS)z*General linear model author: Yichuan Liu N)eigvalsinvsolve matrix_rankpinvsvd)stats) DesignInfo) Substitution)Model)summary2zrestructuredtext ena5hypotheses : list[tuple] Hypothesis `L*B*M = C` to be tested where B is the parameters in regression Y = X*B. Each element is a tuple of length 2, 3, or 4: * (name, contrast_L) * (name, contrast_L, transform_M) * (name, contrast_L, transform_M, constant_C) containing a string `name`, the contrast matrix L, the transform matrix M (for transforming dependent variables), and right-hand side constant matrix constant_C, respectively. contrast_L : 2D array or an array of strings Left-hand side contrast matrix for hypotheses testing. If 2D array, each row is an hypotheses and each column is an independent variable. At least 1 row (1 by k_exog, the number of independent variables) is required. If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint. transform_M : 2D array or an array of strings or None, optional Left hand side transform matrix. If `None` or left out, it is set to a k_endog by k_endog identity matrix (i.e. do not transform y matrix). If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint. constant_C : 2D array or None, optional Right-hand side constant matrix. if `None` or left out it is set to a matrix of zeros Must has the same number of rows as contrast_L and the same number of columns as transform_M If `hypotheses` is None: 1) the effect of each independent variable on the dependent variables will be tested. Or 2) if model is created using a formula, `hypotheses` will be created according to `design_info`. 1) and 2) is equivalent if no additional variables are created by the formula (e.g. dummy variables for categorical variables and interaction terms) r:0yE>c0|}|}|j\}}|j\}} ||krtd||fz|| z } |dkrt|} | |} | | j} t | || krtd|| }t j|j||j|}| | | |fS|dkrt|d\}}}||k t|krtdd|z }|jt j ||j|} |jt j t j |d|} t j ||| }t j|j||j|}| | | |fStd |z) a$ Solve multivariate linear model y = x * params where y is dependent variables, x is independent variables Parameters ---------- endog : array_like each column is a dependent variable exog : array_like each column is a independent variable method : str 'svd' - Singular value decomposition 'pinv' - Moore-Penrose pseudoinverse tolerance : float, a small positive number Tolerance for eigenvalue. Values smaller than tolerance is considered zero. Returns ------- a tuple of matrices or values necessary for hypotheses testing .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm Notes ----- Status: experimental and incomplete z8x(n=%d) and y(n=%d) should have the same number of rows!r)tolzCovariance of x singular!rrg?z%s is not a supported method!) shape ValueErrorrdotTrnpsubtractrsumlendiagpower)endogexogmethod toleranceyxnobsk_endognobs1k_exogdf_residpinv_xparamsinv_covtsscprusvinvss i/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/multivariate/multivariate_ols.py_multivariate_ols_fitr1;s=4 A AGMD'7ME6 u}}!$)4=122 2f}H aA**VX&& w9 - - - 6 6899 9 EE&MM ACGGAJJ 33'511 5a))1a M   3q66 ) )899 9Av''++AC0044Q77#''"'"(4"3"3445599!<< GAJJNN1   ! !