>haoSSKrSSKJr SSKJr SSKJr SSK J r J r SSK J r "SS5r"S S 5rSS jr"S S 5rSrSrSSjr"SS5rSSjrSSjrSSjrSrSSjrSSjrg)N)f)t)stats)clean0fullrank) multipletestscP\rSrSrSrS SjrS SjrSrSrS Sjr SS jr S r g)ContrastResults a@ Class for results of tests of linear restrictions on coefficients in a model. This class functions mainly as a container for `t_test`, `f_test` and `wald_test` for the parameters of a model. The attributes depend on the statistical test and are either based on the normal, the t, the F or the chisquare distribution. Nc X@lUb[SUlX lURUlXPlX`l[ UlXe4Ul[ R"X&U5Ul GOUblSUlXl XlX0l XPl[UlU4UlURR[R"U5U5S-Ul GO>SU;Ga"USUlUSUlUS=Ul n X0l [!["UR5UlUR%SS5UlURS:Xa2URRURU5Ul XPlO[R&"U [R(5Ul [R*"U 5)n URR[R"X55S-URU 'O[R(Ul [R,"UR5Ul URb8[/[1UR55V s/sHn S U -PM sn UlgSUlgs sn f) NFr statistic distribution dist_argschi2zc%d)effectrfvaluerdf_denomdf_numfdistdistrsfpvaluetvaluesd student_tnpabsgetattrrget full_likenanisnansqueezerangelenc_names) selfrr rrrralphakwdsvaluenot_naniis mC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/stats/contrast.py__init__ContrastResults.__init__s = #D K![[DN$M KDI$/DN((1h7DK ] #D KNG$M!DI&[DN)),,rvvay(;a?DK D $^ 4D !+.DN"&{"3 3DK%Gt'8'89DI!XXk26DN  F*"iill4>>8D (  ll5"&&9 88E?*'+yy||BFF5>4J'Ka'O G$&&DKjj- ;; "16s4;;7G1HI1H2EBJ1HIDLDLJs$Jc&URbzURR"SUS- - /URQ76nURX R-- nURX R--n[ R "X445$[S5e)a Returns the confidence interval of the value, `effect` of the constraint. This is currently only available for t and z tests. Parameters ---------- alpha : float, optional The significance level for the confidence interval. ie., The default `alpha` = .05 returns a 95% confidence interval. Returns ------- ci : ndarray, (k_constraints, 2) The array has the lower and the upper limit of the confidence interval in the columns. g@z!Confidence Interval not available)rrppfrrr column_stackNotImplementedError)r*r+qloweruppers r0conf_intContrastResults.conf_intHsv$ ;; " a%"*n>t~~>AKK!gg+-EKK!gg+-E??E>2 2%&IJ Jc>UR5R5$N)summary__str__r*s r0rAContrastResults.__str__cs||~%%''r=cT[UR5S-UR5-$N str __class__rArBs r0__repr__ContrastResults.__repr__f!4>>"T)DLLN::r=c URbUcSnOUS:XaSnURS:HnSnUc URnSSKJn [ R "UR5nU"XRURURXpRU54XQUX2S9nU$[US 5(a:S [UR5URURUR4-$URS :Xa1S URURURUR4-$S UR<SUR<S3$)aSummarize the Results of the hypothesis test Parameters ---------- xname : list[str], optional Default is `c_##` for ## in the number of regressors alpha : float significance level for the confidence intervals. Default is alpha = 0.05 which implies a confidence level of 95%. title : str, optional Title for the params table. If not None, then this replaces the default title Returns ------- smry : str or Summary instance This contains a parameter results table in the case of t or z test in the same form as the parameter results table in the model results summary. For F or Wald test, the return is a string. NzTest for Constraintsr constraintsr)summary_params)ynamexnameuse_ttitler+rz0rz9z)rrr)statsmodels.iolib.summaryrPr atleast_1drrrr;hasattrreprrrr) r*rRr+rTrSrQrPpvaluessumms r0r@ContrastResults.summaryis7, ;; "}."