def plot_slopes(subject_means, color, label):
rlm_coeff = rlm_coeffs(subject_means)
ellipser = regression_ellipsoid(subject_means[:,0], subject_means[:,1])
t = np.linspace(0, np.pi*2, 100)
ex, ey = ellipser(t)
plt.plot(rlm_coeff.c[0], rlm_coeff.c[1], marker='o', color=color, label=label)
plt.plot(ex, ey, color=color, linestyle='--', label='95% confidence region')
plt.xlabel('Slope')
plt.ylabel('Intercept')
def pursuit_yaw_new():
ci = [1,3]
is_control = True
txt = "free" if is_control else "tp"
pdf_out = PdfPages('/tmp/pursuit_vs_yaw_pooled_per_subject_'+str(ci)+'_'+txt+'.pdf')
table = get_pooled_data(ci, is_control)
#invalid = (table['sid'] == 2011081107) & (table['speed'] < -5)
#table = table[ ~invalid ]
xrange = (0,20)
sids = np.unique(table['sid'])
subject_means = []
lsr_coeffs = []
for sid in sids:
d = table[table['sid'] == sid]
ymean = np.mean(d['yaw'])
smean = np.mean(d['speed'])
subject_means.append((ymean, smean))
lsr_fit = np.polyfit(d['yaw'], d['speed'], 1)
lsr = np.poly1d(lsr_fit)
lsr_coeffs.append(lsr)
#print sid, lsr.c, scipy.stats.pearsonr(d['yaw'], d['speed'])
plt.figure()
plt.title(sid)
plt.xlim(xrange)
plt.ylim(-20,20)
plt.plot(d['yaw'], d['speed'], '.k')
plt.plot(xrange, lsr(xrange),'-b')
#plt.plot(xrange, model(xrange), '-g')
plt.xlabel('mean yaw during fixation (deg)')
plt.ylabel('gaze speed (deg/s)')
pdf_out.savefig()
plt.close()
subject_means = np.array(subject_means)
lsr_bs = np.array([x.c[0] for x in lsr_coeffs])
lsr_as = np.array([x.c[1] for x in lsr_coeffs])
fit_all = np.polyfit(table['yaw'], table['speed'], 1)
lsr_all = np.poly1d(fit_all)
print 'lsr all laps b=%f' % (lsr_all.c[0])
#fit_subject = np.polyfit(subject_means[:,0], subject_means[:,1], 1)
#lsr_subject = np.poly1d(fit_subject)
params = np.hstack([subject_means[:,0].reshape(-1,1),np.ones(len(subject_means[:,0])).reshape(-1,1)])
ols_model = sm.OLS(subject_means[:,1].reshape(-1,1), params)
rlm_model = sm.RLM(subject_means[:,1].reshape(-1,1), params, M=sm.robust.norms.HuberT())
yaw_model = np.poly1d([0.5, 0])
ols_results = ols_model.fit()
rlm_results = rlm_model.fit()
ols_coeff = np.poly1d(ols_results.params)
rlm_coeff = np.poly1d(rlm_results.params)
print 'ols subjects b=%f' % (ols_coeff.c[0])
print 'rlm subjects b=%f' % (rlm_coeff.c[0])
print ols_results.summary()
# binomial test
n = len(lsr_bs)
s = np.sum(lsr_bs > 0)
p = 0.5
p_binomial = np.math.factorial(n) / (np.math.factorial(s) * np.math.factorial(n-s)) * p**s * p**(n-s)
print 'binomial p(%i) = %f' % (s, p_binomial)
sy = np.std(subject_means[:,1])
print 'standard deviation of gaze speed %f' % sy
ss_residual = np.sum( (subject_means[:,1]-ols_coeff(subject_means[:,0]))**2 )
sxy = np.sqrt( ss_residual / (len(subject_means[:,0]-2)) )
print 'standard error of estimate %f' % sxy
model_ss_residual = np.sum( (subject_means[:,1]-yaw_model(subject_means[:,0]))**2 )
model_error = np.sqrt( model_ss_residual / (len(subject_means[:,0]-2)) )
print 'error of estimate from model %f' % model_error
# F stat
n = len(subject_means[:,0])
df1 = 2
df2 = n-df1
f = ((model_ss_residual-ss_residual) / df1) / (ss_residual / df2)
p_f = 1-scipy.stats.f(df1,df2).cdf(f)
print 'F=%f, p=%f' % (f, p_f)
# confidence region stuff
from tru.ols_confidence_region import regression_ellipsoid
ellipser = regression_ellipsoid(subject_means[:,0], subject_means[:,1])
t = np.linspace(0, np.pi*2, 100)
ex, ey = ellipser(t)
plt.figure()
plt.plot(table['yaw'], table['speed'], '.k')
plt.plot(xrange, lsr_all(xrange), '-b')
pdf_out.savefig()
plt.close()
plt.figure()
plt.plot(subject_means[:,0], subject_means[:,1], '.k')
plt.plot(xrange, ols_coeff(xrange), '-g', label='Ordinary least squares fit')
plt.plot(xrange, rlm_coeff(xrange), '-r', label='huber t')
plt.plot(xrange, yaw_model(xrange), 'b--', label='Future path model')
plt.xlabel('Mean yaw rate (deg/s)')
plt.ylabel('Mean gaze speed (deg/s)')
plt.legend(loc='lower right')
pdf_out.savefig()
plt.close()
plt.figure()
#plt.plot(lsr_bs, lsr_as, '.k')
plt.plot(ols_coeff.c[0], ols_coeff.c[1], 'og', label='OLS fit')
plt.plot(rlm_coeff.c[0], rlm_coeff.c[1], 'oy', label='huber t fit')
plt.plot(0.5, 0, 'ob', label='Future path model')
plt.plot(0, 0, 'or', label='Tangent point model')
plt.plot(ex, ey, 'k--', label='95% confidence region')
plt.xlabel('Slope')
plt.ylabel('Intercept')
plt.legend(loc='upper right', numpoints=1)
pdf_out.savefig()
plt.close()
"""
model_errors = subject_means[:,1]-ols_coeff(subject_means[:,0])
plt.figure()
plt.hist(model_errors, bins=10)
pdf_out.savefig()
plt.close()
"""
pdf_out.close()
