def __init__(self, endog, exog, **kwargs): super(quantreg, self).__init__(endog, exog, **kwargs) self.PostEstimation = EventHook() self.PreEstimation = EventHook() self.PostVarianceCalculation = EventHook() self.nobs = float(self.endog.shape[0]) self.df_resid = np.float(self.exog.shape[0] - rank(self.exog)) self.df_model = np.float(rank(self.exog)-1)
def test_rank(self):
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
X = standard_normal((40,10))
self.assertEquals(tools.rank(X), np_matrix_rank(X))
X[:,0] = X[:,1] + X[:,2]
self.assertEquals(tools.rank(X), np_matrix_rank(X))
def test_rank(self):
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
X = standard_normal((40, 10))
self.assertEquals(tools.rank(X), np_matrix_rank(X))
X[:, 0] = X[:, 1] + X[:, 2]
self.assertEquals(tools.rank(X), np_matrix_rank(X))
def __init__(self, sys, sigma=None, dfk=None):
if len(sys) % 2 != 0:
raise ValueError("sys must be a list of pairs of endogenous and \
exogenous variables. Got length %s" % len(sys))
if dfk:
if not dfk.lower() in ['dfk1', 'dfk2']:
raise ValueError("dfk option %s not understood" % (dfk))
self._dfk = dfk
M = len(sys[1::2])
self._M = M
# exog = np.zeros((M,M), dtype=object)
# for i,eq in enumerate(sys[1::2]):
# exog[i,i] = np.asarray(eq) # not sure this exog is needed
# used to compute resids for now
exog = np.column_stack(np.asarray(sys[1::2][i]) for i in range(M))
# exog = np.vstack(np.asarray(sys[1::2][i]) for i in range(M))
self.exog = exog # 2d ndarray exog is better
# Endog, might just go ahead and reshape this?
endog = np.asarray(sys[::2])
self.endog = endog
self.nobs = float(
self.endog[0].shape[0]) # assumes all the same length
# Degrees of Freedom
df_resid = []
df_model = []
[df_resid.append(self.nobs - tools.rank(_)) \
for _ in sys[1::2]]
[df_model.append(tools.rank(_) - 1) for _ in sys[1::2]]
self.df_resid = np.asarray(df_resid)
self.df_model = np.asarray(df_model)
# "Block-diagonal" sparse matrix of exog
sp_exog = sparse.lil_matrix(
(int(self.nobs * M),
int(np.sum(self.df_model + 1)))) # linked lists to build
self._cols = np.cumsum(np.hstack((0, self.df_model + 1)))
for i in range(M):
sp_exog[i * self.nobs:(i + 1) * self.nobs,
self._cols[i]:self._cols[i + 1]] = sys[1::2][i]
self.sp_exog = sp_exog.tocsr() # cast to compressed for efficiency
# Deal with sigma, check shape earlier if given
if np.any(sigma):
sigma = np.asarray(sigma) # check shape
elif sigma == None:
resids = []
for i in range(M):
resids.append(
GLS(endog[i],
exog[:, self._cols[i]:self._cols[i + 1]]).fit().resid)
resids = np.asarray(resids).reshape(M, -1)
sigma = self._compute_sigma(resids)
self.sigma = sigma
self.cholsigmainv = np.linalg.cholesky(np.linalg.pinv(\
self.sigma)).T
self.initialize()
def _initialize(self):
"""
Initializes the model for the IRLS fit.
Resets the history and number of iterations.
