def diagnostics(data, params, nafc=2, sigmoid="logistic", core="ab", cuts=None, gammaislambda=False):
# here we need to hack stuff, since data can be either 'real' data, or just
# a list of intensities, or just an empty sequence
# in order to remain compatible with psipy we must check for an empty
# sequence here, and return a specially crafted return value in that case.
# sorry..
if op.isSequenceType(data) and len(data) == 0:
pmf, nparams = sfu.make_pmf(
sfr.PsiData([0], [0], [0], 1), nafc, sigmoid, core, None, gammaislambda=gammaislambda
)
thres = np.array([pmf.getThres(params, cut) for cut in sfu.get_cuts(cuts)])
slope = np.array([pmf.getSlope(params, th) for th in thres])
return np.array([]), np.array([]), 0.0, thres, np.nan, np.nan
shape = np.shape(np.array(data))
intensities_only = False
if len(shape) == 1:
# just intensities, make a dataset with k and n all zero
k = n = [0] * shape[0]
data = [[xx, kk, nn] for xx, kk, nn in zip(data, k, n)]
intensities_only = True
else:
# data is 'real', just do nothing
pass
dataset, pmf, nparams = sfu.make_dataset_and_pmf(data, nafc, sigmoid, core, None, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
params = sfu.get_params(params, nparams)
predicted = np.array([pmf.evaluate(intensity, params) for intensity in dataset.getIntensities()])
if intensities_only:
return predicted
else:
deviance_residuals = pmf.getDevianceResiduals(params, dataset)
deviance = pmf.deviance(params, dataset)
thres = np.array([pmf.getThres(params, cut) for cut in cuts])
slope = np.array([pmf.getSlope(params, th) for th in thres])
rpd = pmf.getRpd(deviance_residuals, params, dataset)
rkd = pmf.getRkd(deviance_residuals, dataset)
return predicted, deviance_residuals, deviance, thres, slope, rpd, rkd
def mapestimate(data, nafc=2, sigmoid="logistic", core="ab", priors=None, cuts=None, start=None, gammaislambda=False):
dataset, pmf, nparams = sfu.make_dataset_and_pmf(data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
opt = sfr.PsiOptimizer(pmf, dataset)
estimate = opt.optimize(pmf, dataset, sfu.get_start(start, nparams) if start is not None else None)
H = pmf.ddnegllikeli(estimate, dataset)
thres = [pmf.getThres(estimate, c) for c in cuts]
slope = [pmf.getSlope(estimate, th) for th in thres]
deviance = pmf.deviance(estimate, dataset)
# convert to numpy stuff
estimate = np.array(estimate)
fisher = np.zeros((nparams, nparams))
for (i, j) in ((i, j) for i in xrange(nparams) for j in xrange(nparams)):
fisher[i, j] = sfr.doublep_value(H(i, j))
thres = np.array(thres)
slope = np.array(slope)
deviance = np.array(deviance)
return estimate, fisher, thres, slope, deviance
def diagnostics(data,
params,
nafc=2,
sigmoid='logistic',
core='ab',
cuts=None,
gammaislambda=False):
""" Some diagnostic statistics for a psychometric function fit.
This function is a bit messy since it has three functions depending on the
type of the `data` argument.
Parameters
----------
data : variable
real 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.
intensities : sequence of floats
The x-values of the psychometric function, then we obtain only the
predicted values.
no data : empty sequence
In this case we evaluate the psychometric function at the cuts. All
other return values are then irrelevant.
params : sequence of len nparams
parameter vector at which the diagnostic information should be evaluated
nafc : int
Number of responses 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.
cuts : sequence of floats
Cuts at which thresholds should be determined. That is if cuts =
(.25,.5,.75), thresholds (F^{-1} ( 0.25 ), F^{-1} ( 0.5 ), F^{-1} ( 0.75
)) are returned. Here F^{-1} denotes the inverse of the function
specified by sigmoid. If cuts==None, this is modified to cuts=[0.5].
