def quantilereg(y,x,p):
'''
estimates quantile regression based on weighted least squares.
constant term is added to x matrix
__________________________________________________________________________
Inputs:
y: Dependent variable
x: matrix of independent variables
p: quantile
Outputs:
beta: estimated Coefficients.
tstats: T- students of the coefficients.
VCboot: Variance-Covariance of coefficients by bootstrapping method.
itrat: number of iterations for convergence to roots.
PseudoR2: in quatile regression another definition of R2 is used namely PseudoR2.
betaboot: estimated coefficients by bootstrapping method.
This code can be used for quantile regression estimation as whole,and LAD
regression as special case of it, when one sets p=0.5.
Copyright(c) Shapour Mohammadi, University of Tehran, 2008
[email protected]
Translated to python with permission from original author by Christian Prinoth (christian at prinoth dot name)
Ref:
1-Birkes, D. and Y. Dodge(1993). Alternative Methods of Regression, John Wiley and Sons.
2-Green,W. H. (2008). Econometric Analysis. Sixth Edition. International Student Edition.
3-LeSage, J. P.(1999),Applied Econometrics Using MATLAB,
Keywords: Least Absolute Deviation(LAD) Regression, Quantile Regression,
Regression, Robust Estimation.
__________________________________________________________________________
'''
tstats=0
VCboot=0
itrat=0
PseudoR2=0
betaboot=0
ry=len(y)
rx, cx=x.shape
x=np.c_[np.ones(rx),x]
cx=cx+1
#______________Finding first estimates by solving the system_______________
# Some lines of this section is based on a code written by
# James P. Lesage in Applied Econometrics Using MATLAB(1999).PP. 73-4.
itrat=0
xstar=x
diff=1
beta=np.ones(cx)
z=np.zeros((rx,cx))
while itrat<1000 and diff>1e-6:
itrat+=1
beta0=beta
beta=dot(inv(dot(xstar.T,x)),xstar.T,y)
resid=y-dot(x,beta)
resid[np.abs(resid)<.000001]=.000001
resid[resid<0]=p*resid[resid<0]
resid[resid>0]=(1-p)*resid[resid>0]
resid=np.abs(resid)
for i in range(cx):
z[:,i] = x[:,i]/resid
xstar=z
beta1=beta
diff=np.max(np.abs(beta1-beta0))
return beta
def quantilereg(y,x,p):
'''
estimates quantile regression based on weighted least squares.
constant term is added to x matrix
__________________________________________________________________________
Inputs:
y: Dependent variable
x: matrix of independent variables
p: quantile
Outputs:
beta: estimated Coefficients.
tstats: T- students of the coefficients.
VCboot: Variance-Covariance of coefficients by bootstrapping method.
itrat: number of iterations for convergence to roots.
PseudoR2: in quatile regression another definition of R2 is used namely PseudoR2.
betaboot: estimated coefficients by bootstrapping method.
This code can be used for quantile regression estimation as whole,and LAD
regression as special case of it, when one sets p=0.5.
Copyright(c) Shapour Mohammadi, University of Tehran, 2008
[email protected]
Translated to python with permission from original author by Christian Prinoth (christian at prinoth dot name)
Ref:
1-Birkes, D. and Y. Dodge(1993). Alternative Methods of Regression, John Wiley and Sons.
2-Green,W. H. (2008). Econometric Analysis. Sixth Edition. International Student Edition.
3-LeSage, J. P.(1999),Applied Econometrics Using MATLAB,
Keywords: Least Absolute Deviation(LAD) Regression, Quantile Regression,
Regression, Robust Estimation.
__________________________________________________________________________
'''
tstats=0
VCboot=0
itrat=0
PseudoR2=0
betaboot=0
ry=len(y)
rx, cx=x.shape
x=np.c_[np.ones(rx),x]