"""
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog, np.transpose(self.pinv_wexog))
self.df_resid = np.float(self.exog.shape[0] - rank(self.exog))
self.df_model = np.float(rank(self.exog) - 1)
self.nobs = float(self.endog.shape[0])
def test_fullrank(self):
X = standard_normal((40, 10))
X[:, 0] = X[:, 1] + X[:, 2]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40, 9))
self.assertEquals(tools.rank(Y), 9)
X[:, 5] = X[:, 3] + X[:, 4]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40, 8))
self.assertEquals(tools.rank(Y), 8)
def __init__(self, sys, sigma=None, dfk=None):
if len(sys) % 2 != 0:
raise ValueError("sys must be a list of pairs of endogenous and \
exogenous variables. Got length %s" % len(sys))
if dfk:
if not dfk.lower() in ['dfk1','dfk2']:
raise ValueError("dfk option %s not understood" % (dfk))
self._dfk = dfk
M = len(sys[1::2])
self._M = M
# exog = np.zeros((M,M), dtype=object)
# for i,eq in enumerate(sys[1::2]):
# exog[i,i] = np.asarray(eq) # not sure this exog is needed
# used to compute resids for now
exog = np.column_stack(np.asarray(sys[1::2][i]) for i in range(M))
# exog = np.vstack(np.asarray(sys[1::2][i]) for i in range(M))
self.exog = exog # 2d ndarray exog is better
# Endog, might just go ahead and reshape this?
endog = np.asarray(sys[::2])
self.endog = endog
self.nobs = float(self.endog[0].shape[0]) # assumes all the same length
# Degrees of Freedom
df_resid = []
df_model = []
[df_resid.append(self.nobs - tools.rank(_)) \
for _ in sys[1::2]]
[df_model.append(tools.rank(_) - 1) for _ in sys[1::2]]
self.df_resid = np.asarray(df_resid)
self.df_model = np.asarray(df_model)
# "Block-diagonal" sparse matrix of exog
sp_exog = sparse.lil_matrix((int(self.nobs*M),
int(np.sum(self.df_model+1)))) # linked lists to build
self._cols = np.cumsum(np.hstack((0, self.df_model+1)))
for i in range(M):
sp_exog[i*self.nobs:(i+1)*self.nobs,
self._cols[i]:self._cols[i+1]] = sys[1::2][i]
self.sp_exog = sp_exog.tocsr() # cast to compressed for efficiency
# Deal with sigma, check shape earlier if given
if np.any(sigma):
sigma = np.asarray(sigma) # check shape
elif sigma == None:
resids = []
for i in range(M):
resids.append(GLS(endog[i],exog[:,
self._cols[i]:self._cols[i+1]]).fit().resid)
resids = np.asarray(resids).reshape(M,-1)
sigma = self._compute_sigma(resids)
self.sigma = sigma
self.cholsigmainv = np.linalg.cholesky(np.linalg.pinv(\
self.sigma)).T
self.initialize()
def _initialize(self):
"""
Initializes the model for the IRLS fit.
Resets the history and number of iterations.
"""
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog,
np.transpose(self.pinv_wexog))
self.df_resid = np.float(self.exog.shape[0] - rank(self.exog))
self.df_model = np.float(rank(self.exog) - 1)
self.nobs = float(self.endog.shape[0])
def test_fullrank(self):
X = standard_normal((40,10))
X[:,0] = X[:,1] + X[:,2]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40,9))
self.assertEquals(tools.rank(Y), 9)
X[:,5] = X[:,3] + X[:,4]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40,8))
self.assertEquals(tools.rank(Y), 8)
def _initialize(self):
"""
Initializes the model for the IRLS fit.
Resets the history and number of iterations.
"""
self.history = {"deviance": [np.inf], "params": [np.inf], "weights": [np.inf], "sresid": [np.inf], "scale": []}
self.iteration = 0
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog, np.transpose(self.pinv_wexog))
self.df_resid = np.float(self.exog.shape[0] - rank(self.exog))
self.df_model = np.float(rank(self.exog) - 1)
self.nobs = float(self.endog.shape[0])
def _initialize(self): self.nobs = float(self.endog.shape[0]) self.df_resid = np.float(self.exog.shape[0] - rank(self.exog)) self.df_model = np.float(rank(self.exog)-1) self.c = -self.endog self.A = np.concatenate([np.identity(self.endog.shape[0]), -np.identity(self.endog.shape[0])], axis=0) self.Aeq = self.exog.T self.b = np.concatenate([np.ones(self.endog.shape[0]), np.zeros(self.endog.shape[0])], axis=0) self.beq = (1-self.tau) * sum(self.exog, 0) self.t = 1 self.eps = 10e-07 self.maxit = 1 self.update = 1.1
def initialize(self):
"""
Initialize a generalized linear model.