Output
------
(predicted, deviance_residuals, deviance, thres, Rpd, Rkd)
predicted : numpy array of length nblocks
predicted values associated with the respective stimulus intensities
deviance_residuals : numpy array of length nblocks
deviance residuals of the data
deviance float
deviance of the data
thres : numpy array length ncuts
the model prediction at the cuts
Rpd : float
correlation between predicted performance and deviance residuals
Rkd : float
correlation between block index and deviance residuals
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)]
>>> prm = [2.75, 1.45, 0.015]
>>> pred,di,D,thres,slope,Rpd,Rkd = diagnostics(d,prm)
>>> D
8.0748485860836254
>>> di[0]
1.6893279652591433
>>> Rpd
-0.19344675783032755
"""
# here we need to hack stuff, since data can be either 'real' data, or just
# a list of intensities, or just an empty sequence
# in order to remain compatible with psipy we must check for an empty
# sequence here, and return a specially crafted return value in that case.
# sorry..
# TODO after removal of psipy we can probably change this.
if op.isSequenceType(data) and len(data) == 0:
pmf, nparams = sfu.make_pmf(sfr.PsiData([0], [0], [0], 1),
nafc,
sigmoid,
core,
None,
gammaislambda=gammaislambda)
thres = np.array(
[pmf.getThres(params, cut) for cut in sfu.get_cuts(cuts)])
slope = np.array([pmf.getSlope(params, th) for th in thres])
return np.array([]), np.array([]), 0.0, thres, np.nan, np.nan
shape = np.shape(np.array(data))
intensities_only = False
if len(shape) == 1:
# just intensities, make a dataset with k and n all zero
k = n = [0] * shape[0]
data = [[xx, kk, nn] for xx, kk, nn in zip(data, k, n)]
intensities_only = True
else:
# data is 'real', just do nothing
pass
dataset, pmf, nparams = sfu.make_dataset_and_pmf(
data, nafc, sigmoid, core, None, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
params = sfu.get_params(params, nparams)
predicted = np.array([
pmf.evaluate(intensity, params)
for intensity in dataset.getIntensities()
])
if intensities_only:
return predicted
else:
deviance_residuals = pmf.getDevianceResiduals(params, dataset)
deviance = pmf.deviance(params, dataset)
thres = np.array([pmf.getThres(params, cut) for cut in cuts])
slope = np.array([pmf.getSlope(params, th) for th in thres])
rpd = pmf.getRpd(deviance_residuals, params, dataset)
rkd = pmf.getRkd(deviance_residuals, dataset)
return predicted, deviance_residuals, deviance, thres, slope, rpd, rkd
def mapestimate(data,
nafc=2,
sigmoid='logistic',
core='ab',
priors=None,
cuts=None,
start=None,
gammaislambda=False):
""" MAP or constrained maximum likelihood estimation for 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.
nafc : int
Number of responses 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
Prior distributions on the parameters of the psychometric function.
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.
if an invalid prior is selected, no constraints are imposed on that
parameter resulting in an improper prior distribution.
cuts : sequence of floats
Cuts at which thresholds should be determined. That is if cuts =
(.25,.5,.75), thresholds (F^{-1} ( 0.25 ), F^{-1} ( 0.5 ), F^{-1} ( 0.75
)) are returned. Here F^{-1} denotes the inverse of the function
specified by sigmoid. If cuts==None, this is modified to cuts=[0.5].
start : sequence of floats of length number of model parameters
Values at which to start the optimization, if None the starting value is
determined using a coarse grid search.
