fig.text(.05, .47, r"logistic", rotation=90, **fontspecs)
fig.text(.1, .47, r"$f(x)=\frac{1}{1+\exp(-x)}$", rotation=90, **fontspecs)
fig.text(.05, .2, r"exponential", rotation=90, **fontspecs)
fig.text(.1, .2, r"$f(x)=1-\exp(-x)$", rotation=90, **fontspecs)
fig.text(.6, .95, r"ab", **fontspecs)
fig.text(.6, .9, r"$g(x,a,b)=\frac{x-a}{b}$", **fontspecs)
fig.text(.85, .95, r"poly", **fontspecs)
fig.text(.85, .9, r"$g(x,a,b)=(\frac{x}{a})^b$", **fontspecs)
axes_ab = [ax_ab, ax_logist, ax_logistab, ax_lgumbel, ax_gumbelab]
axes_wei = [ax_weibull, ax_logistweib, ax_gumbelweib]
abcore = sft.abCore()
weicore = sft.polyCore(sft.PsiData([1, 2, 3], [2, 2, 2], [2, 2, 2], 2))
logistic = sft.PsiLogistic()
gumbel = sft.PsiExponential()
x = p.mgrid[-7:7:1000j]
ax_logist.plot(x, [logistic.f(xx) for xx in x], color="k")
ax_lgumbel.plot(x, [gumbel.f(xx) for xx in x], color="k")
prm = [(1, 2, .02), (2, 2, .02), (1, 1, .02), (2, 1, .02)]
col = ['b', 'r', 'g', 'c']
for pr, c in zip(prm, col):
dab = [abcore.g(xx, pr) for xx in x]
ax_ab.plot(x, dab, color=c)
ax_logistab.plot(x, [logistic.f(dd) for dd in dab], color=c)
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 generate_test_dataset():
x = sfr.vector_double([0.,2.,4.,6., 8., 10.])
k = sfr.vector_int([24, 32, 40,48, 50,48])
n = sfr.vector_int(6*[50])
return sfr.PsiData(x, n, k, 2)