"""
#TODO: intended for public use?
self.history = {'fittedvalues' : [],
'params' : [np.inf],
'deviance' : [np.inf]}
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog,
np.transpose(self.pinv_wexog))
self.df_model = rank(self.exog)-1
self.df_resid = self.exog.shape[0] - rank(self.exog)
def test_fullrank(self):
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
X = standard_normal((40,10))
X[:,0] = X[:,1] + X[:,2]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40,9))
self.assertEquals(tools.rank(Y), 9)
X[:,5] = X[:,3] + X[:,4]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40,8))
warnings.simplefilter("ignore")
self.assertEquals(tools.rank(Y), 8)
def test_fullrank(self):
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
X = standard_normal((40, 10))
X[:, 0] = X[:, 1] + X[:, 2]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40, 9))
self.assertEquals(tools.rank(Y), 9)
X[:, 5] = X[:, 3] + X[:, 4]
Y = tools.fullrank(X)
self.assertEquals(Y.shape, (40, 8))
warnings.simplefilter("ignore")
self.assertEquals(tools.rank(Y), 8)
def spec_hausman(self, dof=None):
'''Hausman's specification test
See Also
--------
spec_hausman : generic function for Hausman's specification test
'''
#use normalized cov_params for OLS
resols = OLS(endog, exog).fit()
normalized_cov_params_ols = resols.model.normalized_cov_params
se2 = resols.mse_resid
params_diff = self._results.params - resols.params
cov_diff = np.linalg.pinv(self.xhatprod) - normalized_cov_params_ols
#TODO: the following is very inefficient, solves problem (svd) twice
#use linalg.lstsq or svd directly
#cov_diff will very often be in-definite (singular)
if not dof:
dof = tools.rank(cov_diff)
cov_diffpinv = np.linalg.pinv(cov_diff)
H = np.dot(params_diff, np.dot(cov_diffpinv, params_diff))/se2
pval = stats.chi2.sf(H, dof)
return H, pval, dof
def initialize(self):
"""
Initialize a generalized linear model.
"""
#TODO: intended for public use?
self.history = {
'fittedvalues': [],
'params': [np.inf],
'deviance': [np.inf]
}
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog,
np.transpose(self.pinv_wexog))
self.df_model = rank(self.exog) - 1
self.df_resid = self.exog.shape[0] - rank(self.exog)
def contrastfromcols(L, D, pseudo=None):
"""
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
"""
L = np.asarray(L)
D = np.asarray(D)
n, p = D.shape
if L.shape[0] != n and L.shape[1] != p:
raise ValueError("shape of L and D mismatched")
if pseudo is None:
pseudo = np.linalg.pinv(D) # D^+ \approx= ((dot(D.T,D))^(-1),D.T)
if L.shape[0] == n:
C = np.dot(pseudo, L).T
else:
C = L
C = np.dot(pseudo, np.dot(D, C.T)).T
Lp = np.dot(D, C.T)
if len(Lp.shape) == 1:
Lp.shape = (n, 1)
if rank(Lp) != Lp.shape[1]:
Lp = fullrank(Lp)
C = np.dot(pseudo, Lp).T
return np.squeeze(C)
def contrastfromcols(L, D, pseudo=None):
"""
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
"""
L = np.asarray(L)
D = np.asarray(D)
n, p = D.shape
if L.shape[0] != n and L.shape[1] != p:
raise ValueError("shape of L and D mismatched")
if pseudo is None:
pseudo = np.linalg.pinv(D) # D^+ \approx= ((dot(D.T,D))^(-1),D.T)
if L.shape[0] == n:
C = np.dot(pseudo, L).T
else:
C = L
C = np.dot(pseudo, np.dot(D, C.T)).T
Lp = np.dot(D, C.T)
if len(Lp.shape) == 1:
Lp.shape = (n, 1)
if rank(Lp) != Lp.shape[1]:
Lp = fullrank(Lp)
C = np.dot(pseudo, Lp).T
return np.squeeze(C)
def __init__(self, sys, indep_endog=None, instruments=None):
if len(sys) % 2 != 0:
raise ValueError("sys must be a list of pairs of endogenous and \
exogenous variables. Got length %s" % len(sys))
M = len(sys[1::2])
self._M = M
# The lists are probably a bad idea
self.endog = sys[::2] # these are just list containers
self.exog = sys[1::2]
self._K = [tools.rank(_) for _ in sys[1::2]]
# fullexog = np.column_stack((_ for _ in self.exog))
self.instruments = instruments
# Keep the Y_j's in a container to get IVs
instr_endog = {}
[instr_endog.setdefault(_, []) for _ in indep_endog.keys()]
for eq_key in indep_endog:
for varcol in indep_endog[eq_key]:
instr_endog[eq_key].append(self.exog[eq_key][:, varcol])
