def bootstrap(data,
start=None,
nsamples=2000,
nafc=2,
sigmoid="logistic",
core="ab",
priors=None,
cuts=None,
parametric=True,
gammaislambda=False):
""" Parametric bootstrap of a psychometric function.
Parameters
----------
data : A list of lists or an array of data.
The first column should be stimulus intensity, the second column should
be number of correct responses (in 2AFC) or number of yes- responses (in
Yes/No), the third column should be number of trials. See also: the examples
section below.
start : sequence of floats of length number of model parameters
Generating values for the bootstrap samples. If this is None, the
generating value will be the MAP estimate. Length should be 4 for Yes/No
and 3 for nAFC.
nsamples : number
Number of bootstrap samples to be drawn.
nafc : int
Number of alternatives for nAFC tasks. If nafc==1 a Yes/No task is
assumed.
sigmoid : string
Name of the sigmoid to be fitted. Valid sigmoids include:
logistic
gauss
gumbel_l
gumbel_r
See `swignifit.utility.available_sigmoids()` for all available sigmoids.
core : string
\"core\"-type of the psychometric function. Valid choices include:
ab (x-a)/b
mw%g midpoint and width
linear a+bx
log a+b log(x)
See `swignifit.utility.available_cores()` for all available sigmoids.
priors : sequence of strings length number of parameters
Constraints on the likelihood estimation. These are expressed in the form of a list of
prior names. Valid prior choices include:
Uniform(%g,%g)
Gauss(%g,%g)
Beta(%g,%g)
Gamma(%g,%g)
nGamma(%g,%g)
if an invalid prior or `None` is selected, no constraints are imposed at all.
See `swignifit.utility.available_priors()` for all available sigmoids.
cuts : a single number or a sequence of numbers.
Cuts indicating the performances that should be considered 'threshold'
performances. This means that in a 2AFC task, cuts==0.5 the 'threshold'
is somewhere around 75%% correct performance, depending on the lapse
rate parametric boolean to indicate whether or not the bootstrap
procedure should be parametric or not.
parametric : boolean
If `True` do parametric, otherwise do a non-parametric bootstrap.
gammaislambda : boolean
Set the gamma == lambda prior.
Returns
-------
(samples,estimates,deviance,
threshold, th_bias, th_acceleration,
slope, slope_bias, slope_accelerateion
Rkd,Rpd,outliers,influential)
samples : numpy array, shape: (nsamples, nblocks)
the bootstrap sampled data
estimates : numpy array, shape: (nsamples, nblocks)
estimated parameters associated with the data sets
deviance : numpy array, length: nsamples
deviances for the bootstraped datasets
threshold : numpy array, shape: (nsamples, ncuts)
thresholds/cuts for each bootstraped datasets
th_bias : numpy array, shape: (ncuts)
the bias term associated with the threshold
th_acc : numpy array, shape: (ncuts)
the acceleration constant associated with the threshold
slope : numpy array, shape: (nsamples, ncuts)
slope at each cuts for each bootstraped datasets
sl_bias : numpy array, shape: (ncuts)
bias term associated with the slope
sl_acc : numpy array, shape: (ncuts)
acceleration term associated with the slope
Rkd : numpy array, length: nsamples
correlations between block index and deviance residuals
Rpd : numpy array, length: nsamples
correlations between model prediction and deviance residuals
outliers : numpy array of booleans, length nblocks
points that are outliers
influential : numpy array of booleans, length nblocks
points that are influential observations
Example
-------
>>> x = [float(2*k) for k in xrange(6)]
>>> k = [34,32,40,48,50,48]
>>> n = [50]*6
>>> d = [[xx,kk,nn] for xx,kk,nn in zip(x,k,n)]
>>> priors = ('flat','flat','Uniform(0,0.1)')
>>> samples,est,D,thres,thbias,thacc,slope,slbias,slacc,Rkd,Rpd,out,influ \
= bootstrap(d,nsamples=2000,priors=priors)
>>> np.mean(est[:,0])
2.7547034408466811
>>> mean(est[:,1])
1.4057297989923003
"""
dataset, pmf, nparams = sfu.make_dataset_and_pmf(
data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
ncuts = len(cuts)
if start is not None:
start = sfu.get_start(start, nparams)
bs_list = sfr.bootstrap(nsamples, dataset, pmf, cuts, start, True,
parametric)
jk_list = sfr.jackknifedata(dataset, pmf)
nblocks = dataset.getNblocks()
# construct the massive tuple of return values
samples = np.zeros((nsamples, nblocks), dtype=np.int32)
estimates = np.zeros((nsamples, nparams))
deviance = np.zeros((nsamples))
thres = np.zeros((nsamples, ncuts))