&&#-EE}  @mmDKK0G!4dggt~~#*MM%,@#B(-%(->> import statsmodels.api as sm >>> from statsmodels.stats.contrast import Contrast >>> import numpy as np >>> np.random.seed(54321) >>> X = np.random.standard_normal((40,10)) # Get a contrast >>> new_term = np.column_stack((X[:,0], X[:,2])) >>> c = Contrast(new_term, X) >>> test = [[1] + [0]*9, [0]*2 + [1] + [0]*7] >>> np.allclose(c.contrast_matrix, test) True Get another contrast >>> P = np.dot(X, np.linalg.pinv(X)) >>> resid = np.identity(40) - P >>> noise = np.dot(resid,np.random.standard_normal((40,5))) >>> new_term2 = np.column_stack((noise,X[:,2])) >>> c2 = Contrast(new_term2, X) >>> print(c2.contrast_matrix) [ -1.26424750e-16 8.59467391e-17 1.56384718e-01 -2.60875560e-17 -7.77260726e-17 -8.41929574e-18 -7.36359622e-17 -1.39760860e-16 1.82976904e-16 -3.75277947e-18] Get another contrast >>> zero = np.zeros((40,)) >>> new_term3 = np.column_stack((zero,X[:,2])) >>> c3 = Contrast(new_term3, X) >>> test2 = [0]*2 + [1] + [0]*7 >>> np.allclose(c3.contrast_matrix, test2) True c\[US5(dUR5 UR$)z# Gets the contrast_matrix property _contrast_matrix)rXcompute_matrixrlrBs r0 _get_matrixContrast._get_matrixs*t/00    !$$$r=cp[R"U5Ul[R"U5Ulgr?)rasarraytermdesign)r*rrrss r0r1Contrast.__init__s"JJt$ jj( r=c4URnURS:Xa USS2S4n[U5UlURUl[ URUR 5UlURRSUl g! SUl g=f)z Construct a contrast matrix C so that colspan(dot(D, C)) = colspan(dot(D, dot(pinv(D), T))) where pinv(D) is the generalized inverse of D=design. r4N) rrndimrTrsDcontrastfromcolsrlmatrixshaperank)r*rws r0rmContrast.compute_matrix s{ II 66Q;!D& A 0 @  ))!,DI DIs -B B)rxrwrlrsr|rrN) rbrcrdrerfrnpropertycontrast_matrixr1rmrgrr=r0riris#?@%{+O)r=ricl[R"U5n[R"U5nURup4URSU:waURSU:wa [S5eUc[RR U5nURSU:Xa![R "X 5RnOAUn[R "U[R "XR55Rn[R "XR5n[UR5S:Xa US4Ul[RRU5URS:wa+[U5n[R "X&5Rn[R"U5$)aF From an n x p design matrix D and a matrix L, tries to determine a p x q contrast matrix C which determines a contrast of full rank, i.e. the n x q matrix dot(transpose(C), pinv(D)) is full rank. L must satisfy either L.shape[0] == n or L.shape[1] == p. If L.shape[0] == n, then L is thought of as representing columns in the column space of D. If L.shape[1] == p, then L is thought of as what is known as a contrast matrix. In this case, this function returns an estimable contrast corresponding to the dot(D, L.T) Note that this always produces a meaningful contrast, not always with the intended properties because q is always non-zero unless L is identically 0. That is, it produces a contrast that spans the column space of L (after projection onto the column space of D). Parameters ---------- L : array_like D : array_like rr4zshape of L and D mismatched) rrqr{ ValueErrorlinalgpinvdotrwr( matrix_rankrr&)LrxpseudonpCLps r0ryry s)< 1 A 1 A 77DAwwqzQ1771:?677 ~"wwqzQ FF6     FF6266!SS> * , , 33B 288}q6 yyR BHHQK/ b\ FF6   ::a=r=cD\rSrSrS Sjr\S5rSrSrSr Sr g) WaldTestResultsi\NcX@lX lXlX0lUbbUSRUlUSRUlUSRUlURS:XaUSRUlggURS:Xa*[RUl URSUlOJURS:Xa/[RUl URuUlUlO [S5eUc7URR"[R"U5/UQ76UlgXPlg) Nrr df_constraintr rrrz)only F and chi2 are possible distribution)tablerrrvaluesrZdf_constraintsrrrrrrrrr )r*rrrrrZs r0r1WaldTestResults.__init___s  (""  ";/66DN ?11DL"'"8"?"?D   C' %j 1 8 8 (  F*!JJ &*nnQ&7#""c)!GG 59^^2#T]!!LMM#yy||BFF9,=J J & r=cSUR-nURUS/nURS:XaURS5 U$)z'column names for summary table zP>%sz df constraintr zdf denom)rappend)r*pr_test col_namess r0rWaldTestResults.col_namessH 4,,,&&A    #   Z (r=c[US5(a UR$[[URR UR 55nURRUS9UlUR$)N_dframe)columns) rXrdictziprrrrenamedframe)r*renamings r0r_WaldTestResults.summary_frames[ 4 # #<< DJJ..?