Source code for statsmodels.multivariate.cancorr

"""Canonical correlation analysis

author: Yichuan Liu
"""
import numpy as np
from numpy.linalg import svd
import scipy
import pandas as pd

from statsmodels.base.model import Model
from statsmodels.iolib import summary2
from .multivariate_ols import multivariate_stats


[docs] class CanCorr(Model): """ Canonical correlation analysis using singular value decomposition For matrices exog=x and endog=y, find projections x_cancoef and y_cancoef such that: x1 = x * x_cancoef, x1' * x1 is identity matrix y1 = y * y_cancoef, y1' * y1 is identity matrix and the correlation between x1 and y1 is maximized. Attributes ---------- endog : ndarray See Parameters. exog : ndarray See Parameters. cancorr : ndarray The canonical correlation values y_cancoef : ndarray The canonical coefficients for endog x_cancoef : ndarray The canonical coefficients for exog References ---------- .. [*] http://numerical.recipes/whp/notes/CanonCorrBySVD.pdf .. [*] http://www.csun.edu/~ata20315/psy524/docs/Psy524%20Lecture%208%20CC.pdf .. [*] http://www.mathematica-journal.com/2014/06/canonical-correlation-analysis/ """ # noqa:E501 def __init__(self, endog, exog, tolerance=1e-8, missing='none', hasconst=None, **kwargs): super().__init__(endog, exog, missing=missing, hasconst=hasconst, **kwargs) self._fit(tolerance) def _fit(self, tolerance=1e-8): """Fit the model A ValueError is raised if there are singular values smaller than the tolerance. The treatment of singular arrays might change in future. Parameters ---------- tolerance : float eigenvalue tolerance, values smaller than which is considered 0 """ nobs, k_yvar = self.endog.shape nobs, k_xvar = self.exog.shape k = np.min([k_yvar, k_xvar]) x = np.array(self.exog) x = x - x.mean(0) y = np.array(self.endog) y = y - y.mean(0) ux, sx, vx = svd(x, 0) # vx_ds = vx.T divided by sx vx_ds = vx.T mask = sx > tolerance if mask.sum() < len(mask): raise ValueError('exog is collinear.') vx_ds[:, mask] /= sx[mask] uy, sy, vy = svd(y, 0) # vy_ds = vy.T divided by sy vy_ds = vy.T mask = sy > tolerance if mask.sum() < len(mask): raise ValueError('endog is collinear.') vy_ds[:, mask] /= sy[mask] u, s, v = svd(ux.T.dot(uy), 0) # Correct any roundoff self.cancorr = np.array([max(0, min(s[i], 1)) for i in range(len(s))]) self.x_cancoef = vx_ds.dot(u[:, :k]) self.y_cancoef = vy_ds.dot(v.T[:, :k])
[docs] def corr_test(self): """Approximate F test Perform multivariate statistical tests of the hypothesis that there is no canonical correlation between endog and exog. For each canonical correlation, testing its significance based on Wilks' lambda. Returns ------- CanCorrTestResults instance """ nobs, k_yvar = self.endog.shape nobs, k_xvar = self.exog.shape eigenvals = np.power(self.cancorr, 2) stats = pd.DataFrame(columns=['Canonical Correlation', "Wilks' lambda", 'Num DF','Den DF', 'F Value','Pr > F'], index=list(range(len(eigenvals) - 1, -1, -1))) prod = 1 for i in range(len(eigenvals) - 1, -1, -1): prod *= 1 - eigenvals[i] p = k_yvar - i q = k_xvar - i r = (nobs - k_yvar - 1) - (p - q + 1) / 2 u = (p * q - 2) / 4 df1 = p * q if p ** 2 + q ** 2 - 5 > 0: t = np.sqrt(((p * q) ** 2 - 4) / (p ** 2 + q ** 2 - 5)) else: t = 1 df2 = r * t - 2 * u lmd = np.power(prod, 1 / t) F = (1 - lmd) / lmd * df2 / df1 stats.loc[i, 'Canonical Correlation'] = self.cancorr[i] stats.loc[i, "Wilks' lambda"] = prod stats.loc[i, 'Num DF'] = df1 stats.loc[i, 'Den DF'] = df2 stats.loc[i, 'F Value'] = F pval = scipy.stats.f.sf(F, df1, df2) stats.loc[i, 'Pr > F'] = pval ''' # Wilk's Chi square test of each canonical correlation df = (p - i + 1) * (q - i + 1) chi2 = a * np.log(prod) pval = stats.chi2.sf(chi2, df) stats.loc[i, 'Canonical correlation'] = self.cancorr[i] stats.loc[i, 'Chi-square'] = chi2 stats.loc[i, 'DF'] = df stats.loc[i, 'Pr > ChiSq'] = pval ''' ind = stats.index.values[::-1] stats = stats.loc[ind, :] # Multivariate tests (remember x has mean removed) stats_mv = multivariate_stats(eigenvals, k_yvar, k_xvar, nobs - k_xvar - 1) return CanCorrTestResults(stats, stats_mv)
class CanCorrTestResults: """ Canonical correlation results class Attributes ---------- stats : DataFrame Contain statistical tests results for each canonical correlation stats_mv : DataFrame Contain the multivariate statistical tests results """ def __init__(self, stats, stats_mv): self.stats = stats self.stats_mv = stats_mv def __str__(self): return self.summary().__str__() def summary(self): summ = summary2.Summary() summ.add_title('Cancorr results') summ.add_df(self.stats) summ.add_dict({'': ''}) summ.add_dict({'Multivariate Statistics and F Approximations': ''}) summ.add_df(self.stats_mv) return summ

Last update: May 25, 2024