# ^ copy needed?
# self._instr_endog = instr_endog
self._indep_endog = indep_endog
_col_map = np.cumsum(np.hstack((0, self._K))) # starting col no.s
# move this check to whiten since we're not going to build a full exog?
for eq_key in indep_endog:
try:
iter(indep_endog[eq_key])
except:
# eq_key = [eq_key]
raise TypeError("The values of the indep_exog dict must be\
iterable. Got type %s for converter %s" % (type(del_col)))
# for del_col in indep_endog[eq_key]:
# fullexog = np.delete(fullexog, _col_map[eq_key]+del_col, 1)
# _col_map[eq_key+1:] -= 1
# Josef's example for deleting reoccuring "rows"
# fullexog = np.unique(fullexog.T.view([('',fullexog.dtype)]*\
# fullexog.shape[0])).view(fullexog.dtype).reshape(\
# fullexog.shape[0],-1)
# From http://article.gmane.org/gmane.comp.python.numeric.general/32276/
# Or Jouni' suggetsion of taking a hash:
# http://www.mail-archive.com/[email protected]/msg04209.html
# not clear to me how this would work though, only if they are the *same*
# elements?
# self.fullexog = fullexog
self.wexog = self.whiten(instr_endog)
def __init__(self, sys, indep_endog=None, instruments=None):
if len(sys) % 2 != 0:
raise ValueError("sys must be a list of pairs of endogenous and \
exogenous variables. Got length %s" % len(sys))
M = len(sys[1::2])
self._M = M
# The lists are probably a bad idea
self.endog = sys[::2] # these are just list containers
self.exog = sys[1::2]
self._K = [tools.rank(_) for _ in sys[1::2]]
# fullexog = np.column_stack((_ for _ in self.exog))
self.instruments = instruments
# Keep the Y_j's in a container to get IVs
instr_endog = {}
[instr_endog.setdefault(_,[]) for _ in list(indep_endog.keys())]
for eq_key in indep_endog:
for varcol in indep_endog[eq_key]:
instr_endog[eq_key].append(self.exog[eq_key][:,varcol])
# ^ copy needed?
# self._instr_endog = instr_endog
self._indep_endog = indep_endog
_col_map = np.cumsum(np.hstack((0,self._K))) # starting col no.s
# move this check to whiten since we're not going to build a full exog?
for eq_key in indep_endog:
try:
iter(indep_endog[eq_key])
except:
# eq_key = [eq_key]
raise TypeError("The values of the indep_exog dict must be\
iterable. Got type %s for converter %s" % (type(del_col)))