@jj'''9 {{r=c>UR5R5$r?)r_ to_stringrBs r0rAWaldTestResults.__str__s!!#--//r=cT[UR5S-UR5-$rErGrBs r0rJWaldTestResults.__repr__rLr=) rrrrrrrZrr)NN) rbrcrdrer1r~rr_rArJrgrr=r0rr\s5BF 'D0;r=rc[R"US5n[U6Vs/sHnXSSXS3PM nnU$s snf)z8helper function for labels for pairwise comparisons r4-r)r triu_indicesr)k_level level_names idx_pairs_allnamelabelss r0_get_pairs_labelsrs^OOGQ/M}-/-$!W%&a G(<'=>- / M/sAcUS- n[R"US5n[US5n[R"XS45nSU[R"U5US4'SU[R"U5US4'[R "U5n[R "Xv4SS9nURSn [R"X45n XSS2X"U-24'U $)acreate pairwise contrast for reference coding currently not used, using encoding contrast matrix is more general, but requires requires factor information from patsy design_info. Parameters ---------- k_params : int number of parameters k_level : int number of levels or categories (including reference case) idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. Returns ------- contrasts : ndarray restriction matrix with k_params columns and number of rows equal to the number of restrictions. r4r)axisN)rrr(zerosarangeeye concatenater{) k_paramsr idx_start k_level_m1 idx_pairskc_pairs c_referenceck_all contrastss r0_contrast_pairsrs21J A.I IaLAhh'G*,GBIIaL)A, &'*+GBIIaL)A, &'&&$K  -A6A GGAJE%*+I78a3334 r=cURU5nURUS9n[U5[LaU/nUH-n[ UR XS9n U SUSU-'U SUSU-'M/ U$)asperform t_test and add multiplicity correction to results dataframe Parameters ---------- result results instance results of an estimated model contrasts : ndarray restriction matrix for t_test method : str or list of strings method for multiple testing p-value correction, default is'hs'. alpha : float significance level for multiple testing reject decision. ci_method : None not used yet, will be for multiplicity corrected confidence intervals contrast_names : {list[str], None} If contrast_names are provided, then they are used in the index of the returned dataframe, otherwise some generic default names are created. Returns ------- res_df : pandas DataFrame The dataframe contains the results of the t_test and additional columns for multiplicity corrected p-values and boolean indicator for whether the Null hypothesis is rejected. )rR)methodr+r4z pvalue-%srz reject-%s)t_testr_typelistrr) resultrrr+ ci_methodcontrast_namesttres_dfmethmts r0 t_test_multirs6 y !B   N  3F F|4 299T ?%'U{T!"%'U{T!" Mr=c\rSrSrSrSrSrg)MultiCompResultiz\class to hold return of t_test_pairwise currently just a minimal class to hold attributes. c :URRU5 gr?)__dict__update)r*kwargss r0r1MultiCompResult.__init__s V$r=rN)rbrcrdrerfr1rgrr=r0rrs %r=rcURupE[R"XA45nUcXSS2X"U-24'U$XSS2U4'U$)ahelper function to expand constraints to a full restriction matrix Parameters ---------- contrasts : ndarray restriction matrix for t_test k_params : int number of parameters idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. index : slice or ndarray Column index if constraints do not form a block in the full restriction matrix, i.e. if parameters that are subject to restrictions are not consecutive in the list of parameters. If index is not None, then idx_start is ignored. Returns ------- contrasts : ndarray restriction matrix with k_params columns and number of rows equal to the number of restrictions. N)r{rr)rrrindexk_ck_prs r0_embed_constraintsrsQ4HC #!A },5!YS ( () H !U( Hr=cUnURupVSSKJs Js Jn US;aUR U5*nO [ S5eURU5n UbUc [S5e[XU5n U $)ahelper function to create constraints based on