cx=cx+1
#______________Finding first estimates by solving the system_______________
# Some lines of this section is based on a code written by
# James P. Lesage in Applied Econometrics Using MATLAB(1999).PP. 73-4.
itrat=0
xstar=x
diff=1
beta=np.ones(cx)
z=np.zeros((rx,cx))
while itrat<1000 and diff>1e-6:
itrat+=1
beta0=beta
beta=dot(inv(dot(xstar.T,x)),xstar.T,y)
resid=y-dot(x,beta)
resid[np.abs(resid)<.000001]=.000001
resid[resid<0]=p*resid[resid<0]
resid[resid>0]=(1-p)*resid[resid>0]
resid=np.abs(resid)
for i in range(cx):
z[:,i] = x[:,i]/resid
xstar=z
beta1=beta
diff=np.max(np.abs(beta1-beta0))
return beta
#_______estimating variances based on Green 2008(quantile regression)______
e=y-dot(x,beta)
iqre=np.percentile(e,0.75)-np.percentile(e,0.25)
if p==0.5:
h=0.9*np.std(e)/(ry**0.2)
else:
h=0.9*np.min(np.std(e),iqre/1.34)/(ry**0.2)
u=(e/h)
fhat0=(1/(ry*h))*(sum(exp(-u)/((1+exp(-u))**2)))
D=np.zeros((ry,ry))
DIAGON=np.diag(D)
DIAGON[e>0]=(p/fhat0)**2
DIAGON[e<=0]=((1-p)/fhat0)**2
D=np.diag(DIAGON)
VCQ=np.dot(inv(dot(x.T,x)),dot(x.T,D,x),inv(np.dot(x.T,x)))
#____________________Standarad errores and t-stats_________________________
tstats=beta/np.sqrt(np.diag(VCQ))
stderrors=np.sqrt(np.diag(VCQ))
PValues=2*(1-stats.t.cdf(np.abs(tstats),ry-cx))
#______________________________ Quasi R square_____________________________
ef=y-dot(x,beta)
ef[ef<0]=(1-p)*ef[ef<0]
ef[ef>0]=p*ef[ef>0]
ef=np.abs(ef)
ered=y-np.percentile(y,p)
ered[ered<0]=(1-p)*ered[ered<0]
ered[ered>0]=p*ered[ered>0]
ered=np.abs(ered)
PseudoR2=1-np.sum(ef)/np.sum(ered)
#__________________Bootstrap standard deviation (Green 2008)_______________
betaboot=np.zeros((cx,cx))
for ii in range(100):
bootm, estar=bootstrp(1,np.mean,e)
#
ystar=dot(x,beta)+e[estar]
#
itratstar=0
xstarstar=x
diffstar=1
betastar=np.ones(cx)
while itratstar<1000 and diffstar>1e-6:
itratstar=itratstar+1
betastar0=betastar
betastar=dot(inv(dot(xstarstar.T,x)),xstarstar.T,ystar)
#
residstar=ystar-dot(x,betastar)
residstar[np.abs(residstar)<.000001]=.000001
residstar[residstar<0]=p*residstar[residstar<0]
residstar[residstar>0]=(1-p)*residstar[residstar>0]
residstar=np.abs(residstar)
zstar=np.zeros((rx,cx))
for i in range(cx):
zstar[:,i] = x[:,i]/residstar
xstarstar=zstar
beta1star=betastar
diffstar=np.max(np.abs(beta1star-betastar0))
#
betaboot=[betaboot + dot((betastar-beta),(betastar-beta).T)]
VCboot=(1/100)*betaboot
#
tstatsboot=beta/diag(VCboot)**0.5
stderrorsboot=diag(VCboot)**0.5
PValuesboot=2*(1-stats.t.cdf(np.abs(tstatsboot),ry-cx))
#_______________________________Display Results____________________________
print
print(' Results of Quantile Regression')
print('_'*70)
print("%10s %10s %10s %10s %10s %10s %10s" % ['Coef.', 'SE.Ker', 't.Ker', 'P.Ker', 'SE.Boot', 't.Boot', 'P.Boot'])
print('_'*70)
print("%10f %10f %10f %10f %10f %10f %10f" % [ beta,stderrors,tstats,PValues,stderrorsboot,tstatsboot,PValuesboot])
print('_'*70)
print('Pseudo R2: %10f' % PseudoR2 )
print('_'*70)
def quantilereg(y,x,p):
'''
estimates quantile regression based on weighted least squares.
constant term is added to x matrix
__________________________________________________________________________
Inputs:
y: Dependent variable
x: matrix of independent variables
p: quantile
Outputs:
beta: estimated Coefficients.
tstats: T- students of the coefficients.
VCboot: Variance-Covariance of coefficients by bootstrapping method.
itrat: number of iterations for convergence to roots.
PseudoR2: in quatile regression another definition of R2 is used namely PseudoR2.
betaboot: estimated coefficients by bootstrapping method.
This code can be used for quantile regression estimation as whole,and LAD
regression as special case of it, when one sets p=0.5.
Copyright(c) Shapour Mohammadi, University of Tehran, 2008
[email protected]
Translated to python with permission from original author by Christian Prinoth (christian at prinoth dot name)
Ref:
1-Birkes, D. and Y. Dodge(1993). Alternative Methods of Regression, John Wiley and Sons.
2-Green,W. H. (2008). Econometric Analysis. Sixth Edition. International Student Edition.
3-LeSage, J. P.(1999),Applied Econometrics Using MATLAB,
Keywords: Least Absolute Deviation(LAD) Regression, Quantile Regression,
Regression, Robust Estimation.