# for del_col in indep_endog[eq_key]:
# fullexog = np.delete(fullexog, _col_map[eq_key]+del_col, 1)
# _col_map[eq_key+1:] -= 1
# Josef's example for deleting reoccuring "rows"
# fullexog = np.unique(fullexog.T.view([('',fullexog.dtype)]*\
# fullexog.shape[0])).view(fullexog.dtype).reshape(\
# fullexog.shape[0],-1)
# From http://article.gmane.org/gmane.comp.python.numeric.general/32276/
# Or Jouni' suggetsion of taking a hash:
# http://www.mail-archive.com/[email protected]/msg04209.html
# not clear to me how this would work though, only if they are the *same*
# elements?
# self.fullexog = fullexog
self.wexog = self.whiten(instr_endog)
def spec_hausman(params_e, params_i, cov_params_e, cov_params_i, dof=None):
'''Hausmans specification test
Parameters
----------
params_e : array
efficient and consistent under Null hypothesis,
inconsistent under alternative hypothesis
params_i: array
consistent under Null hypothesis,
consistent under alternative hypothesis
cov_params_e : array, 2d
covariance matrix of parameter estimates for params_e
cov_params_i : array, 2d
covariance matrix of parameter estimates for params_i
example instrumental variables OLS estimator is `e`, IV estimator is `i`
Notes
-----
Todos,Issues
- check dof calculations and verify for linear case
- check one-sided hypothesis
References
----------
Greene section 5.5 p.82/83
'''
params_diff = (params_i - params_e)
cov_diff = cov_params_i - cov_params_e
#TODO: the following is very inefficient, solves problem (svd) twice
#use linalg.lstsq or svd directly
#cov_diff will very often be in-definite (singular)
if not dof:
dof = tools.rank(cov_diff)
cov_diffpinv = np.linalg.pinv(cov_diff)
H = np.dot(params_diff, np.dot(cov_diffpinv, params_diff))
pval = stats.chi2.sf(H, dof)
evals = np.linalg.eigvalsh(cov_diff)
return H, pval, dof, evals
def setupClass(cls):
from results.results_regression import Longley
data = longley.load()
data.exog = add_constant(data.exog, prepend=False)
res1 = OLS(data.endog, data.exog).fit()
res2 = Longley()
res2.wresid = res1.wresid # workaround hack
cls.res1 = res1
cls.res2 = res2
res_qr = OLS(data.endog, data.exog).fit(method="qr")
model_qr = OLS(data.endog, data.exog)
Q, R = np.linalg.qr(data.exog)
model_qr.exog_Q, model_qr.exog_R = Q, R
model_qr.normalized_cov_params = np.linalg.inv(np.dot(R.T, R))
model_qr.rank = rank(R)
res_qr2 = model_qr.fit(method="qr")
cls.res_qr = res_qr
cls.res_qr_manual = res_qr2
def setupClass(cls):
from results.results_regression import Longley
data = longley.load()
data.exog = add_constant(data.exog, prepend=False)
res1 = OLS(data.endog, data.exog).fit()
res2 = Longley()
res2.wresid = res1.wresid # workaround hack
cls.res1 = res1
cls.res2 = res2
res_qr = OLS(data.endog, data.exog).fit(method="qr")
model_qr = OLS(data.endog, data.exog)
Q, R = np.linalg.qr(data.exog)
model_qr.exog_Q, model_qr.exog_R = Q, R
model_qr.normalized_cov_params = np.linalg.inv(np.dot(R.T, R))
model_qr.rank = rank(R)
res_qr2 = model_qr.fit(method="qr")
cls.res_qr = res_qr
cls.res_qr_manual = res_qr2
def test_rank(self):
X = standard_normal((40, 10))
self.assertEquals(tools.rank(X), 10)
X[:, 0] = X[:, 1] + X[:, 2]
self.assertEquals(tools.rank(X), 9)
def test_rank(self):
X = standard_normal((40,10))
self.assertEquals(tools.rank(X), 10)
X[:,0] = X[:,1] + X[:,2]
self.assertEquals(tools.rank(X), 9)
def fit(self, q=.5, vcov='robust', kernel='epa', bandwidth='hsheather',
max_iter=1000, p_tol=1e-6, **kwargs):
'''Solve by Iterative Weighted Least Squares
Parameters
----------
q : float
Quantile must be between 0 and 1
vcov : string, method used to calculate the variance-covariance matrix
