def test_compute_boot_esci(self):
"""Test function compute_bootci
Compare with Matlab bootci function
"""
# This is the `lawdata` dataset in Matlab
# >>> load lawdata
# >>> x_m = gpa;
# >>> y_m = lsat;
x_m = [3.39, 3.3, 2.81, 3.03, 3.44, 3.07, 3.0, 3.43, 3.36, 3.13,
3.12, 2.74, 2.76, 2.88, 2.96]
y_m = [576, 635, 558, 578, 666, 580, 555, 661, 651, 605, 653, 575,
545, 572, 594]
# 1. bootci around a pearson correlation coefficient
# Matlab: bootci(n_boot, {@corr, x_m, y_m}, 'type', 'norm');
ci = compute_bootci(x_m, y_m, method='norm', seed=123)
assert ci[0] == 0.52 and ci[1] == 1.05
ci = compute_bootci(x_m, y_m, method='per', seed=123)
assert ci[0] == 0.45 and ci[1] == 0.96
ci = compute_bootci(x_m, y_m, method='cper', seed=123)
assert ci[0] == 0.39 and ci[1] == 0.95
# 2. Univariate function: mean
ci_n = compute_bootci(x_m, func='mean', method='norm', seed=42)
ci_p = compute_bootci(x_m, func='mean', method='per', seed=42)
ci_c = compute_bootci(x_m, func='mean', method='cper', seed=42)
assert ci_n[0] == 2.98 and ci_n[1] == 3.21
assert ci_p[0] == 2.98 and ci_p[1] == 3.21
assert ci_c[0] == 2.98 and round(ci_c[1], 1) == 3.2
# 3. Univariate custom function: skewness
from scipy.stats import skew
n_boot = 10000
ci_n = compute_bootci(x_m, func=skew, method='norm', n_boot=n_boot,
decimals=1, seed=42)
ci_p = compute_bootci(x_m, func=skew, method='per', n_boot=n_boot,
decimals=1, seed=42)
ci_c = compute_bootci(x_m, func=skew, method='cper', n_boot=n_boot,
decimals=1, seed=42)
assert ci_n[0] == -0.7 and ci_n[1] == 0.8
assert ci_p[0] == -0.7 and ci_p[1] == 0.8
assert ci_c[0] == -0.7 and ci_c[1] == 0.8
# 4. Bivariate custom function: paired T-test
from scipy.stats import ttest_rel
ci_n = compute_bootci(x_m, y_m, func=lambda x, y: ttest_rel(x, y)[0],
method='norm', n_boot=n_boot, decimals=0,
seed=42)
ci_p = compute_bootci(x_m, y_m, func=lambda x, y: ttest_rel(x, y)[0],
method='per', n_boot=n_boot, decimals=0,
seed=42)
ci_c = compute_bootci(x_m, y_m, func=lambda x, y: ttest_rel(x, y)[0],
method='cper', n_boot=n_boot, decimals=0,
seed=42)
assert ci_n[0] == -69 and ci_n[1] == -35
assert ci_p[0] == -79 and ci_p[1] == -48
assert ci_c[0] == -68 and ci_c[1] == -47
# 5. Test all combinations
from itertools import product
methods = ['norm', 'per', 'cper']
funcs = ['spearman', 'pearson', 'cohen', 'hedges']
paired = [True, False]
pr = list(product(methods, funcs, paired))
for m, f, p in pr:
compute_bootci(x, y, func=f, method=m, seed=123, n_boot=100)
# Now the univariate function
funcs = ['mean', 'std', 'var']
for m, f in list(product(methods, funcs)):
compute_bootci(x, func=f, method=m, seed=123, n_boot=100)
with pytest.raises(ValueError):
compute_bootci(x, y, func='wrong')
# Using a custom function
compute_bootci(x, y,
func=lambda x, y: np.sum(np.exp(x) / np.exp(y)),
n_boot=10000, decimals=4, confidence=.68, seed=None)
# Get the bootstrapped distribution
_, bdist = compute_bootci(x, y, return_dist=True, n_boot=1500)
assert bdist.size == 1500
def plot_skipped_corr(x, y, xlabel=None, ylabel=None, n_boot=2000, seed=None):
"""Plot the bootstrapped 95% confidence intervals and distribution
of a robust Skipped correlation.
Parameters
----------
x, y : 1D-arrays or list
Samples
xlabel, ylabel : str
Axes labels
n_boot : int
Number of bootstrap iterations for the computation of the
confidence intervals
seed : int
Random seed generator for the bootstrap confidence intervals.
Returns
--------
fig : matplotlib Figure instance
Matplotlib Figure. To get the individual axes, use fig.axes.
Notes
-----
This function is inspired by the Matlab Robust Correlation Toolbox (Pernet,
Wilcox and Rousselet, 2012). It uses the skipped correlation to determine
the outliers. Note that this function requires the scikit-learn package.
