U Qv f5@sXddlZddlZddlmZddlmZmZdddgZ d ddZ dd dZ dd dZ dS)N) namedtuple) remove_na_postprocess_dataframemultivariate_normalitymultivariate_ttestbox_m皙?c Csddlm}t|}|jdks(td|t|jdd}|j\}}|dksZtd|dksjtd tj |d d d }tj j |d d  |j }||d}ttj |||jg}tj |||jg} d| jtt| j||dtt| j|df} dtdd|ddd|d|d|d} tj ||kr|d|dttt| d d| dd| d| dd|tt| ddd| d |dd| d| d} n|d} d| ddd| d} dd| d}d|| dd|| d|||d| dd|d}ddd| d| dd|| dd|| d|dd||d| dd|dd| | ddd|| dd| ||d| dd| d}tt|d||d}tt||d}|j| |t|d}||krd nd }tddddg}|| ||dS)aHenze-Zirkler multivariate normality test. Parameters ---------- X : np.array Data matrix of shape (n_samples, n_features). alpha : float Significance level. Returns ------- hz : float The Henze-Zirkler test statistic. pval : float P-value. normal : boolean True if X comes from a multivariate normal distribution. See Also -------- normality : Test the univariate normality of one or more variables. homoscedasticity : Test equality of variance. sphericity : Mauchly's test for sphericity. Notes ----- The Henze-Zirkler test [1]_ has a good overall power against alternatives to normality and works for any dimension and sample size. Adapted to Python from a Matlab code [2]_ by Antonio Trujillo-Ortiz and tested against the `MVN `_ R package. Rows with missing values are automatically removed. References ---------- .. [1] Henze, N., & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics-Theory and Methods, 19(10), 3595-3617. .. [2] Trujillo-Ortiz, A., R. Hernandez-Walls, K. Barba-Rojo and L. Cupul-Magana. (2007). HZmvntest: Henze-Zirkler's Multivariate Normality Test. A MATLAB file. Examples -------- >>> import pingouin as pg >>> data = pg.read_dataset('multivariate') >>> X = data[['Fever', 'Pressure', 'Aches']] >>> pg.multivariate_normality(X, alpha=.05) HZResults(hz=0.540086101851555, pval=0.7173686509622386, normal=True) r)lognormz+X must be of shape (n_samples, n_features).axiszX must have at least 3 rows.z!X must have at least two columns.FT)rowvarZbiasZ hermitian)Zscale HZResultshzpvalnormal)rrr) scipy.statsr npasarrayndimAssertionErrorisnananyshapecovlinalgpinvZastypeZdtypemeanZdiagZ multi_dotTrepeatreshapeZtilesqrtZ matrix_ranksumexploglog1psfr)Xalphar npSZS_invZdifTZDjYZDjkbrwbamuZsi2Zpmupsirrrr99/tmp/pip-unpacked-wheel-2te3nxqf/pingouin/multivariate.pyr sh6   >:.( F> : FcCszddlm}t|}|jdks(td|dkrZt|jd}|t|j dd}n|j\}}t|}|jdkstd |jdkr|j |kstn8d }|jd|kst||rd }|jd|kst|t |||d d \}}|j\}} |jd} |dks td|jdks"|dkr|} |jdkrPtj |dd} | d|} n&tj ||dd} | d| d} tjj| dd}| || | }n|| d} tj |dd}tj |dd}|d|| d|| d}tjjd|d| |dd}| d| d} | || }|| | | | d}| }| | }||||}|||||d}tj|dgd}t|S)a Hotelling T-squared test (= multivariate T-test) Parameters ---------- X : np.array First data matrix of shape (n_samples, n_features). Y : np.array or None Second data matrix of shape (n_samples, n_features). If ``Y`` is a 1D array of shape (n_features), a one-sample test is performed where the null hypothesis is defined in ``Y``. If ``Y`` is None, a one-sample is performed against np.zeros(n_features). paired : boolean Specify whether the two observations are related (i.e. repeated measures) or independent. If ``paired`` is True, ``X`` and ``Y`` must have exactly the same shape. Returns ------- stats : :py:class:`pandas.DataFrame` * ``'T2'``: T-squared value * ``'F'``: F-value * ``'df1'``: first degree of freedom * ``'df2'``: second degree of freedom * ``'p-val'``: p-value See Also -------- multivariate_normality : Multivariate normality test. ttest : Univariate T-test. Notes ----- The Hotelling 's T-squared test [1]_ is the multivariate counterpart of the T-test. Rows with missing values are automatically removed using the :py:func:`remove_na` function. Tested against the `Hotelling `_ R package. References ---------- .. [1] Hotelling, H. The Generalization of Student's Ratio. Ann. Math. Statist. 