encoding matrix Parameters ---------- encoding_matrix : ndarray contrast matrix for the encoding of a factor as defined by patsy. The number of rows should be equal to the number of levels or categories of the factor, the number of columns should be equal to the number of parameters for this factor. comparison : str Currently only 'pairwise' is implemented. The restriction matrix can be used for testing the hypothesis that all pairwise differences are zero. k_params : int number of parameters idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. Returns ------- contrast : ndarray Contrast or restriction matrix that can be used in hypothesis test of model results. The number of columns is k_params. rN)pairwisepwpairsz!currentlyonly pairwise comparisonz3if k_params is not None, then idx_start is required) r{#statsmodels.sandbox.stats.multicompsandboxr multicompcontrast_allpairsr7rrr) encoding_matrix comparisonrrcmrrmcc_allrs r0_constraints_factorr&s: B88LG4400%%g..!"EFF " I  () )&yIF r=c .URRRnURR U5nUR UnUR URn U(d$[UR5S:a [S5eURSn URU Rn Ub2[U5[U 5:XaUn O[S[U 5-5e[U 5n URUSRU Rn [UR 5n[#X5nSSKJs Js Jn UR-U 5*nUR/U 5n[1UX5n[3UUUSX?S9n[5UUUUU S9nU$)a Perform pairwise t_test with multiple testing corrected p-values. This uses the formula design_info encoding contrast matrix and should work for all encodings of a main effect. Parameters ---------- result : result instance The results of an estimated model with a categorical main effect. term_name : str name of the term for which pairwise comparisons are computed. Term names for categorical effects are created by patsy and correspond to the main part of the exog names. method : {str, list[str]} multiple testing p-value correction, default is 'hs', see stats.multipletesting alpha : float significance level for multiple testing reject decision. factor_labels : {list[str], None} Labels for the factor levels used for pairwise labels. If not provided, then the labels from the formula design_info are used. ignore : bool Turn off some of the exceptions raised by input checks. Returns ------- MultiCompResult The results are stored as attributes, the main attributes are the following two. Other attributes are added for debugging purposes or as background information. - result_frame : pandas DataFrame with t_test results and multiple testing corrected p-values. - contrasts : matrix of constraints of the null hypothesis in the t_test. Notes ----- Status: experimental. Currently only checked for treatment coding with and without specified reference level. Currently there are no multiple testing corrected confidence intervals available. r4z%interaction effects not yet supportedrNz0factor_labels has the wrong length, should be %d)rrr+r) result_framerrrcontrast_labelsterm_encoding_matrix)modeldata design_info term_namesrterms term_slicesstartr(factorsr factor_infos categories term_codingscontrast_matricesrzparamsrrrrrrrrrr)r term_namerr+ factor_labelsignoredesinfoterm_idxrrrfactorcatrrrrr c_all_pairs contrasts_subrrress r0t_test_pairwiserUszbll++G!!'' 2H == "D##D)//I c$,,'!+@AA \\!