def cohens_kappa(annotations1, annotations2, nclasses=None):
"""Compute Cohen's kappa for two annotators.
Assumes that the annotators draw annotations at random with different but
constant frequencies.
See also :func:`~pyanno.measures.helpers.pairwise_matrix`.
**References:**
* Cohen, Jacob (1960). A coefficient of agreement for nominal scales.
Educational and Psychological Measurement, 20, 37--46.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Cohen%27s_kappa>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug('No valid annotations')
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
chance_agreement = chance_agreement_different_frequency(annotations1,
annotations2,
nclasses)
observed_agreement = observed_agreement_frequency(annotations1,
annotations2,
nclasses)
return chance_adjusted_agreement(observed_agreement.sum(),
chance_agreement.sum())
def scotts_pi(annotations1, annotations2, nclasses=None):
"""Return Scott's pi statistic for two annotators.
Assumes that the annotators draw random annotations with the same
frequency as the combined observed annotations.
See also :func:`~pyanno.measures.helpers.pairwise_matrix`.
**References:**
* Scott, W. (1955). "Reliability of content analysis: The case of nominal
scale coding." Public Opinion Quarterly, 19(3), 321-325.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Scott%27s_Pi>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug('No valid annotations')
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
chance_agreement = chance_agreement_same_frequency(annotations1,
annotations2,
nclasses)
observed_agreement = observed_agreement_frequency(annotations1,
annotations2,
nclasses)
return chance_adjusted_agreement(observed_agreement.sum(),
chance_agreement.sum())
def cohens_kappa(annotations1, annotations2, nclasses=None):
"""Compute Cohen's kappa for two annotators.
Assumes that the annotators draw annotations at random with different but
constant frequencies.
See also :func:`~pyanno.measures.helpers.pairwise_matrix`.
**References:**
* Cohen, Jacob (1960). A coefficient of agreement for nominal scales.
Educational and Psychological Measurement, 20, 37--46.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Cohen%27s_kappa>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug("No valid annotations")
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
chance_agreement = chance_agreement_different_frequency(annotations1, annotations2, nclasses)
observed_agreement = observed_agreement_frequency(annotations1, annotations2, nclasses)
return chance_adjusted_agreement(observed_agreement.sum(), chance_agreement.sum())
def scotts_pi(annotations1, annotations2, nclasses=None):
"""Return Scott's pi statistic for two annotators.
Assumes that the annotators draw random annotations with the same
frequency as the combined observed annotations.
See also :func:`~pyanno.measures.helpers.pairwise_matrix`.
**References:**
* Scott, W. (1955). "Reliability of content analysis: The case of nominal
scale coding." Public Opinion Quarterly, 19(3), 321-325.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Scott%27s_Pi>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug("No valid annotations")
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
chance_agreement = chance_agreement_same_frequency(annotations1, annotations2, nclasses)
observed_agreement = observed_agreement_frequency(annotations1, annotations2, nclasses)
return chance_adjusted_agreement(observed_agreement.sum(), chance_agreement.sum())
def fleiss_kappa(annotations, nclasses=None):
"""Compute Fleiss' kappa for multiple annotators.
**References:**
* Fleiss, J. L. (1971). "Measuring nominal scale agreement among many
raters.". Psychological Bulletin, Vol 76(5), 378-382
* `Wikipedia entry <http://en.wikipedia.org/wiki/Fleiss%27_kappa>`_
Arguments
---------
annotations : ndarray, shape = (n_items, n_annotators)
Array of annotations for multiple annotators. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations):
logger.debug("No valid annotations")
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations)
# transform raw annotations into the number of annotations per class
# for each item
nitems = annotations.shape[0]
nannotations = np.zeros((nitems, nclasses))
for k in range(nclasses):
nannotations[:, k] = (annotations == k).sum(1)
return _fleiss_kappa_nannotations(nannotations)
def fleiss_kappa(annotations, nclasses=None):
"""Compute Fleiss' kappa for multiple annotators.