& ) ) ACGGAJJ 33'51186ABBBc|}|}|}tj||g}||k} | } || } tjd| D} tj||z dz dz } ||z dz dz }gd}gd}t j||}d}|tjd| z |jd<|| |jd <|| |jd <|| |jd <|||z dzdz z }||zdz d z }||z}||z||zzd z dkr0tj ||z|z|zd z ||z||zzd z z }nd}||zd|zz }|jd}tj |d|z }d|z |z |z|z }||jd<||jd<||jd<tj |||}||jd<|jd }|d| z|zdzz}|d|z|zdzz}||z |z||z z }||jd<||jd<||jd<tj |||}||jd<|jd }|dkrP|d|zz|d|zzzdz d|zdzz |dz z }||z}d ||zdz|dz z z}|dz dz |z }||z |z|z }n$|d| z|zdzz}|||zdzz}||z |z |z}||jd<||jd<||jd<tj |||}||jd<|jd }tj ||g}|}||z |z}||z |z}||jd<||jd<||jd<tj |||}||jd<|S)aV For multivariate linear model Y = X * B Testing hypotheses L*B*M = 0 where L is contrast matrix, B is the parameters of the multivariate linear model and M is dependent variable transform matrix. T = L*inv(X'X)*L' H = M'B'L'*inv(T)*LBM E = M'(Y'Y - B'X'XB)M Parameters ---------- eigenvals : ndarray The eigenvalues of inv(E + H)*H r_err_sscp : int Rank of E + H r_contrast : int Rank of T matrix df_resid : int Residual degree of freedom (n_samples minus n_variables of X) tolerance : float smaller than which eigenvalue is considered 0 Returns ------- A DataFrame References ---------- .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm cg|] }|d|z z  S)).0is r0 z&multivariate_stats..s 111aa1q5k111r2r5r)ValueNum DFDen DFF ValuePr > F) Wilks' lambdaPillai's traceHotelling-Lawley traceRoy's greatest root)columnsindexc8tj|gdS)Nr)rreal)r!s r0fnzmultivariate_stats..fnsws||Ar2)r?r:)r@r:)rAr:)rBr:r)r?r;)r?r<)r?r=)r?r>)r@r;)r@r<)r@r=)r@r>)rAr;)rAr<)rAr=)rAr>)rBr;)rBr<)rBr=)rBr>)rminrarrayabspd DataFrameprodlocmaxsqrtrr fsf) eigenvals r_err_sscp r_contrastr&rr.pqr-indn_eeigv2eigv1mncolsrDresultsrGrr,df1r*df2lmdFpvalVUbcsigmas r0multivariate_statsrm}sD AAA 1vA i C ''))C cNE H115111 2 2E A aA QaA = = =D > > >El4!&(((G-/Brwq5y/A/A,B,BGK()-/R __GK)*57R __GK1224"UYY[[//GK./ QUQYMA 1qA A a%CsQqSy1}q GQqSU1Wq[QqS1Q3Y]3 4 4  A#!)C +. /C (3A  C SC##A-0GK)*-0GK)*./GK*+ 7::ac " "D-1GK)* -.A qsQw{ C qsQw{ C c A QA.1GK*+.1GK*+/0GK+, 7::ac " "D.2GK*+ 56A1uu 1WQqS !A %1q 1QU ;!e1Q37q1u%% 1WMA  #IMA 1Q37Q;1Q37m #IMA 69GK2369GK2378GK34 7::ac " "D6:GK23 K6 7E 1vA C a%!)C c EA36GK/036GK/045GK01 7::ac " "D37GK/0 Nr2c2fd}t||||S)Nc \}}}}||||z }|||j}t|} |jt||} |j||} | | | |fSN)rrrr) LMCr(r&r)r+t1t2rYHE fit_resultss r0rGz"_multivariate_ols_test..fns,7('5 UU6]]  q ! !A % UU7^^   $ $ OO DHHSWW   ! !" % % CGGENN  q ! !!Q  r2)_multivariate_test) hypothesesrx exog_names endog_namesrGs ` r0_multivariate_ols_testr}s2 ! ! ! ! ! j*k2 F FFr2hypotheses_docc  t|}t|}i}|D]_}t|dkr |\}} d} d} nVt|dkr |\}} } d} n:t|dkr|\}} } } ntdt|ztd| Dr(t|| j} nqt | tjrt| j dkrtd| j d|krtd | j d|fz| tj |} ntd | Dr-t|| jj } ns| qt | tjrt| j dkrtd | j d |krtd | j d |fz| -tj | j d | j dg} n)t | tjstd| j d | j d kr*td| j d | j d fz| j d| j dkr*td| j d| j dfz|| | | \} } }}tj | | }t|}tjt!t#|| }t%||||}|| | | | | d||<a|S)ac Multivariate linear model hypotheses testing For y = x * params, where y are the dependent variables and x are the independent variables, testing L * params * M = 0 where L is the contrast matrix for hypotheses testing and M is the transformation matrix for transforming the dependent variables in y. Algorithm: T = L*inv(X'X)*L' H = M'B'L'*inv(T)*LBM E = M'(Y'Y - B'X'XB)M where H and E correspond to the numerator and denominator of a univariate F-test. Then find the eigenvalues of inv(H + E)*H from which the multivariate test statistics are calculated. .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML /default/viewer.htm#statug_introreg_sect012.htm Parameters ---------- %(hypotheses_doc)s k_xvar : int The number of independent variables k_yvar : int The number of dependent variables fn : function a function fn(contrast_L, transform_M) that returns E, H, q, df_resid where q is the rank of T matrix Returns ------- results : MANOVAResults rNrHzBhypotheses must be a tuple of length 2, 3 or 4. len(hypotheses)=%dc3@K|]}t|tVdSrp isinstancestrr7js r0 z%_multivariate_test..