2 (1931), no. 3, 360--378. See also http://www.real-statistics.com/multivariate-statistics/ Examples -------- Two-sample independent Hotelling T-squared test >>> import pingouin as pg >>> data = pg.read_dataset('multivariate') >>> dvs = ['Fever', 'Pressure', 'Aches'] >>> X = data[data['Condition'] == 'Drug'][dvs] >>> Y = data[data['Condition'] == 'Placebo'][dvs] >>> pg.multivariate_ttest(X, Y) T2 F df1 df2 pval hotelling 4.228679 1.326644 3 32 0.282898 Two-sample paired Hotelling T-squared test >>> pg.multivariate_ttest(X, Y, paired=True) T2 F df1 df2 pval hotelling 4.468456 1.314252 3 15 0.306542 One-sample Hotelling T-squared test with a specified null hypothesis >>> null_hypothesis_means = [37.5, 70, 5] >>> pg.multivariate_ttest(X, Y=null_hypothesis_means) T2 F df1 df2 pval hotelling 253.230991 74.479703 3 15 3.081281e-09 r)fr z*x must be of shape (n_samples, n_features)Nr r )r r zY must be 1D or 2D.z:X and Y must have the same number of features (= columns).z4X and Y must have the same number of rows if paired.Zrows)pairedr z#At least five samples are required.TF)rr)ZT2Fdf1df2rZ hotelling)index)rr;rrrrzerosr rrsizerr!r$r"r#r-pd DataFramer)r.r3r<r;xyZnxZkxerrknyr0r!ZdiffZinv_covt2Zx_covZy_covZ pooled_covZfvalr?r@rstatsr9r9r:r}sVM            MbP?cCsddlm}t|tjs td||jks2tdt||jsJtd|j |dd|}|j dksntd |j dd }|j j \}}|jd d df} | } | d} |||d }|| d jdd| |} tj| } tj|| | d}tt| dkrX|dd|dd|dd||d| |d}nHd|dd|dd|d|d}|d| d| 9}dd|t|}d||d|d}|||}||krdnd}tjdg|g|g|g|gdd}t|S)aJ Test equality of covariance matrices using the Box's M test. Parameters ---------- data : :py:class:`pandas.DataFrame` Long-format dataframe. dvs : list Dependent variables. group : str Grouping variable. alpha : float Significance level. Default is 0.001 as recommended in [2]_. A non-significant p-value (higher than alpha) indicates that the covariance matrices are homogenous (= equal). Returns ------- stats : :py:class:`pandas.DataFrame` * ``'Chi2'``: Test statistic * ``'pval'``: p-value * ``'df'``: The Chi-Square statistic's degree of freedom * ``'equal_cov'``: True if ``data`` has equal covariance Notes ----- .. warning:: Box's M test is susceptible to errors if the data does not meet the assumption of multivariate normality or if the sample size is too large or small [3]_. Pingouin uses :py:meth:`pandas.DataFrameGroupBy.cov` to calculate the variance-covariance matrix of each group. Missing values are automatically excluded from the calculation by Pandas. Mathematical expressions can be found in [1]_. This function has been tested against the boxM package of the `biotools` R package [4]_. References ---------- .. [1] Rencher, A. C. (2003). Methods of multivariate analysis (Vol. 492). John Wiley & Sons. .. [2] Hahs-Vaughn, D. (2016). Applied Multivariate Statistical Concepts. Taylor & Francis. .. [3] https://en.wikipedia.org/wiki/Box%27s_M_test .. [4] https://cran.r-project.org/web/packages/biotools/index.html Examples -------- 1. Box M test with 3 dependent variables of 4 groups (equal sample size) >>> import pandas as pd >>> import pingouin as pg >>> from scipy.stats import multivariate_normal as mvn >>> data = pd.DataFrame(mvn.rvs(size=(100, 3), random_state=42), ... columns=['A', 'B', 'C']) >>> data['group'] = [1] * 25 + [2] * 25 + [3] * 25 + [4] * 25 >>> data.head() A B C group 0 0.496714 -0.138264 0.647689 1 1 1.523030 -0.234153 -0.234137 1 2 1.579213 0.767435 -0.469474 1 3 0.542560 -0.463418 -0.465730 1 4 0.241962 -1.913280 -1.724918 1 >>> pg.box_m(data, dvs=['A', 'B', 'C'], group='group') Chi2 df pval equal_cov box 11.634185 18.0 0.865537 True 2. Box M test with 3 dependent variables of 2 groups (unequal sample size) >>> data = pd.DataFrame(mvn.rvs(size=(30, 2), random_state=42), ... columns=['A', 'B']) >>> data['group'] = [1] * 20 + [2] * 10 >>> pg.box_m(data, dvs=['A', 'B'], group='group') Chi2 df pval equal_cov box 0.706709 3.0 0.871625 True r)chi2z data must be a pandas dataframe.z%The grouping variable is not in data.zThe DVs are not in data.T)Zobservedr z$Data must have at least two columns.)Z numeric_onlyNr).NNr r rrg?FZbox)ZChi2dfr equal_cov)rAdata)rrN isinstancerDrErcolumnssetissubsetgroupbyZngroupsr!rAZlevshapecountZilocZto_numpyr)r'rr"Zdetprodlenuniquer+r-r)rRZdvsgroupr/rNgrpZcovsZn_covsZn_dvsZn_sampZnobsvr2ZS_detMcurPr1rQrLr9r9r:r s<T    , )r)NF)rM) ZnumpyrZpandasrD collectionsrZpingouin.utilsrr__all__rrrr9r9r9r:s   t