__________________________________________________________________________
'''
tstats=0
VCboot=0
itrat=0
PseudoR2=0
betaboot=0
ry=len(y)
rx, cx=x.shape
x=np.c_[np.ones(rx),x]
cx=cx+1
#______________Finding first estimates by solving the system_______________
# Some lines of this section is based on a code written by
# James P. Lesage in Applied Econometrics Using MATLAB(1999).PP. 73-4.
itrat=0
xstar=x
diff=1
beta=np.ones(cx)
z=np.zeros((rx,cx))
while itrat<1000 and diff>1e-6:
itrat+=1
beta0=beta
beta=dot(inv(dot(xstar.T,x)),xstar.T,y)
resid=y-dot(x,beta)
resid[np.abs(resid)<.000001]=.000001
resid[resid<0]=p*resid[resid<0]
resid[resid>0]=(1-p)*resid[resid>0]
resid=np.abs(resid)
for i in range(cx):
z[:,i] = x[:,i]/resid
xstar=z
beta1=beta
diff=np.max(np.abs(beta1-beta0))
return beta
#_______estimating variances based on Green 2008(quantile regression)______
e=y-dot(x,beta)
iqre=np.percentile(e,0.75)-np.percentile(e,0.25)
if p==0.5:
h=0.9*np.std(e)/(ry**0.2)
else:
h=0.9*np.min(np.std(e),iqre/1.34)/(ry**0.2)
u=(e/h)
fhat0=(1/(ry*h))*(sum(exp(-u)/((1+exp(-u))**2)))
D=np.zeros((ry,ry))
DIAGON=np.diag(D)
DIAGON[e>0]=(p/fhat0)**2
DIAGON[e<=0]=((1-p)/fhat0)**2
D=np.diag(DIAGON)
VCQ=np.dot(inv(dot(x.T,x)),dot(x.T,D,x),inv(np.dot(x.T,x)))
#____________________Standarad errores and t-stats_________________________
tstats=beta/np.sqrt(np.diag(VCQ))
stderrors=np.sqrt(np.diag(VCQ))
PValues=2*(1-stats.t.cdf(np.abs(tstats),ry-cx))
#______________________________ Quasi R square_____________________________
ef=y-dot(x,beta)
ef[ef<0]=(1-p)*ef[ef<0]
ef[ef>0]=p*ef[ef>0]
ef=np.abs(ef)
ered=y-np.percentile(y,p)
ered[ered<0]=(1-p)*ered[ered<0]
ered[ered>0]=p*ered[ered>0]
ered=np.abs(ered)
PseudoR2=1-np.sum(ef)/np.sum(ered)
#__________________Bootstrap standard deviation (Green 2008)_______________
betaboot=np.zeros((cx,cx))
for ii in range(100):
bootm, estar=bootstrp(1,np.mean,e)
#
ystar=dot(x,beta)+e[estar]
#
itratstar=0
xstarstar=x
diffstar=1
betastar=np.ones(cx)
while itratstar<1000 and diffstar>1e-6:
itratstar=itratstar+1
betastar0=betastar
betastar=dot(inv(dot(xstarstar.T,x)),xstarstar.T,ystar)
#
residstar=ystar-dot(x,betastar)
residstar[np.abs(residstar)<.000001]=.000001
residstar[residstar<0]=p*residstar[residstar<0]
residstar[residstar>0]=(1-p)*residstar[residstar>0]
residstar=np.abs(residstar)
zstar=np.zeros((rx,cx))
for i in range(cx):
zstar[:,i] = x[:,i]/residstar
xstarstar=zstar
beta1star=betastar
diffstar=np.max(np.abs(beta1star-betastar0))
#
betaboot=[betaboot + dot((betastar-beta),(betastar-beta).T)]
VCboot=(1/100)*betaboot
#
tstatsboot=beta/diag(VCboot)**0.5
stderrorsboot=diag(VCboot)**0.5
PValuesboot=2*(1-stats.t.cdf(np.abs(tstatsboot),ry-cx))
#_______________________________Display Results____________________________
print
print(' Results of Quantile Regression')
print('_'*70)
print("%10s %10s %10s %10s %10s %10s %10s" % ['Coef.', 'SE.Ker', 't.Ker', 'P.Ker', 'SE.Boot', 't.Boot', 'P.Boot'])
print('_'*70)
print("%10f %10f %10f %10f %10f %10f %10f" % [ beta,stderrors,tstats,PValues,stderrorsboot,tstatsboot,PValuesboot])
print('_'*70)
print('Pseudo R2: %10f' % PseudoR2 )
print('_'*70)