slope = np.zeros((nsamples, ncuts))
Rpd = np.zeros((nsamples))
Rkd = np.zeros((nsamples))
for row_index in xrange(nsamples):
samples[row_index] = bs_list.getData(row_index)
estimates[row_index] = bs_list.getEst(row_index)
deviance[row_index] = bs_list.getdeviance(row_index)
thres[row_index] = [
bs_list.getThres_byPos(row_index, j) for j in xrange(ncuts)
]
slope[row_index] = [
bs_list.getSlope_byPos(row_index, j) for j in xrange(ncuts)
]
Rpd[row_index] = bs_list.getRpd(row_index)
Rkd[row_index] = bs_list.getRkd(row_index)
thacc = np.zeros((ncuts))
thbias = np.zeros((ncuts))
slacc = np.zeros((ncuts))
slbias = np.zeros((ncuts))
for cut in xrange(ncuts):
thacc[cut] = bs_list.getAcc_t(cut)
thbias[cut] = bs_list.getBias_t(cut)
slacc[cut] = bs_list.getAcc_s(cut)
slbias[cut] = bs_list.getBias_s(cut)
ci_lower = sfr.vector_double(nparams)
ci_upper = sfr.vector_double(nparams)
for param in xrange(nparams):
ci_lower[param] = bs_list.getPercentile(0.025, param)
ci_upper[param] = bs_list.getPercentile(0.975, param)
outliers = np.zeros((nblocks), dtype=np.bool)
influential = np.zeros((nblocks))
for block in xrange(nblocks):
outliers[block] = jk_list.outlier(block)
influential[block] = jk_list.influential(block, ci_lower, ci_upper)
return samples, estimates, deviance, thres, thbias, thacc, slope, slbias, slacc, Rpd, Rkd, outliers, influential
def generate_test_bootstrap_list():
data = TestData.generate_test_dataset()
psi = TestPsychometric.generate_test_model()
cuts = sfr.vector_double([1, 0.5])
return sfr.bootstrap(999, data, psi, cuts)
def generate_test_bootstrap_list():
data = TestData.generate_test_dataset()
psi = TestPsychometric.generate_test_model()
cuts = sfr.vector_double([1, 0.5])
return sfr.bootstrap(999, data, psi, cuts)
def bootstrap(data, start=None, nsamples=2000, nafc=2, sigmoid="logistic",
core="ab", priors=None, cuts=None, parametric=True, gammaislambda=False ):
""" Parametric bootstrap of a psychometric function.
Parameters
----------
data : A list of lists or an array of data.
The first column should be stimulus intensity, the second column should
be number of correct responses (in 2AFC) or number of yes- responses (in
Yes/No), the third column should be number of trials. See also: the examples
section below.
start : sequence of floats of length number of model parameters
Generating values for the bootstrap samples. If this is None, the
generating value will be the MAP estimate. Length should be 4 for Yes/No
and 3 for nAFC.
nsamples : number
Number of bootstrap samples to be drawn.
nafc : int
Number of alternatives for nAFC tasks. If nafc==1 a Yes/No task is
assumed.
sigmoid : string
Name of the sigmoid to be fitted. Valid sigmoids include:
logistic (1+exp(-x))**-1 [Default]
gauss Phi(x)
gumbel_l 1 - exp(-exp(x))
gumbel_r exp(-exp(-x))
exponential x>0: 1 - exp(-x); else: 0
cauchy atan(x)/pi + 0.5
id x; only useful in conjunction with NakaRushton core
See `swignifit.utility.available_sigmoids()` for all available sigmoids.
core : string
\"core\"-type of the psychometric function. Valid choices include:
ab (x-a)/b [Default]
mw%g midpoint and width, with "%g" a number larger than 0 and less than 0.5.
mw%g corresponds to a parameterization in terms of midpoint and width of
the rising part of the sigmoid. This width is defined as the length of the
interval on which the sigmoidal part reaches from "%g" to 1-"%g".
linear a+b*x
log a+b*log(x)
weibull 2*s*m*(log(x)-log(m))/log(2) + log(log(2))
This will give you a weibull if combined with the gumbel_l sigmoid and a
reverse weibull if combined with the gumbel_r sigmoid.
poly (x/a)**b Will give you a weibull if combined with an exp sigmoid
NakaRushton The Naka-Rushton nonlinearity; should only be used with an id core
See `swignifit.utility.available_cores()` for all available cores.
priors : sequence of strings length number of parameters
Constraints on the likelihood estimation. These are expressed in the form of a list of
prior names. Valid prior choices include:
Uniform(%g,%g) Uniform distribution on an interval
Gauss(%g,%g) Gaussian distribution with mean and standard deviation
Beta(%g,%g) Beta distribution
Gamma(%g,%g) Gamma distribution
nGamma(%g,%g) Gamma distribution on the negative axis
invGamma(%g,%g) inverse Gamma distribution
ninvGamma(%g,%g) inverse Gamma distribution on the negative axis
if an invalid prior or `None` is selected, no constraints are imposed at all.