Output
------
estimate, fisher, thres, slope, deviance
estimate : numpy array length nparams
the map/cml estimate
fisher : numpy array shape (nparams, nparams)
the fisher matrix
thres : numpy array length ncuts
the model prediction at the cuts
slope : numpy array length ncuts
the gradient of the psychometric function at the cuts
deviance : numpy array length 1
the deviance for the estimate
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)')
>>> estimate, fisher, thres, slope, deviance = mapestimate ( d, priors=priors )
>>> estimate
array([ 2.75180624, 1.45717745, 0.01555658])
>>> deviance
array(8.0713313642328242)
"""
dataset, pmf, nparams = sfu.make_dataset_and_pmf(
data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
opt = sfr.PsiOptimizer(pmf, dataset)
estimate = opt.optimize(
pmf, dataset,
sfu.get_start(start, nparams) if start is not None else None)
H = pmf.ddnegllikeli(estimate, dataset)
thres = [pmf.getThres(estimate, c) for c in cuts]
slope = [pmf.getSlope(estimate, th) for th in thres]
deviance = pmf.deviance(estimate, dataset)
# convert to numpy stuff
estimate = np.array(estimate)
fisher = np.zeros((nparams, nparams))
for (i, j) in ((i, j) for i in xrange(nparams) for j in xrange(nparams)):
fisher[i, j] = sfr.doublep_value(H(i, j))
thres = np.array(thres)
slope = np.array(slope)
deviance = np.array(deviance)
return estimate, fisher, thres, slope, deviance
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 test_get_cuts(self):
# this used to cause an error since
# operator.isNumberType() on an ndarry is always true
cuts = np.array([1.0, 2.0, 3.0])
sfu.get_cuts(cuts)
def test_get_cuts(self):
# this used to cause an error since
# operator.isNumberType() on an ndarry is always true
cuts = np.array([1.0, 2.0, 3.0])
sfu.get_cuts(cuts)
def bootstrap(
data,
start=None,
nsamples=2000,
nafc=2,
sigmoid="logistic",
core="ab",
priors=None,
cuts=None,
parametric=True,
gammaislambda=False,
):
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_t(cut)
slbias[cut] = bs_list.getBias_t(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 diagnostics(data, params, nafc=2, sigmoid='logistic', core='ab', cuts=None, gammaislambda=False):
""" Some diagnostic statistics for a psychometric function fit.
This function is a bit messy since it has three functions depending on the
type of the `data` argument.
Parameters
----------
data : variable
real 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.
intensities : sequence of floats
The x-values of the psychometric function, then we obtain only the
predicted values.
no data : empty sequence
In this case we evaluate the psychometric function at the cuts. All
other return values are then irrelevant.
params : sequence of len nparams
parameter vector at which the diagnostic information should be evaluated
nafc : int
Number of responses 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.
cuts : sequence of floats
Cuts at which thresholds should be determined. That is if cuts =
(.25,.5,.75), thresholds (F^{-1} ( 0.25 ), F^{-1} ( 0.5 ), F^{-1} ( 0.75
)) are returned. Here F^{-1} denotes the inverse of the function
specified by sigmoid. If cuts==None, this is modified to cuts=[0.5].
Output
------
(predicted, deviance_residuals, deviance, thres, Rpd, Rkd)
predicted : numpy array of length nblocks
predicted values associated with the respective stimulus intensities
deviance_residuals : numpy array of length nblocks
deviance residuals of the data
deviance float
deviance of the data
thres : numpy array length ncuts
the model prediction at the cuts
Rpd : float
correlation between predicted performance and deviance residuals
Rkd : float
correlation between block index and deviance residuals
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)]
>>> prm = [2.75, 1.45, 0.015]
>>> pred,di,D,thres,slope,Rpd,Rkd = diagnostics(d,prm)
>>> D
8.0748485860836254
>>> di[0]
1.6893279652591433
>>> Rpd
-0.19344675783032755
"""
