B ZM@sdZddlmZddlZddlmZmZmZm Z m Z m Z ddl m Z ddlZddlmZddlmZddlmZdd lmZd Zd ZdddZdddZddZddZdede_GdddeZGdddeZ GdddeZ!dS) z*General linear model author: Yichuan Liu )divisionN)eigvalsinvsolve matrix_rankpinvsvd)stats) DesignInfo) string_types)Model)summary2zrestructuredtext ena=hypotheses: A list of tuples 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>cCsx|}|}|j\}}|j\}} ||kr4td||f|| } |dkrt|} | |} | | j} t| |d| krztd|| }t|j||j|}| | | |fS|dkrht|d\}}}||k t |krtdd|}|jt ||j|} |jt t |d|} t ||| }t|j||j|}| | | |fStd |d S) 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 : string '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)ZtolzCovariance of x singular!rrg?z%s is not a supported method!N) shape ValueErrorrdotTrnpsubtractrsumlenZdiagpower)endogexogmethod toleranceyxZnobsZk_endogZnobs1Zk_exogdf_residZpinv_xparamsinv_covtsscprusvZinvsr'Hlib/python3.7/site-packages/statsmodels/multivariate/multivariate_ols.py_multivariate_ols_fit?s8           r)c Cs|}|}|}t||g}||k} | } || } tdd| D} t||dd} ||dd}ddddd g}d d d d g}tj||d}dd}|td| |jd<|| |jd<|| |jd<|| |jd<|||dd}||dd}||}||||ddkr`t ||||d||||d}nd}||d|}|jd}t |d|}d||||}||jd<||jd<||jd<t j |||}||jd<|jd}|d| |d}|d||d}|||||}||jd<||jd<||jd<t j |||}||jd<|jd}|dkr|d||d|dd|d|d}||}d||d|d}|dd|}||||}n4|d| |d}|||d}||||}||jd <||jd!<||jd"<t j |||}||jd#<|jd}t ||g}|}|||}|||}||jd$<||jd%<||jd&<t j |||}||jd'<|S)(aT For multivariate linear model Y = X * B Testing hypotheses L*B*M = 0 where L is contrast matrix, B is the parameters of the multivariate linear model and M is dependent variable transform matrix. T = L*inv(X'X)*L' H = M'B'L'*inv(T)*LBM E = M'(Y'Y - B'X'XB)M Parameters ---------- eigenvals : array The eigenvalues of inv(E + H)*H r_err_sscp : int Rank of E + H r_contrast : int Rank of T matrix df_resid : int Residual degree of freedom (n_samples minus n_variables of X) tolerance : float smaller than which eigenvalue is considered 0 Returns ------- A DataFrame References ---------- .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm cSsg|]}|d|qS)r').0ir'r'r( sz&multivariate_stats..r*rValuezNum DFzDen DFzF ValuezPr > Fz Wilks' lambdazPillai's tracezHotelling-Lawley tracezRoy's greatest root)columnsindexcSst|gdS)Nr)rreal)rr'r'r(fnszmultivariate_stats..fn)z Wilks' lambdar.)zPillai's tracer.)zHotelling-Lawley tracer.)zRoy's greatest rootr.r)z Wilks' lambdazNum DF)z Wilks' lambdazDen DF)z Wilks' lambdazF Value)z Wilks' lambdazPr > F)zPillai's tracezNum DF)zPillai's tracezDen DF)zPillai's tracezF Value)zPillai's tracezPr > F)zHotelling-Lawley tracezNum DF)zHotelling-Lawley tracezDen DF)zHotelling-Lawley tracezF Value)zHotelling-Lawley tracezPr > F)zRoy's greatest rootzNum DF)zRoy's greatest rootzDen DF)zRoy's greatest rootzF Value)zRoy's greatest rootzPr > F)rminrZarrayabspd DataFrameZprodlocmaxZsqrtrr fZsf) Z eigenvalsZ r_err_sscpZ r_contrastrrr&pqr%ZindZn_eeigv2Zeigv1mnZcolsr0resultsr2rr$Zdf1r"Zdf2ZlmdFZpvalVUbcZsigmar'r'r(multivariate_statss"0            0           rHcsfdd}t||||S)Nc sn\}}}}||||}|||j}t|} |jt||} |j||} | | | |fS)N)rrrr) LMCr rr!r#Zt1Zt2r=HE) fit_resultsr'r(r2s z"_multivariate_ols_test..fn)_multivariate_test) hypothesesrN exog_names endog_namesr2r')rNr(_multivariate_ols_tests rScCst|}t|}i}xl|D]b}t|dkr@|\}} d} d} nFt|dkr\|\}} } d} n*t|dkrv|\}} } } ntdt|tdd| Drt|| j} nFt| tjrt| j dkrtd| j d|krtd | j d|f| dkrt |} n~td d| Dr.t|| jj } nV| dk rt| tjrVt| j dkr^td | j d |krtd | j d |f| dkrt | j d | j dg} nt| tjstd| j d | j d krtd| j d | j d f| j d| j dkr$td| j d| j df|| | | \} } }}t | | }t|}ttt|| }t||||}|| | | d||<qW|S)Nrr3zBhypotheses must be a tuple of length 2, 3 or 4. len(hypotheses)=%dcss|]}t|tVqdS)N) isinstancer )r+jr'r'r( sz%_multivariate_test..z&Contrast matrix L must be a 2-d array!r*zJContrast matrix L should have the same number of columns as exog! %d != %dcss|]}t|tVqdS)N)rUr )r+rVr'r'r(rW(sz'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_C)rranyr Zlinear_constraintZcoefsrUrZndarrayreyerzerosaddrsortrrrH)rPrQrRr2k_xvarZk_yvarrAZhyponamerIrJrKrMrLr=rZEHr<r>Z stat_tabler'r'r(rO sd          rOa 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 And then finding the eigenvalues of inv(H + E)*H .