reconnect moved files to git repo
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"""
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Created on Sun Nov 14 08:21:41 2010
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Author: josef-pktd
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License: BSD (3-clause)
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"""
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import numpy as np
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import statsmodels.api as sm
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from statsmodels.sandbox.tools import pca
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from statsmodels.sandbox.tools.cross_val import LeaveOneOut
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#converting example Principal Component Regression to a class
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#from sandbox/example_pca_regression.py
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class FactorModelUnivariate:
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'''
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Todo:
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check treatment of const, make it optional ?
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add hasconst (0 or 1), needed when selecting nfact+hasconst
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options are arguments in calc_factors, should be more public instead
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cross-validation is slow for large number of observations
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'''
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def __init__(self, endog, exog):
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#do this in a superclass?
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self.endog = np.asarray(endog)
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self.exog = np.asarray(exog)
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def calc_factors(self, x=None, keepdim=0, addconst=True):
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'''get factor decomposition of exogenous variables
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This uses principal component analysis to obtain the factors. The number
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of factors kept is the maximum that will be considered in the regression.
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'''
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if x is None:
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x = self.exog
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else:
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x = np.asarray(x)
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xred, fact, evals, evecs = pca(x, keepdim=keepdim, normalize=1)
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self.exog_reduced = xred
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#self.factors = fact
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if addconst:
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self.factors = sm.add_constant(fact, prepend=True)
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self.hasconst = 1 #needs to be int
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else:
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self.factors = fact
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self.hasconst = 0 #needs to be int
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self.evals = evals
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self.evecs = evecs
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def fit_fixed_nfact(self, nfact):
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if not hasattr(self, 'factors_wconst'):
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self.calc_factors()
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return sm.OLS(self.endog, self.factors[:,:nfact+1]).fit()
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def fit_find_nfact(self, maxfact=None, skip_crossval=True, cv_iter=None):
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'''estimate the model and selection criteria for up to maxfact factors
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The selection criteria that are calculated are AIC, BIC, and R2_adj. and
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additionally cross-validation prediction error sum of squares if `skip_crossval`
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is false. Cross-validation is not used by default because it can be
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time consuming to calculate.
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By default the cross-validation method is Leave-one-out on the full dataset.
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A different cross-validation sample can be specified as an argument to
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cv_iter.
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Results are attached in `results_find_nfact`
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'''
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#print 'OLS on Factors'
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if not hasattr(self, 'factors'):
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self.calc_factors()
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hasconst = self.hasconst
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if maxfact is None:
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maxfact = self.factors.shape[1] - hasconst
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if (maxfact+hasconst) < 1:
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raise ValueError('nothing to do, number of factors (incl. constant) should ' +
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'be at least 1')
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#temporary safety
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maxfact = min(maxfact, 10)
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y0 = self.endog
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results = []
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#xred, fact, eva, eve = pca(x0, keepdim=0, normalize=1)
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for k in range(1, maxfact+hasconst): #k includes now the constnat
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#xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1)
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# this is faster and same result
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fact = self.factors[:,:k]
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res = sm.OLS(y0, fact).fit()
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## print 'k =', k
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## print res.params
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## print 'aic: ', res.aic
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## print 'bic: ', res.bic
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## print 'llf: ', res.llf
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## print 'R2 ', res.rsquared
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## print 'R2 adj', res.rsquared_adj
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if not skip_crossval:
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if cv_iter is None:
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cv_iter = LeaveOneOut(len(y0))
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prederr2 = 0.
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for inidx, outidx in cv_iter:
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res_l1o = sm.OLS(y0[inidx], fact[inidx,:]).fit()
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#print data.endog[outidx], res.model.predict(data.exog[outidx,:]),
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prederr2 += (y0[outidx] -
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res_l1o.model.predict(res_l1o.params, fact[outidx,:]))**2.
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else:
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prederr2 = np.nan
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results.append([k, res.aic, res.bic, res.rsquared_adj, prederr2])
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self.results_find_nfact = results = np.array(results)
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self.best_nfact = np.r_[(np.argmin(results[:,1:3],0), np.argmax(results[:,3],0),
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np.argmin(results[:,-1],0))]
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def summary_find_nfact(self):
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'''provides a summary for the selection of the number of factors
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Returns
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-------
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sumstr : str
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summary of the results for selecting the number of factors
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'''
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if not hasattr(self, 'results_find_nfact'):
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self.fit_find_nfact()
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results = self.results_find_nfact
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sumstr = ''
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sumstr += '\n' + 'Best result for k, by AIC, BIC, R2_adj, L1O'
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# best = np.r_[(np.argmin(results[:,1:3],0), np.argmax(results[:,3],0),
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# np.argmin(results[:,-1],0))]
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sumstr += '\n' + ' '*19 + '%5d %4d %6d %5d' % tuple(self.best_nfact)
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from statsmodels.iolib.table import SimpleTable
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headers = 'k, AIC, BIC, R2_adj, L1O'.split(', ')
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numformat = ['%6d'] + ['%10.3f']*4 #'%10.4f'
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txt_fmt1 = dict(data_fmts = numformat)
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tabl = SimpleTable(results, headers, None, txt_fmt=txt_fmt1)
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sumstr += '\n' + "PCA regression on simulated data,"
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sumstr += '\n' + "DGP: 2 factors and 4 explanatory variables"
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sumstr += '\n' + tabl.__str__()
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sumstr += '\n' + "Notes: k is number of components of PCA,"
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sumstr += '\n' + " constant is added additionally"
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sumstr += '\n' + " k=0 means regression on constant only"
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sumstr += '\n' + " L1O: sum of squared prediction errors for leave-one-out"
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return sumstr
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if __name__ == '__main__':
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examples = [1]
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if 1 in examples:
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nobs = 500
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f0 = np.c_[np.random.normal(size=(nobs,2)), np.ones((nobs,1))]
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f2xcoef = np.c_[np.repeat(np.eye(2),2,0),np.arange(4)[::-1]].T
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f2xcoef = np.array([[ 1., 1., 0., 0.],
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[ 0., 0., 1., 1.],
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[ 3., 2., 1., 0.]])
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f2xcoef = np.array([[ 0.1, 3., 1., 0.],
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[ 0., 0., 1.5, 0.1],
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[ 3., 2., 1., 0.]])
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x0 = np.dot(f0, f2xcoef)
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x0 += 0.1*np.random.normal(size=x0.shape)
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ytrue = np.dot(f0,[1., 1., 1.])
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y0 = ytrue + 0.1*np.random.normal(size=ytrue.shape)
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mod = FactorModelUnivariate(y0, x0)
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print(mod.summary_find_nfact())
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print("with cross validation - slower")
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mod.fit_find_nfact(maxfact=None, skip_crossval=False, cv_iter=None)
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print(mod.summary_find_nfact())
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