of the parameters. Default is ``robust``:
- robust : heteroskedasticity robust standard errors (as suggested
in Greene 6th edition)
- iid : iid errors (as in Stata 12)
kernel : string, kernel to use in the kernel density estimation for the
asymptotic covariance matrix:
- epa: Epanechnikov
- cos: Cosine
- gau: Gaussian
- par: Parzene
bandwidth: string, Bandwidth selection method in kernel density
estimation for asymptotic covariance estimate (full
references in QuantReg docstring):
- hsheather: Hall-Sheather (1988)
- bofinger: Bofinger (1975)
- chamberlain: Chamberlain (1994)
'''
if q < 0 or q > 1:
raise Exception('p must be between 0 and 1')
kern_names = ['biw', 'cos', 'epa', 'gau', 'par']
if kernel not in kern_names:
raise Exception("kernel must be one of " + ', '.join(kern_names))
else:
kernel = kernels[kernel]
if bandwidth == 'hsheather':
bandwidth = hall_sheather
elif bandwidth == 'bofinger':
bandwidth = bofinger
elif bandwidth == 'chamberlain':
bandwidth = chamberlain
else:
raise Exception("bandwidth must be in 'hsheather', 'bofinger', 'chamberlain'")
endog = self.endog
exog = self.exog
nobs = self.nobs
exog_rank = rank(self.exog)
self.rank = exog_rank
self.df_model = float(self.rank - self.k_constant)
self.df_resid = self.nobs - self.rank
n_iter = 0
xstar = exog
beta = np.ones(exog_rank)
# TODO: better start, initial beta is used only for convergence check
# Note the following doesn't work yet,
# the iteration loop always starts with OLS as initial beta
# if start_params is not None:
# if len(start_params) != rank:
# raise ValueError('start_params has wrong length')
# beta = start_params
# else:
# # start with OLS
# beta = np.dot(np.linalg.pinv(exog), endog)
diff = 10
cycle = False
history = dict(params = [], mse=[])
while n_iter < max_iter and diff > p_tol and not cycle:
n_iter += 1
beta0 = beta
xtx = np.dot(xstar.T, exog)
xty = np.dot(xstar.T, endog)
beta = np.dot(pinv(xtx), xty)
resid = endog - np.dot(exog, beta)
mask = np.abs(resid) < .000001
resid[mask] = np.sign(resid[mask]) * .000001
resid = np.where(resid < 0, q * resid, (1-q) * resid)
resid = np.abs(resid)
xstar = exog / resid[:, np.newaxis]
diff = np.max(np.abs(beta - beta0))
history['params'].append(beta)
history['mse'].append(np.mean(resid*resid))
if (n_iter >= 300) and (n_iter % 100 == 0):
# check for convergence circle, shouldn't happen
for ii in range(2, 10):
if np.all(beta == history['params'][-ii]):
cycle = True
break
warnings.warn("Convergence cycle detected")
if n_iter == max_iter:
warnings.warn("Maximum number of iterations (1000) reached.")
e = endog - np.dot(exog, beta)
# Greene (2008, p.407) writes that Stata 6 uses this bandwidth:
# h = 0.9 * np.std(e) / (nobs**0.2)
# Instead, we calculate bandwidth as in Stata 12
iqre = stats.scoreatpercentile(e, 75) - stats.scoreatpercentile(e, 25)
h = bandwidth(nobs, q)
h = min(np.std(endog),
iqre / 1.34) * (norm.ppf(q + h) - norm.ppf(q - h))
fhat0 = 1. / (nobs * h) * np.sum(kernel(e / h))
if vcov == 'robust':
d = np.where(e > 0, (q/fhat0)**2, ((1-q)/fhat0)**2)
xtxi = pinv(np.dot(exog.T, exog))
xtdx = np.dot(exog.T * d[np.newaxis, :], exog)
vcov = chain_dot(xtxi, xtdx, xtxi)
elif vcov == 'iid':
vcov = (1. / fhat0)**2 * q * (1 - q) * pinv(np.dot(exog.T, exog))
else:
raise Exception("vcov must be 'robust' or 'iid'")
lfit = QuantRegResults(self, beta, normalized_cov_params=vcov)
lfit.q = q
lfit.iterations = n_iter
lfit.sparsity = 1. / fhat0
lfit.bandwidth = h
lfit.history = history
return RegressionResultsWrapper(lfit)
def fit(self,
q=.5,
vcov='robust',
kernel='epa',
bandwidth='hsheather',
max_iter=1000,
p_tol=1e-6,
**kwargs):
'''Solve by Iterative Weighted Least Squares