=s,--az!S!!------r2z&Contrast matrix L must be a 2-d array!r5zJContrast matrix L should have the same number of columns as exog! %d != %dc3@K|]}t|tVdSrprrs r0rz%_multivariate_test..Hs,//As##//////r2z'Transform matrix M must be a 2-d array!rzbTransform matrix M should have the same number of rows as the number of columns of endog! %d != %dz&Constant matrix C must be a 2-d array!zCcontrast L and constant C must have the same number of rows! %d!=%dzGtransform M and constant C must have the same number of columns! %d!=%d)stat contrast_L transform_M constant_Crwrv)rranyr linear_constraintcoefsrrndarrayreyerzerosaddrsortrrrm)rzr{r|rGk_xvark_yvarrahyponamerqrrrsrwrvrYr&EHrXr\ stat_tables r0ryrysJ__F   FG:):) t99q==GD!AAA YY!^^JD!QAA YY!^^ MD!Q358YY?@@ @ --1--- - - 7:&&88;;AAAa,, KAG 0A0A !IJJJwqzV## "G"#'!*f!5"6777 9vAA //Q/// / / ;;''99!<<BDAA}!!RZ00PCLLA4E4E$%NOOO71:''$&:'(gaj&%9&:;;; 9!'!*agaj122AAArz** GEFF F 71: # #6 ! AGAJ7899 9 71: # #9 ! AGAJ7899 9Bq!QKK1a VAq\\ OOb! --..'q!X>> !+1()a))  Nr2c0eZdZdZdZdfd ZddZxZS) _MultivariateOLSa Multivariate linear model via least squares Parameters ---------- endog : array_like Dependent variables. A nobs x k_endog array where nobs is the number of observations and k_endog is the number of dependent variables exog : array_like Independent variables. A nobs x k_exog array where nobs is the number of observations and k_exog is the number of independent variables. An intercept is not included by default and should be added by the user (models specified using a formula include an intercept by default) Attributes ---------- endog : ndarray See Parameters. exog : ndarray See Parameters. Nnonec t|jdks|jddkrtdtj||f||d|dS)Nr5zGThere must be more than one dependent variable to fit multivariate OLS!)missinghasconst)rrrsuper__init__)selfrrrrkwargs __class__s r0rz_MultivariateOLS.__init__s u{  q EKNa$7$79:: : Lg8@ L LDJ L L L L Lr2rcbt|j|j||_t |S)N)r)r1rr _fittedmod_MultivariateOLSResults)rrs r0fitz_MultivariateOLS.fits1/ J &222&t,,,r2)rN)r)__name__ __module__ __qualname____doc___formula_max_endogrr __classcell__)rs@r0rrnsi0LLLLLL--------r2rcPeZdZdZdZdZeed dZdZ dS) rz( _MultivariateOLS results class ct|dr't|jdr|jj|_nd|_|j|_|j|_|j|_dS)Ndata design_info)hasattrrrr{r|r)r fitted_mv_olss r0rz _MultivariateOLSResults.__init__se M6 * * $ *M:: $,1=D  #D '2(4'2r2cN|Srpsummary__str__rs r0rz_MultivariateOLSResults.__str__||~~%%'''r2r~NFct|j}||jY|jj}g}|D]G}|r|dkr t j|||ddf}|||dgHnLg}t|D]:}d|z}t jd|g} d| |<||| dg;t||j |j|j } t| |j |jS)aO Linear hypotheses testing Parameters ---------- %(hypotheses_doc)s skip_intercept_test : bool If true, then testing the intercept is skipped, the model is not changed. Note: If a term has a numerically insignificant effect, then an exception because of emtpy arrays may be raised. This can happen for the intercept if the data has been demeaned. Returns ------- results: _MultivariateOLSResults Notes ----- Tests hypotheses of the form L * params * M = C where `params` is the regression coefficient matrix for the linear model y = x * params, `L` is the contrast matrix, `M` is the dependent variable transform matrix and C is the constant matrix. N Interceptzx%dr5) rr{rterm_name_slicesrrappendrangerr}rr|MultivariateTestResults) rrzskip_intercept_testrtermskey L_contrastr8rrqras r0mv_testz_MultivariateOLSResults.mv_tests7:T_%%  +(9  ??C*!sk/A/A !