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm Parameters ---------- ag 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 cs,eZdZdZd fdd Zd ddZZS) _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 : array See Parameters. exog : array See Parameters. noneNc sHt|jdks|jddkr$tdtt|j||f||d|dS)Nr*zGThere must be more than one dependent variable to fit multivariate OLS!)missinghasconst)rrrsuperrc__init__)selfrrrerfkwargs) __class__r'r(rhsz_MultivariateOLS.__init__rcCst|j|j|d|_t|S)N)r)r)rr _fittedmod_MultivariateOLSResults)rirr'r'r(fitsz_MultivariateOLS.fit)rdN)r)__name__ __module__ __qualname____doc__rhrn __classcell__r'r')rkr(rcosrcc@s@eZdZdZddZddZd ddZd ed e_d d ZdS)rmz) _MultivariateOLS results class cCsDt|dr"t|jdr"|jj|_nd|_|j|_|j|_|j|_dS)Ndata design_info)hasattrrtrurQrRrl)riZ fitted_mv_olsr'r'r(rhs   z _MultivariateOLSResults.__init__cCs |S)N)summary__str__)rir'r'r(rxsz_MultivariateOLSResults.__str__Nc Cst|j}|dkr|jdk rb|jj}g}x||D].}t|||ddf}|||dgq.WnDg}x>t|D]2}d|}td|g}d||<|||dgqpWt ||j |j|j } t | |j |jS)Nzx%dr*) rrQruZterm_name_slicesrr]appendranger^rSrlrRMultivariateTestResults) rirPraZtermskeyZ L_contrastr,rbrIrAr'r'r(mv_tests&    z_MultivariateOLSResults.mv_testz2 Linear hypotheses testing Parameters ---------- a9 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. cCstdS)N)NotImplementedError)rir'r'r(rwsz_MultivariateOLSResults.summary)N) rorprqrrrhrxr}_hypotheses_docrwr'r'r'r(rms  rmc@s>eZdZdZddZddZddZedd Zdd d Z d S)r{ab Multivariate test results class Returned by `mv_test` method of `_MultivariateOLSResults` class Attributes ----------- results : dict For hypothesis name `key`: results[key]['stat'] contains the multivaraite test results results[key]['contrast_L'] contains the contrast_L matrix results[key]['transform_M'] contains the transform_M matrix results[key]['constant_C'] contains the constant_C matrix endog_names : string exog_names : string summary_frame : multiindex dataframe Returns results as a multiindex dataframe cCs||_||_||_dS)N)rArRrQ)riZ mv_test_dfrRrQr'r'r(rhsz MultivariateTestResults.__init__cCs |S)N)rwrx)rir'r'r(rxszMultivariateTestResults.__str__cCs |j|S)N)rA)riitemr'r'r( __getitem__sz#MultivariateTestResults.__getitem__cCszg}x@|jD]6}|j|d}||jdddf<||q Wtj|dd}|ddg}|jj ddgdd |S) z: Return results as a multiindex dataframe rXNZEffectr)Zaxisr0Z StatisticT)Zinplace) rAcopyr9ry reset_indexr7concatZ set_indexr0Z set_names)ridfr|Ztmpr'r'r( summary_frames z%MultivariateTestResults.summary_frameFcCst}|dx|jD]}|ddi|j|d}|}|jj}||d<||_ddddg|_ | ||r||dit j |j|d|j d}| ||r||dit j |j|d |jd }| ||r||d it |j|d }| |qW|S) z Parameters ---------- contrast_L : True or False Whether to show contrast_L matrix transform_M : True or False Whether to show transform_M matrix zMultivariate linear modelrXrz contrast L=rY)r/z transform M=rZ)r0z constant C=r[)r ZSummaryZ add_titlerAZadd_dictrrr/valuesr0Zadd_dfr7r8rQrR)riZshow_contrast_LZshow_transform_MZshow_constant_CZsummr|rrGr'r'r(rws4       zMultivariateTestResults.summaryN)FFF) rorprqrrrhrxrpropertyrrwr'r'r'r(r{s r{)rr)r)"rrZ __future__rZnumpyrZ numpy.linalgrrrrrrZscipyr Zpandasr7Zpatsyr Zstatsmodels.compatr Zstatsmodels.base.modelr Zstatsmodels.iolibr Z __docformat__rr)rHrSrOrcobjectrmr{r'r'r'r(s(       * E uS&C