_F   v & 1 1C } S )CORUVYRZZ[ [#hG   d #A & 8 8 @ G GB6==!H w ,F44''00KOOB'M"=(FI &)Fd %>F v$-#*0/1  3C Jr=cX-nX-nX4- $)zoffset to the value of a linear constraint for new params usage: (cm, v) is original constraint vo = offset_constraint(cm, res2.params, params_alt) fs = res2.wald_test((cm, v + vo)) nc = fs.statistic * fs.df_num r)r_matrix params_est params_altdiff_estdiff_alts r0_offset_constraintr s$H$H  r=cUcX-U- nURUS9nU(a$U[RRXd5-nU$U[R"[R "U55- nU$)aMoncentrality parameter for a wald test in model results The null hypothesis is ``diff = r_matrix @ params - value = 0`` Parameters ---------- params : ndarray parameters of the model at which to evaluate noncentrality. This can be estimated parameters or parameters under an alternative. r_matrix : ndarray Restriction matrix or contrasts for the Null hypothesis value : None or ndarray Value of the linear combination of parameters under the null hypothesis. If value is None, then it will be replaced by zero. results : Results instance of a model The results instance is used to compute the covariance matrix of the linear constraints using `cov_params. diff : None or ndarray If diff is not None, then it will be used instead of ``diff = r_matrix @ params - value`` joint : bool If joint is True, then the noncentrality parameter for the joint hypothesis will be returned. If joint is True, then an array of noncentrality parameters will be returned, where elements correspond to rows of the restriction matrix. This correspond to the `t_test` in models and is not a quadratic form. Returns ------- nc : float or ndarray Noncentrality parameter for Wald tests, correspondig to `wald_test` or `t_test` depending on whether `joint` is true or not. It needs to be divided by nobs to obtain effect size. Notes ----- Status : experimental, API will likely change )r) cov_paramsrrsolvesqrtdiag)rrr-resultsdiffjointcov_cncs r0wald_test_noncentrsmR | 5(     1E BIIOOE0 0 IBGGBGGEN+ + Ir=c,UcSnUcX-U- nUnURU5RUR5nU(a$U[RR Xt5-nU$U[R "[R "U55- nU$)a8noncentrality parameter for a wald test The null hypothesis is ``diff = r_matrix @ params - value = 0`` Parameters ---------- params : ndarray parameters of the model at which to evaluate noncentrality. This can be estimated parameters or parameters under an alternative. r_matrix : ndarray Restriction matrix or contrasts for the Null hypothesis value : None or ndarray Value of the linear combination of parameters under the null hypothesis. If value is None, then it will be replace by zero. cov_params : ndarray covariance matrix of the parameter estimates diff : None or ndarray If diff is not None, then it will be used instead of ``diff = r_matrix @ params - value`` joint : bool If joint is True, then the noncentrality parameter for the joint hypothesis will be returned. If joint is True, then an array of noncentrality parameters will be returned, where elements correspond to rows of the restriction matrix. This correspond to the `t_test` in models and is not a quadratic form. Returns ------- nc : float or ndarray Noncentrality parameter for Wald tests, correspondig to `wald_test` or `t_test` depending on whether `joint` is true or not. It needs to be divided by nobs to obtain effect size. Notes ----- Status : experimental, API will likely change r)rrwrrrrr) rrr-r rrrrrs r0wald_test_noncent_genericrsR } | 5(A EE*  ! !!## &E BIIOOE0 0 IBGGBGGEN+ + Ir=r?)hsraNN)rNN)rraNF)NT)numpyr scipy.statsrrrrscipyrstatsmodels.tools.toolsrrstatsmodels.stats.multitestrr riryrrrrrrrrr rrrr=r0rs"&45mDmDbbbJ8x?;?;J'THL $$N%%  FJN"&,^;?/4Qh  1hIM$(5r=