# here we need to hack stuff, since data can be either 'real' data, or just
# a list of intensities, or just an empty sequence
# in order to remain compatible with psipy we must check for an empty
# sequence here, and return a specially crafted return value in that case.
# sorry..
# TODO after removal of psipy we can probably change this.
if op.isSequenceType(data) and len(data) == 0:
pmf, nparams = sfu.make_pmf(sfr.PsiData([0],[0],[0],1), nafc, sigmoid, core, None, gammaislambda=gammaislambda )
thres = np.array([pmf.getThres(params, cut) for cut in sfu.get_cuts(cuts)])
slope = np.array([pmf.getSlope(params, th ) for th in thres])
return np.array([]), np.array([]), 0.0, thres, np.nan, np.nan
shape = np.shape(np.array(data))
intensities_only = False
if len(shape) == 1:
# just intensities, make a dataset with k and n all zero
k = n = [0] * shape[0]
data = [[xx,kk,nn] for xx,kk,nn in zip(data,k,n)]
intensities_only = True
else:
# data is 'real', just do nothing
pass
dataset, pmf, nparams = sfu.make_dataset_and_pmf(data, nafc, sigmoid, core, None, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
params = sfu.get_params(params, nparams)
predicted = np.array([pmf.evaluate(intensity, params) for intensity in
dataset.getIntensities()])
if intensities_only:
return predicted
else:
deviance_residuals = pmf.getDevianceResiduals(params, dataset)
deviance = pmf.deviance(params, dataset)
thres = np.array([pmf.getThres(params, cut) for cut in cuts])
slope = np.array([pmf.getSlope(params, th ) for th in thres])
rpd = pmf.getRpd(deviance_residuals, params, dataset)
rkd = pmf.getRkd(deviance_residuals, dataset)
return predicted, deviance_residuals, deviance, thres, slope, rpd, rkd
def mapestimate ( data, nafc=2, sigmoid='logistic', core='ab', priors=None,
cuts = None, start=None, gammaislambda=False):
""" MAP or constrained maximum likelihood estimation for 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.
nafc : int
Number of responses 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
Prior distributions on the parameters of the psychometric function.
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.
if an invalid prior is selected, no constraints are imposed on that
parameter resulting in an improper prior distribution.
cuts : sequence of floats
Cuts at which thresholds should be determined. That is if cuts =
(.25,.5,.75), thresholds (F^{-1} ( 0.25 ), F^{-1} ( 0.5 ), F^{-1} ( 0.75
)) are returned. Here F^{-1} denotes the inverse of the function
specified by sigmoid. If cuts==None, this is modified to cuts=[0.5].
start : sequence of floats of length number of model parameters
Values at which to start the optimization, if None the starting value is
determined using a coarse grid search.
Output
------
estimate, fisher, thres, slope, deviance
estimate : numpy array length nparams
the map/cml estimate
fisher : numpy array shape (nparams, nparams)
the fisher matrix
thres : numpy array length ncuts
the model prediction at the cuts
slope : numpy array length ncuts
the gradient of the psychometric function at the cuts
deviance : numpy array length 1
the deviance for the estimate
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)')
>>> estimate, fisher, thres, slope, deviance = mapestimate ( d, priors=priors )
>>> estimate
array([ 2.75180624, 1.45717745, 0.01555658])
>>> deviance
array(8.0713313642328242)
"""
dataset, pmf, nparams = sfu.make_dataset_and_pmf(data,
nafc, sigmoid, core, priors, gammaislambda=gammaislambda)
cuts = sfu.get_cuts(cuts)
opt = sfr.PsiOptimizer(pmf, dataset)
estimate = opt.optimize(pmf, dataset, sfu.get_start(start, nparams) if start is not
None else None)
H = pmf.ddnegllikeli(estimate, dataset)
thres = [pmf.getThres(estimate, c) for c in cuts]
slope = [pmf.getSlope(estimate, th) for th in thres]
deviance = pmf.deviance(estimate, dataset)
# convert to numpy stuff
estimate = np.array(estimate)
fisher = np.zeros((nparams,nparams))
for (i,j) in ((i,j) for i in xrange(nparams) for j in xrange(nparams)):
fisher[i,j] = sfr.doublep_value(H(i,j))
thres = np.array(thres)
slope = np.array(slope)
deviance = np.array(deviance)
return estimate, fisher, thres, slope, deviance
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
