def test_pca_princomp():
pcares = pca(xf)
check_pca_princomp(pcares, princomp1)
pcares = pca(xf[:20,:])
check_pca_princomp(pcares, princomp2)
pcares = pca(xf[:20,:]-xf[:20,:].mean(0))
check_pca_princomp(pcares, princomp3)
pcares = pca(xf[:20,:]-xf[:20,:].mean(0), demean=0)
check_pca_princomp(pcares, princomp3)
def test_pca_princomp():
pcares = pca(xf)
check_pca_princomp(pcares, princomp1)
pcares = pca(xf[:20, :])
check_pca_princomp(pcares, princomp2)
pcares = pca(xf[:20, :] - xf[:20, :].mean(0))
check_pca_princomp(pcares, princomp3)
pcares = pca(xf[:20, :] - xf[:20, :].mean(0), demean=0)
check_pca_princomp(pcares, princomp3)
def test_pca_svd():
xreduced, factors, evals, evecs = pca(xf)
factors_wconst = np.c_[factors, np.ones((factors.shape[0],1))]
beta = np.dot(np.linalg.pinv(factors_wconst), xf)
#np.dot(np.linalg.pinv(factors_wconst),x2/1000.).T[:,:4] - evecs
assert_array_almost_equal(beta.T[:,:4], evecs, 14)
xred_svd, factors_svd, evals_svd, evecs_svd = pcasvd(xf, keepdim=0)
assert_array_almost_equal(evals_svd, evals, 14)
msign = (evecs/evecs_svd)[0]
assert_array_almost_equal(msign*evecs_svd, evecs, 14)
assert_array_almost_equal(msign*factors_svd, factors, 13)
assert_array_almost_equal(xred_svd, xreduced, 14)
pcares = pca(xf, keepdim=2)
pcasvdres = pcasvd(xf, keepdim=2)
check_pca_svd(pcares, pcasvdres)
def test_pca_svd():
xreduced, factors, evals, evecs = pca(xf)
factors_wconst = np.c_[factors, np.ones((factors.shape[0], 1))]
beta = np.dot(np.linalg.pinv(factors_wconst), xf)
#np.dot(np.linalg.pinv(factors_wconst),x2/1000.).T[:,:4] - evecs
assert_array_almost_equal(beta.T[:, :4], evecs, 14)
xred_svd, factors_svd, evals_svd, evecs_svd = pcasvd(xf, keepdim=0)
assert_array_almost_equal(evals_svd, evals, 14)
msign = (evecs / evecs_svd)[0]
assert_array_almost_equal(msign * evecs_svd, evecs, 14)
assert_array_almost_equal(msign * factors_svd, factors, 13)
assert_array_almost_equal(xred_svd, xreduced, 14)
pcares = pca(xf, keepdim=2)
pcasvdres = pcasvd(xf, keepdim=2)
check_pca_svd(pcares, pcasvdres)
def calc_factors(self, x=None, keepdim=0, addconst=True):
'''get factor decomposition of exogenous variables
This uses principal component analysis to obtain the factors. The number
of factors kept is the maximum that will be considered in the regression.
'''
if x is None:
x = self.exog
else:
x = np.asarray(x)
xred, fact, evals, evecs = pca(x, keepdim=keepdim, normalize=1)
self.exog_reduced = xred
#self.factors = fact
if addconst:
self.factors = sm.add_constant(fact, prepend=True)
self.hasconst = 1 #needs to be int
else:
self.factors = fact
self.hasconst = 0 #needs to be int
self.evals = evals
self.evecs = evecs
def calc_factors(self, x=None, keepdim=0, addconst=True):
'''get factor decomposition of exogenous variables
This uses principal component analysis to obtain the factors. The number
of factors kept is the maximum that will be considered in the regression.
'''
if x is None:
x = self.exog
else:
x = np.asarray(x)
xred, fact, evals, evecs = pca(x, keepdim=keepdim, normalize=1)
self.exog_reduced = xred
#self.factors = fact
if addconst:
self.factors = sm.add_constant(fact, prepend=True)
self.hasconst = 1 #needs to be int
else:
self.factors = fact
self.hasconst = 0 #needs to be int
self.evals = evals
self.evecs = evecs
# Example: principal component regression
nobs = 1000
f0 = np.c_[np.random.normal(size=(nobs,2)), np.ones((nobs,1))]
f2xcoef = np.c_[np.repeat(np.eye(2),2,0),np.arange(4)[::-1]].T
f2xcoef = np.array([[ 1., 1., 0., 0.],
[ 0., 0., 1., 1.],
[ 3., 2., 1., 0.]])
f2xcoef = np.array([[ 0.1, 3., 1., 0.],
[ 0., 0., 1.5, 0.1],
[ 3., 2., 1., 0.]])
x0 = np.dot(f0, f2xcoef)
x0 += 0.1*np.random.normal(size=x0.shape)
ytrue = np.dot(f0,[1., 1., 1.])
y0 = ytrue + 0.1*np.random.normal(size=ytrue.shape)
xred, fact, eva, eve = pca(x0, keepdim=0)
print eve
print fact[:5]
print f0[:5]
import scikits.statsmodels as sm
res = sm.OLS(y0, sm.add_constant(x0)).fit()
print 'OLS on original data'
print res.params
print res.aic
print res.rsquared
#print 'OLS on Factors'
#for k in range(x0.shape[1]):
# xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1)
import scikits.statsmodels.api as sm from scikits.statsmodels.sandbox.tools import pca from scikits.statsmodels.sandbox.tools.cross_val import LeaveOneOut # Example: principal component regression nobs = 1000 f0 = np.c_[np.random.normal(size=(nobs, 2)), np.ones((nobs, 1))] f2xcoef = np.c_[np.repeat(np.eye(2), 2, 0), np.arange(4)[::-1]].T f2xcoef = np.array([[1., 1., 0., 0.], [0., 0., 1., 1.], [3., 2., 1., 0.]]) f2xcoef = np.array([[0.1, 3., 1., 0.], [0., 0., 1.5, 0.1], [3., 2., 1., 0.]]) x0 = np.dot(f0, f2xcoef) x0 += 0.1 * np.random.normal(size=x0.shape) ytrue = np.dot(f0, [1., 1., 1.]) y0 = ytrue + 0.1 * np.random.normal(size=ytrue.shape) xred, fact, eva, eve = pca(x0, keepdim=0) print eve print fact[:5] print f0[:5] import scikits.statsmodels.api as sm res = sm.OLS(y0, sm.add_constant(x0)).fit() print 'OLS on original data' print res.params print res.aic print res.rsquared #print 'OLS on Factors' #for k in range(x0.shape[1]): # xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1)