Parameters
----------
q : float
Quantile must be between 0 and 1
vcov : string, method used to calculate the variance-covariance matrix
of the parameters. Default is ``robust``:
- robust : heteroskedasticity robust standard errors (as suggested
in Greene 6th edition)
- iid : iid errors (as in Stata 12)
kernel : string, kernel to use in the kernel density estimation for the
asymptotic covariance matrix:
- epa: Epanechnikov
- cos: Cosine
- gau: Gaussian
- par: Parzene
bandwidth: string, Bandwidth selection method in kernel density
estimation for asymptotic covariance estimate (full
references in QuantReg docstring):
- hsheather: Hall-Sheather (1988)
- bofinger: Bofinger (1975)
- chamberlain: Chamberlain (1994)
'''
if q < 0 or q > 1:
raise Exception('p must be between 0 and 1')
kern_names = ['biw', 'cos', 'epa', 'gau', 'par']
if kernel not in kern_names:
raise Exception("kernel must be one of " + ', '.join(kern_names))
else:
kernel = kernels[kernel]
if bandwidth == 'hsheather':
bandwidth = hall_sheather
elif bandwidth == 'bofinger':
bandwidth = bofinger
elif bandwidth == 'chamberlain':
bandwidth = chamberlain
else:
raise Exception(
"bandwidth must be in 'hsheather', 'bofinger', 'chamberlain'")
endog = self.endog
exog = self.exog
nobs = self.nobs
exog_rank = rank(self.exog)
self.rank = exog_rank
self.df_model = float(self.rank - self.k_constant)
self.df_resid = self.nobs - self.rank
n_iter = 0
xstar = exog
beta = np.ones(exog_rank)
# TODO: better start, initial beta is used only for convergence check
# Note the following doesn't work yet,
# the iteration loop always starts with OLS as initial beta
# if start_params is not None:
# if len(start_params) != rank:
# raise ValueError('start_params has wrong length')
# beta = start_params
# else:
# # start with OLS
# beta = np.dot(np.linalg.pinv(exog), endog)
diff = 10
cycle = False
history = dict(params=[], mse=[])
while n_iter < max_iter and diff > p_tol and not cycle:
n_iter += 1
beta0 = beta
xtx = np.dot(xstar.T, exog)
xty = np.dot(xstar.T, endog)
beta = np.dot(pinv(xtx), xty)
resid = endog - np.dot(exog, beta)
mask = np.abs(resid) < .000001
resid[mask] = np.sign(resid[mask]) * .000001
resid = np.where(resid < 0, q * resid, (1 - q) * resid)
resid = np.abs(resid)
xstar = exog / resid[:, np.newaxis]
diff = np.max(np.abs(beta - beta0))
history['params'].append(beta)
history['mse'].append(np.mean(resid * resid))
if (n_iter >= 300) and (n_iter % 100 == 0):
# check for convergence circle, shouldn't happen
for ii in range(2, 10):
if np.all(beta == history['params'][-ii]):
cycle = True
break
warnings.warn("Convergence cycle detected")
if n_iter == max_iter:
warnings.warn("Maximum number of iterations (1000) reached.")
e = endog - np.dot(exog, beta)
# Greene (2008, p.407) writes that Stata 6 uses this bandwidth:
# h = 0.9 * np.std(e) / (nobs**0.2)
# Instead, we calculate bandwidth as in Stata 12
iqre = stats.scoreatpercentile(e, 75) - stats.scoreatpercentile(e, 25)
h = bandwidth(nobs, q)
h = min(np.std(endog),
iqre / 1.34) * (norm.ppf(q + h) - norm.ppf(q - h))
fhat0 = 1. / (nobs * h) * np.sum(kernel(e / h))
if vcov == 'robust':
d = np.where(e > 0, (q / fhat0)**2, ((1 - q) / fhat0)**2)
xtxi = pinv(np.dot(exog.T, exog))
xtdx = np.dot(exog.T * d[np.newaxis, :], exog)
vcov = chain_dot(xtxi, xtdx, xtxi)
elif vcov == 'iid':
vcov = (1. / fhat0)**2 * q * (1 - q) * pinv(np.dot(exog.T, exog))
else:
raise Exception("vcov must be 'robust' or 'iid'")
lfit = QuantRegResults(self, beta, normalized_cov_params=vcov)
lfit.q = q
lfit.iterations = n_iter
lfit.sparsity = 1. / fhat0
lfit.bandwidth = h
lfit.history = history
return RegressionResultsWrapper(lfit)