See `swignifit.utility.available_priors()` for all available sigmoids.
cuts : a single number or a sequence of numbers.
Cuts indicating the performances that should be considered 'threshold'
performances. This means that in a 2AFC task, cuts==0.5 the 'threshold'
is somewhere around 75%% correct performance, depending on the lapse
rate parametric boolean to indicate whether or not the bootstrap
procedure should be parametric or not.
parametric : boolean
If `True` do parametric, otherwise do a non-parametric bootstrap.
gammaislambda : boolean
Set the gamma == lambda prior.
Returns
-------
(samples,estimates,deviance,
threshold, th_bias, th_acceleration,
slope, slope_bias, slope_accelerateion
Rkd,Rpd,outliers,influential)
samples : numpy array, shape: (nsamples, nblocks)
the bootstrap sampled data
estimates : numpy array, shape: (nsamples, nblocks)
estimated parameters associated with the data sets
deviance : numpy array, length: nsamples
deviances for the bootstraped datasets
threshold : numpy array, shape: (nsamples, ncuts)
thresholds/cuts for each bootstraped datasets
th_bias : numpy array, shape: (ncuts)
the bias term associated with the threshold
th_acc : numpy array, shape: (ncuts)
the acceleration constant associated with the threshold
slope : numpy array, shape: (nsamples, ncuts)
slope at each cuts for each bootstraped datasets
sl_bias : numpy array, shape: (ncuts)
bias term associated with the slope
sl_acc : numpy array, shape: (ncuts)
acceleration term associated with the slope
Rkd : numpy array, length: nsamples
correlations between block index and deviance residuals
Rpd : numpy array, length: nsamples
correlations between model prediction and deviance residuals
outliers : numpy array of booleans, length nblocks
points that are outliers
influential : numpy array of booleans, length nblocks
points that are influential observations
Example
-------
>>> x = [float(2*k) for k in xrange(6)]
>>> k = [34,32,40,48,50,48]
>>> n = [50]*6
>>> d = [[xx,kk,nn] for xx,kk,nn in zip(x,k,n)]
>>> priors = ('flat','flat','Uniform(0,0.1)')
>>> samples,est,D,thres,thbias,thacc,slope,slbias,slacc,Rkd,Rpd,out,influ \
= bootstrap(d,nsamples=2000,priors=priors)
>>> np.mean(est[:,0])
2.7547034408466811
>>> mean(est[:,1])
1.4057297989923003
"""
dataset, pmf, nparams = sfu.make_dataset_and_pmf(data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
ncuts = len(cuts)
if start is not None:
start = sfu.get_start(start, nparams)
bs_list = sfr.bootstrap(nsamples, dataset, pmf, cuts, start, True, parametric)
jk_list = sfr.jackknifedata(dataset, pmf)
nblocks = dataset.getNblocks()
# construct the massive tuple of return values
samples = np.zeros((nsamples, nblocks), dtype=np.int32)
estimates = np.zeros((nsamples, nparams))
deviance = np.zeros((nsamples))
thres = np.zeros((nsamples, ncuts))
slope = np.zeros((nsamples, ncuts))
Rpd = np.zeros((nsamples))
Rkd = np.zeros((nsamples))
for row_index in xrange(nsamples):
samples[row_index] = bs_list.getData(row_index)
estimates[row_index] = bs_list.getEst(row_index)
deviance[row_index] = bs_list.getdeviance(row_index)
thres[row_index] = [bs_list.getThres_byPos(row_index, j) for j in xrange(ncuts)]
slope[row_index] = [bs_list.getSlope_byPos(row_index, j) for j in xrange(ncuts)]
Rpd[row_index] = bs_list.getRpd(row_index)
Rkd[row_index] = bs_list.getRkd(row_index)
thacc = np.zeros((ncuts))
thbias = np.zeros((ncuts))
slacc = np.zeros((ncuts))
slbias = np.zeros((ncuts))
for cut in xrange(ncuts):
thacc[cut] = bs_list.getAcc_t(cut)
thbias[cut] = bs_list.getBias_t(cut)
slacc[cut] = bs_list.getAcc_s(cut)
slbias[cut] = bs_list.getBias_s(cut)
ci_lower = sfr.vector_double(nparams)
ci_upper = sfr.vector_double(nparams)
for param in xrange(nparams):
ci_lower[param] = bs_list.getPercentile(0.025, param)
ci_upper[param] = bs_list.getPercentile(0.975, param)
outliers = np.zeros((nblocks), dtype=np.bool)
influential = np.zeros((nblocks))
for block in xrange(nblocks):
outliers[block] = jk_list.outlier(block)
influential[block] = jk_list.influential(block, ci_lower, ci_upper)
return samples, estimates, deviance, thres, thbias, thacc, slope, slbias, slacc, Rpd, Rkd, outliers, influential