brainbox.behavior.pyschofit

(DEPRECATED) The psychofit toolbox contains tools to fit two-alternative psychometric data. The fitting is done using maximal likelihood estimation: one assumes that the responses of the subject are given by a binomial distribution whose mean is given by the psychometric function. The data can be expressed in fraction correct (from .5 to 1) or in fraction of one specific choice (from 0 to 1). To fit them you can use these functions:

weibull50: Weibull function from 0.5 to 1, with lapse rate

weibull: Weibull function from 0 to 1, with lapse rate

erf_psycho: erf function from 0 to 1, with lapse rate

erf_psycho_2gammas: erf function from 0 to 1, with two lapse rates

Functions in the toolbox are:

mle_fit_psycho: Maximumum likelihood fit of psychometric function
neg_likelihood: Negative likelihood of a psychometric function

For more info, see:

Examples: Examples of use of psychofit toolbox

Matteo Carandini, 2000-2015

NB: USE THE PSYCHOFIT PIP PACKAGE INSTEAD.

Functions

`erf_psycho`	erf function from 0 to 1, with lapse rate.
`erf_psycho_2gammas`	erf function from 0 to 1, with two lapse rates.
`mle_fit_psycho`	Maximumum likelihood fit of psychometric function.
`neg_likelihood`	Negative likelihood of a psychometric function.
`weibull`	Weibull function from 0 to 1, with lapse rate.
`weibull50`	Weibull function from 0.5 to 1, with lapse rate.

mle_fit_psycho(data, P_model='weibull', parstart=None, parmin=None, parmax=None, nfits=5)[source]

Maximumum likelihood fit of psychometric function.

Parameters:

data – 3 x n matrix where first row corresponds to stim levels, the second to number of trials for each stim level (int), the third to proportion correct / proportion rightward (float between 0 and 1)
P_model – The psychometric function. Possibilities include ‘weibull’ (DEFAULT), ‘weibull50’, ‘erf_psycho’ and ‘erf_psycho_2gammas’
parstart – Non-zero starting parameters, used to try to avoid local minima. The parameters are [threshold, slope, gamma], or if using the ‘erf_psycho_2gammas’ model append a second gamma value. Recommended to use a value > 1. If None, some reasonable defaults are used.
parmin – Minimum parameter values. If None, some reasonable defaults are used
parmax – Maximum parameter values. If None, some reasonable defaults are used
nfits – The number of fits

Returns:

The parameters from the best of the fits L: The likelihood of the best fit

Return type:

pars

Raises:

TypeError – data must be a list or numpy array
ValueError – data must be m by 3 matrix

Examples

Below we fit a Weibull function to some data: >>> import numpy as np >>> import matplotlib.pyplot as plt >>> cc = np.array([-8., -6., -4., -2., 0., 2., 4., 6., 8.]) # contrasts >>> nn = np.full((9,), 10) # number of trials at each contrast >>> pp = np.array([5., 8., 20., 41., 54., 59., 79., 92., 96])/100 # proportion “rightward” >>> pars, L = mle_fit_psycho(np.vstack((cc, nn, pp)), ‘erf_psycho’) >>> plt.plot(cc, pp, ‘bo’, mfc=’b’) >>> plt.plot(np.arange(-8, 8, 0.1), erf_psycho(pars, np.arange(-8, 8, 0.1)), ‘-b’)

Information:: 1999-11 FH wrote it 2000-01 MC cleaned it up 2000-04 MC took care of the 50% case 2009-12 MC replaced fmins with fminsearch 2010-02 MC, AZ added nfits 2013-02 MC+MD fixed bug with dealing with NaNs 2018-08 MW ported to Python

neg_likelihood(pars, data, P_model='weibull', parmin=None, parmax=None)[source]

Negative likelihood of a psychometric function.

Parameters:

pars – Model parameters [threshold, slope, gamma], or if using the ‘erf_psycho_2gammas’ model append a second gamma value.
data – 3 x n matrix where first row corresponds to stim levels, the second to number of trials for each stim level (int), the third to proportion correct / proportion rightward (float between 0 and 1)
P_model – The psychometric function. Possibilities include ‘weibull’ (DEFAULT), ‘weibull50’, ‘erf_psycho’ and ‘erf_psycho_2gammas’
parmin – Minimum bound for parameters. If None, some reasonable defaults are used
parmax – Maximum bound for parameters. If None, some reasonable defaults are used

Returns:

The likelihood of the parameters. The equation is:

sum(nn.*(pp.*log10(P_model)+(1-pp).*log10(1-P_model)))

See the the appendix of Watson, A.B. (1979). Probability summation over time. Vision Res 19, 515-522.

Return type:

ll

Raises:

ValueError – invalid model, options are “weibull”, “weibull50”, “erf_psycho” and “erf_psycho_2gammas”
TypeError – data must be a list or numpy array
ValueError data must be m by 3 matrix –

Information:: 1999-11 FH wrote it 2000-01 MC cleaned it up 2000-07 MC made it indep of Weibull and added parmin and parmax 2018-08 MW ported to Python

weibull(pars, xx)[source]

Weibull function from 0 to 1, with lapse rate.

Parameters:

pars – Model parameters [alpha, beta, gamma].
xx – vector of stim levels.

Returns:

A vector of length xx

Raises:

ValueError – pars must be of length 3
TypeError – pars must be list-like or numpy array

Information:: 1999-11 FH wrote it 2000-01 MC cleaned it up 2018-08 MW ported to Python

weibull50(pars, xx)[source]

Weibull function from 0.5 to 1, with lapse rate.

Parameters:

pars – Model parameters [alpha, beta, gamma].
xx – vector of stim levels.

Returns:

A vector of length xx

Raises:

ValueError – pars must be of length 3
TypeError – pars must be list-like or numpy array

Information:: 2000-04 MC wrote it 2018-08 MW ported to Python

erf_psycho(pars, xx)[source]

erf function from 0 to 1, with lapse rate.

Parameters:

pars – Model parameters [bias, slope, lapse].
xx – vector of stim levels.

Returns:

A vector of length xx

Return type:

ff

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> xx = np.arange(-50, 50)
>>> ff = erf_psycho(np.array([-10., 10., 0.1]), xx)
>>> plt.plot(xx, ff)

Raises:

ValueError – pars must be of length 3
TypeError – pars must be a list or numpy array

Information:: 2000 MC wrote it 2018-08 MW ported to Python

erf_psycho_2gammas(pars, xx)[source]

erf function from 0 to 1, with two lapse rates.

Parameters:

pars – Model parameters [bias, slope, gamma].
xx – vector of stim levels (%)

Returns:

A vector of length xx

Return type:

ff

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> xx = np.arange(-50, 50)
>>> ff = erf_psycho_2gammas(np.array([-10., 10., 0.2, 0.]), xx)
>>> plt.plot(xx, ff)

Raises:

ValueError – pars must be of length 4
TypeError – pars must be list-like or numpy array

Information:: 2000 MC wrote it 2018-08 MW ported to Python