metadpy.mle.fit_metad#

metadpy.mle.fit_metad(nR_S1: ~numpy.ndarray, nR_S2: ~numpy.ndarray, nRatings: int, nCriteria: ~typing.Optional[int] = None, s: int = 1, verbose: int = 0, fninv: ~typing.Callable = <bound method rv_continuous.ppf of <scipy.stats._continuous_distns.norm_gen object>>, fncdf: ~typing.Callable = <numba._DUFunc 'norm_cdf'>) → Dict[source]#

Fit metad model using MLE.

Parameters
nR_S1, nR_S2

These are vectors containing the total number of responses in each response category, conditional on presentation of S1 and S2. If nR_S1 = [100, 50, 20, 10, 5, 1], then when stimulus S1 was presented, the subject had the following response counts: * responded ‘S1’, rating=`3` : 100 times * responded ‘S1’, rating=`2` : 50 times * responded ‘S1’, rating=`1` : 20 times * responded ‘S2’, rating=`1` : 10 times * responded ‘S2’, rating=`2` : 5 times * responded ‘S2’, rating=`3` : 1 time

The ordering of response / rating counts for S2 should be the same as it is for S1. e.g. if nR_S2 = [3, 7, 8, 12, 27, 89], then when stimulus S2 was presented, the subject had the following response counts: * responded ‘S1’, rating=`3` : 3 times * responded ‘S1’, rating=`2` : 7 times * responded ‘S1’, rating=`1` : 8 times * responded ‘S2’, rating=`1` : 12 times * responded ‘S2’, rating=`2` : 27 times * responded ‘S2’, rating=`3` : 89 times

nRatings

Number of discrete ratings. If a continuous rating scale was used, and the number of unique ratings does not match nRatings, will convert to discrete ratings using metadpy.utils.discreteRatings(). Default is set to 4.

nCriteria

(Optional) Number criteria to be fitted. If None, the number of criteria is set to nCriteria = int(2 * nRatings - 1).

s

Ratio of standard deviations for type 1 distributions as: s = np.std(S1) / np.std(S2). If not specified, s is set to a default value of 1. For most purposes, it is recommended to set s=1. See http://www.columbia.edu/~bsm2105/type2sdt for further discussion.

verbose
Level of algorithm’s verbosity:

  • 0 (default) : work silently.

  • 1 : display a termination report.

  • 2 : display progress during iterations.

  • 3 : display progress during iterations (more complete report).

fninv

A function handle for the inverse CDF of the type 1 distribution. If not specified, fninv defaults to scipy.stats.norm.ppf().

fncdf

A function handle for the CDF of the type 1 distribution. If not specified, fncdf defaults to scipy.stats.norm.cdf().

Returns
results

In the following, S1 and S2 represent the distributions of evidence generated by stimulus classes S1 and S2: * ‘dprime’ : mean(S2) - mean(S1), in root-mean-square(sd(S1), sd(S2))

units

  • ‘s’ : sd(S1) / sd(S2)

  • ‘meta_d’ : meta-d’ in RMS units

  • ‘m_diff’ : meta_da - da

  • ‘m_ratio’ : meta_da / da

  • ‘meta_ca’ : type 1 criterion for meta-d’ fit, RMS units.

  • ‘t2ca_rS1’ : type 2 criteria of “S1” responses for meta-d’ fit, RMS

units. * ‘t2ca_rS2’ : type 2 criteria of “S2” responses for meta-d’ fit,

RMS units.

  • ‘logL’ : log likelihood of the data fit

  • ‘est_HR2_rS1’ : estimated (from meta-d’ fit) type 2 hit rates for S1

responses. * ‘obs_HR2_rS1’ : actual type 2 hit rates for S1 responses. * ‘est_FAR2_rS1’ : estimated type 2 false alarm rates for S1 responses. * ‘obs_FAR2_rS1’ : actual type 2 false alarm rates for S1 responses. * ‘est_HR2_rS2’ : estimated type 2 hit rates for S2 responses. * ‘obs_HR2_rS2’ : actual type 2 hit rates for S2 responses. * ‘est_FAR2_rS2’ : estimated type 2 false alarm rates for S2 responses. * ‘obs_FAR2_rS2’ : actual type 2 false alarm rates for S2 responses.