**References:**
* Fleiss, J. L. (1971). "Measuring nominal scale agreement among many
raters.". Psychological Bulletin, Vol 76(5), 378-382
* `Wikipedia entry <http://en.wikipedia.org/wiki/Fleiss%27_kappa>`_
Arguments
---------
annotations : ndarray, shape = (n_items, n_annotators)
Array of annotations for multiple annotators. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations):
logger.debug('No valid annotations')
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations)
# transform raw annotations into the number of annotations per class
# for each item
nitems = annotations.shape[0]
nannotations = np.zeros((nitems, nclasses))
for k in range(nclasses):
nannotations[:,k] = (annotations==k).sum(1)
return _fleiss_kappa_nannotations(nannotations)
def krippendorffs_alpha(annotations, metric_func=diagonal_distance, nclasses=None):
"""Compute Krippendorff's alpha for multiple annotators.
**References:**
* Klaus Krippendorff (2004). "Content Analysis, an Introduction to Its
Methodology", 2nd Edition. Thousand Oaks, CA: Sage Publications.
In particular, Chapter 11, pages 219--250.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Krippendorff%27s_Alpha>`_
See also:
:func:`~pyanno.measures.distances.diagonal_distance`,
:func:`~pyanno.measures.distances.binary_distance`,
Arguments
---------
annotations : ndarray, shape = (n_items, n_annotators)
Array of annotations for multiple annotators. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
weights_func : function(m_i, m_j)
Weights function that receives two matrices of indices
i, j and returns the matrix of weights between them.
Default is :func:`~pyanno.measures.distances.diagonal_distance`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations):
logger.debug("No valid annotations")
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations)
coincidences = coincidence_matrix(annotations, nclasses)
nc = coincidences.sum(1)
n = coincidences.sum()
# ---- coincidences expected by chance
chance_coincidences = np.empty((nclasses, nclasses), dtype=float)
for c in range(nclasses):
for k in range(nclasses):
if c == k:
chance_coincidences[c, k] = nc[c] * (nc[k] - 1.0) / (n - 1.0)
else:
chance_coincidences[c, k] = nc[c] * nc[k] / (n - 1.0)
# build weights matrix from weights function
weights = np.fromfunction(metric_func, shape=(nclasses, nclasses), dtype=float) ** 2.0
alpha = 1.0 - ((weights * coincidences).sum() / (weights * chance_coincidences).sum())
return alpha
def cohens_weighted_kappa(annotations1, annotations2, weights_func=diagonal_distance, nclasses=None):
"""Compute Cohen's weighted kappa for two annotators.
Assumes that the annotators draw annotations at random with different but
constant frequencies. Disagreements are weighted by a weights
w_ij representing the "seriousness" of disagreement. For ordered codes,
it is often set to the distance from the diagonal, i.e. `w_ij = |i-j|`.
When w_ij is 0.0 on the diagonal and 1.0 elsewhere,
Cohen's weighted kappa is equivalent to Cohen's kappa.
See also:
:func:`~pyanno.measures.distances.diagonal_distance`,
:func:`~pyanno.measures.distances.binary_distance`,
:func:`~pyanno.measures.agreement.cohens_kappa`,
:func:`~pyanno.measures.helpers.pairwise_matrix`
**References:**
* Cohen, J. (1968). "Weighed kappa: Nominal scale agreement with provision
for scaled disagreement or partial credit". Psychological Bulletin
70 (4): 213-220.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Cohen%27s_kappa>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
weights_func : function(m_i, m_j)
Weights function that receives two matrices of indices
i, j and returns the matrix of weights between them.
Default is :func:`~pyanno.measures.distances.diagonal_distance`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug("No valid annotations")
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
# observed probability of each combination of annotations
observed_freq = confusion_matrix(annotations1, annotations2, nclasses)
observed_freq_sum = observed_freq.sum()
if observed_freq_sum == 0:
return np.nan
observed_freq /= observed_freq_sum
# expected probability of each combination of annotations if annotators
# draw annotations at random with different but constant frequencies
freq1 = labels_frequency(annotations1, nclasses)
freq2 = labels_frequency(annotations2, nclasses)
chance_freq = np.outer(freq1, freq2)
# build weights matrix from weights function
weights = np.fromfunction(weights_func, shape=(nclasses, nclasses), dtype=float)
kappa = 1.0 - (weights * observed_freq).sum() / (weights * chance_freq).sum()
return kappa
def krippendorffs_alpha(annotations, metric_func=diagonal_distance,
nclasses=None):
"""Compute Krippendorff's alpha for multiple annotators.