#c AAA !>J%%sJ&=>>>> ?  v77A A;D!V--AAaD%%tQo6666(T_*./4;KMM'w'+'7'+88 8r2ctrp)NotImplementedErrorrs r0rz_MultivariateOLSResults.summarys!!r2)NF) rrrrrrr _hypotheses_docrrr6r2r0rrsz333(((\1113838382138j"""""r2rcFeZdZdZdZdZdZedZ d dZ dS) raE Multivariate test results class Returned by `mv_test` method of `_MultivariateOLSResults` class Parameters ---------- results : dict[str, dict] Dictionary containing test results. See the description below for the expected format. endog_names : sequence[str] A list or other sequence of endogenous variables names exog_names : sequence[str] A list of other sequence of exogenous variables names Attributes ---------- results : dict Each hypothesis is contained in a single`key`. Each test must have the following keys: * 'stat' - contains the multivariate test results * 'contrast_L' - contains the contrast_L matrix * 'transform_M' - contains the transform_M matrix * 'constant_C' - contains the constant_C matrix * 'H' - contains an intermediate Hypothesis matrix, or the between groups sums of squares and cross-products matrix, corresponding to the numerator of the univariate F test. * 'E' - contains an intermediate Error matrix, corresponding to the denominator of the univariate F test. The Hypotheses and Error matrices can be used to calculate the same test statistics in 'stat', as well as to calculate the discriminant function (canonical correlates) from the eigenvectors of inv(E)H. endog_names : list[str] The endogenous names exog_names : list[str] The exogenous names summary_frame : DataFrame Returns results as a MultiIndex DataFrame cd||_t||_t||_dSrp)ralistr|r{)rrar|r{s r0rz MultivariateTestResults.__init__ s,  ,,z**r2cN|Srprrs r0rzMultivariateTestResults.__str__rr2c|j|Srp)ra)ritems r0 __getitem__z#MultivariateTestResults.__getitem__s|D!!r2chg}|jD]\}|j|d}||jdddf<||]t j|d}|ddg}|j ddgd |S) z: Return results as a multiindex dataframe rNEffectr)axisrD StatisticT)inplace) racopyrPr reset_indexrMconcat set_indexrD set_names)rdfrtmps r0 summary_framez%MultivariateTestResults.summary_frames < ) )C,s#F+0022C#&CGAAAxK IIcoo'' ( ( ( ( Yr " " " \\8W- . . Hk2DAAA r2Fctj}|d|jD]}|ddi|j|d}|}t|j}||d<||_gd|_ | ||rX||ditj |j|d|j }| ||rX||d itj |j|d |j }| ||rQ||d itj |j|d }| ||S)a6 Summary of test results Parameters ---------- show_contrast_L : bool Whether to show contrast_L matrix show_transform_M : bool Whether to show transform_M matrix show_constant_C : bool Whether to show the constant_C zMultivariate linear modelrr)rrrrz contrast L=r)rCz transform M=r)rDz constant C=r)r Summary add_titleraadd_dictrrrrCrDadd_dfrMrNr{r|)rshow_contrast_Lshow_transform_Mshow_constant_Csummrrrks r0rzMultivariateTestResults.summary's!! 2333<  C MM2r( # # #c"6*//11B!!BRZ  AAaDBJ'''BH KKOOO  sN3444\$,s"3L"A*./;;; B  sO4555\$,s"3M"B(,(8::: B  sN3444\$,s"3L"ABB B r2N)FFF) rrrrrrrpropertyrrr6r2r0rrs))V+++ ((("""  X ?D %''''''r2r)rr)r)rnumpyr numpy.linalgrrrrrrscipyr pandasrMpatsyr statsmodels.compat.pandasr statsmodels.base.modelr statsmodels.iolibr __docformat__rr1rmr}ryrrrr6r2r0rsDDDDDDDDDDDDDDDD222222((((((&&&&&&% 'V?C?C?C?CH8<ttttnGGG(_---bb.-bJ%-%-%-%-%-u%-%-%-PH"H"H"H"H"H"H"H"Vmmmmmmmmmmr2