References
----------
.. [1] Pernet, C.R., Wilcox, R., Rousselet, G.A., 2012. Robust correlation
analyses: false positive and power validation using a new open
source matlab toolbox. Front. Psychol. 3, 606.
https://doi.org/10.3389/fpsyg.2012.00606
Examples
--------
Plot a robust Skipped correlation with bootstrapped confidence intervals
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> mean, cov, n = [170, 70], [[20, 10], [10, 20]], 30
>>> x, y = np.random.multivariate_normal(mean, cov, n).T
>>> # Introduce two outliers
>>> x[10], y[10] = 160, 100
>>> x[8], y[8] = 165, 90
>>> fig = pg.plot_skipped_corr(x, y, xlabel='Height', ylabel='Weight')
"""
from pingouin.correlation import skipped
from scipy.stats import pearsonr
from pingouin.effsize import compute_bootci
# Safety check
x = np.asarray(x)
y = np.asarray(y)
assert x.size == y.size
# Skipped Spearman / Pearson correlations
r, p, outliers = skipped(x, y, method='spearman')
r_pearson, _ = pearsonr(x[~outliers], y[~outliers])
# Bootstrapped skipped Spearman distribution & CI
spearman_ci, spearman_dist = compute_bootci(x=x[~outliers],
y=y[~outliers],
func='spearman',
n_boot=n_boot,
return_dist=True,
seed=seed)
# Bootstrapped skipped Pearson distribution & CI
pearson_ci, pearson_dist = compute_bootci(x=x[~outliers],
y=y[~outliers],
func='pearson',
n_boot=n_boot,
return_dist=True,
seed=seed)
# START THE PLOT
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(12, 4.2))
# plt.subplots_adjust(wspace=0.3)
sns.despine()
# Scatter plot and regression lines
sns.regplot(x[~outliers], y[~outliers], ax=ax1, color='darkcyan')
ax1.scatter(x[outliers], y[outliers], color='indianred', label='outliers')
ax1.scatter(x[~outliers], y[~outliers], color='seagreen', label='good')
# Labels
xlabel = 'x' if xlabel is None else xlabel
ylabel = 'y' if ylabel is None else ylabel
ax1.set_xlabel(xlabel)
ax1.set_ylabel(ylabel)
ax1.set_title('Outliers (n={})'.format(sum(outliers)), y=1.05)
# Spearman distribution
sns.distplot(spearman_dist, kde=True, ax=ax2, color='darkcyan')
for i in spearman_ci:
ax2.axvline(x=i, color='coral', lw=2)
ax2.axvline(x=0, color='k', ls='--', lw=1.5)
ax2.set_ylabel('Density of bootstrap samples')
ax2.set_xlabel('Correlation coefficient')
ax2.set_title('Skipped Spearman r = {}\n95% CI = [{}, {}]'.format(
r.round(2), spearman_ci[0], spearman_ci[1]),
y=1.05)
# Pearson dististribution
sns.distplot(pearson_dist, kde=True, ax=ax3, color='steelblue')
for i in pearson_ci:
ax3.axvline(x=i, color='coral', lw=2)
ax3.axvline(x=0, color='k', ls='--', lw=1.5)
ax3.set_xlabel('Correlation coefficient')
ax3.set_title('Skipped Pearson r = {}\n95% CI = [{}, {}]'.format(
r_pearson.round(2), pearson_ci[0], pearson_ci[1]),
y=1.05)
# Optimize layout
plt.tight_layout()
return fig
def test_compute_boot_esci(self):
"""Test function compute_bootci"""
# Compare with Matlab
x_m = [
3.39, 3.3, 2.81, 3.03, 3.44, 3.07, 3.0, 3.43, 3.36, 3.13, 3.12,
2.74, 2.76, 2.88, 2.96
]
y_m = [
576, 635, 558, 578, 666, 580, 555, 661, 651, 605, 653, 575, 545,
572, 594
]
ci = compute_bootci(x_m, y_m, method='norm', seed=123, decimals=2)
assert ci[0] == 0.52 and ci[1] == 1.05
ci = compute_bootci(x_m, y_m, method='per', seed=123, decimals=2)
assert ci[0] == 0.45 and ci[1] == 0.96
ci = compute_bootci(x_m, y_m, method='cper', seed=123, decimals=2)
assert ci[0] == 0.39 and ci[1] == 0.95
# Test all combinations
from itertools import product
methods = ['norm', 'per', 'cper']
funcs = ['spearman', 'pearson', 'cohen', 'hedges']
paired = [True, False]
pr = list(product(methods, funcs, paired))
for m, f, p in pr:
compute_bootci(x, y, func=f, method=m, seed=123, n_boot=100)
# Now the univariate function
funcs = ['mean', 'std', 'var']
for m, f in list(product(methods, funcs)):
compute_bootci(x, func=f, method=m, seed=123, n_boot=100)
with pytest.raises(ValueError):
compute_bootci(x, y, func='wrong')
# Using a custom function
compute_bootci(x,
y,
func=lambda x, y: np.sum(np.exp(x) / np.exp(y)),
n_boot=10000,
decimals=4,
confidence=.68,
seed=None)
# Get the bootstrapped distribution
_, bdist = compute_bootci(x, y, return_dist=True, n_boot=1500)
assert bdist.size == 1500