**References:**
* Klaus Krippendorff (2004). "Content Analysis, an Introduction to Its
Methodology", 2nd Edition. Thousand Oaks, CA: Sage Publications.
In particular, Chapter 11, pages 219--250.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Krippendorff%27s_Alpha>`_
See also:
:func:`~pyanno.measures.distances.diagonal_distance`,
:func:`~pyanno.measures.distances.binary_distance`,
Arguments
---------
annotations : ndarray, shape = (n_items, n_annotators)
Array of annotations for multiple annotators. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
weights_func : function(m_i, m_j)
Weights function that receives two matrices of indices
i, j and returns the matrix of weights between them.
Default is :func:`~pyanno.measures.distances.diagonal_distance`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations):
logger.debug('No valid annotations')
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations)
coincidences = coincidence_matrix(annotations, nclasses)
nc = coincidences.sum(1)
n = coincidences.sum()
# ---- coincidences expected by chance
chance_coincidences = np.empty((nclasses, nclasses), dtype=float)
for c in range(nclasses):
for k in range(nclasses):
if c == k:
chance_coincidences[c,k] = nc[c]*(nc[k]-1.) / (n-1.)
else:
chance_coincidences[c,k] = nc[c]*nc[k] / (n-1.)
# build weights matrix from weights function
weights = np.fromfunction(metric_func, shape=(nclasses, nclasses),
dtype=float) ** 2.
alpha = 1. - ((weights*coincidences).sum()
/ (weights*chance_coincidences).sum())
return alpha
def cohens_weighted_kappa(annotations1, annotations2,
weights_func = diagonal_distance,
nclasses=None):
"""Compute Cohen's weighted kappa for two annotators.
Assumes that the annotators draw annotations at random with different but
constant frequencies. Disagreements are weighted by a weights
w_ij representing the "seriousness" of disagreement. For ordered codes,
it is often set to the distance from the diagonal, i.e. `w_ij = |i-j|`.
When w_ij is 0.0 on the diagonal and 1.0 elsewhere,
Cohen's weighted kappa is equivalent to Cohen's kappa.
See also:
:func:`~pyanno.measures.distances.diagonal_distance`,
:func:`~pyanno.measures.distances.binary_distance`,
:func:`~pyanno.measures.agreement.cohens_kappa`,
:func:`~pyanno.measures.helpers.pairwise_matrix`
**References:**
* Cohen, J. (1968). "Weighed kappa: Nominal scale agreement with provision
for scaled disagreement or partial credit". Psychological Bulletin
70 (4): 213-220.
* `Wikipedia entry <http://en.wikipedia.org/wiki/Cohen%27s_kappa>`_
Arguments
---------
annotations1 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
annotations2 : ndarray, shape = (n_items, )
Array of annotations for a single annotator. Missing values should be
indicated by :attr:`pyanno.util.MISSING_VALUE`
weights_func : function(m_i, m_j)
Weights function that receives two matrices of indices
i, j and returns the matrix of weights between them.
Default is :func:`~pyanno.measures.distances.diagonal_distance`
nclasses : int
Number of annotation classes. If None, `nclasses` is inferred from the
values in the annotations
Returns
-------
stat : float
The value of the statistics
"""
if all_invalid(annotations1, annotations2):
logger.debug('No valid annotations')
return np.nan
if nclasses is None:
nclasses = compute_nclasses(annotations1, annotations2)
# observed probability of each combination of annotations
observed_freq = confusion_matrix(annotations1, annotations2, nclasses)
observed_freq_sum = observed_freq.sum()
if observed_freq_sum == 0:
return np.nan
observed_freq /= observed_freq_sum
# expected probability of each combination of annotations if annotators
# draw annotations at random with different but constant frequencies
freq1 = labels_frequency(annotations1, nclasses)
freq2 = labels_frequency(annotations2, nclasses)
chance_freq = np.outer(freq1, freq2)
# build weights matrix from weights function
weights = np.fromfunction(weights_func, shape=(nclasses, nclasses),
dtype=float)
kappa = 1. - (weights*observed_freq).sum() / (weights*chance_freq).sum()
return kappa