"""
Second-level fMRI model: two-sample test, unpaired and paired
=============================================================

Full step-by-step example of fitting a :term:`GLM`
to perform a second level analysis
in experimental data and visualizing the results

More specifically:

1. A sample of n=16 visual activity fMRIs are downloaded.

2. An unpaired, two-sample t-test is applied to the brain maps in order to
see the effect of the contrast difference across subjects.

3. A paired, two-sample t-test is applied to the brain maps in order to see
the effect of the contrast difference across subjects,
considering subject intercepts

The contrast is between responses to retinotopically distinct
vertical versus horizontal checkerboards. At the individual level,
these stimuli are sometimes used to map the borders of primary visual areas.
At the group level, such a mapping is not possible. Yet, we may
observe some significant effects in these areas.

"""

# %%
import pandas as pd

from nilearn.datasets import fetch_localizer_contrasts
from nilearn.plotting import plot_design_matrix, plot_glass_brain, show

# %%
# Fetch dataset
# -------------
# We download a list of left vs right button press contrasts from a
# localizer dataset.
n_subjects = 16
sample_vertical = fetch_localizer_contrasts(
    ["vertical checkerboard"],
    n_subjects,
)
sample_horizontal = fetch_localizer_contrasts(
    ["horizontal checkerboard"],
    n_subjects,
)

# Implicitly, there is a one-to-one correspondence between the two samples:
# the first image of both samples comes from subject S1,
# the second from subject S2 etc.

# %%
# Estimate second level models
# ----------------------------
# We define the input maps and the design matrix for the second level model
# and fit it.
second_level_input = sample_vertical["cmaps"] + sample_horizontal["cmaps"]

# %%
# Next, we model the effect of conditions (sample 1 vs sample 2).
import numpy as np

condition_effect = np.hstack(([1] * n_subjects, [0] * n_subjects))

# %%
# The design matrix for the unpaired test needs to add an intercept,
# For the paired test, we include an intercept for each subject.
subject_effect = np.vstack((np.eye(n_subjects), np.eye(n_subjects)))
subjects = [f"S{i:02d}" for i in range(1, n_subjects + 1)]

# %%
# We then assemble those into design matrices
unpaired_design_matrix = pd.DataFrame(
    {
        "vertical vs horizontal": condition_effect,
        "intercept": 1,
    }
)

paired_design_matrix = pd.DataFrame(
    np.hstack((condition_effect[:, np.newaxis], subject_effect)),
    columns=["vertical vs horizontal", *subjects],
)

# %%
# and plot the designs.
import matplotlib.pyplot as plt

_, (ax_unpaired, ax_paired) = plt.subplots(
    1,
    2,
    gridspec_kw={"width_ratios": [1, 17]},
    constrained_layout=True,
)


plot_design_matrix(unpaired_design_matrix, rescale=False, axes=ax_unpaired)
plot_design_matrix(paired_design_matrix, rescale=False, axes=ax_paired)
ax_unpaired.set_title("unpaired design", fontsize=12)
ax_paired.set_title("paired design", fontsize=12)

show()

# %%
# We specify the analysis models and fit them.
from nilearn.glm.second_level import SecondLevelModel

second_level_model_unpaired = SecondLevelModel(n_jobs=2, verbose=1).fit(
    second_level_input, design_matrix=unpaired_design_matrix
)

second_level_model_paired = SecondLevelModel(n_jobs=2, verbose=1).fit(
    second_level_input, design_matrix=paired_design_matrix
)

# %%
# Estimating the :term:`contrast` is simple. To do so, we provide the column
# name of the design matrix. The argument 'output_type' is set to return all
# available outputs so that we can compare differences in the effect size,
# variance, and z-score.
stat_maps_unpaired = second_level_model_unpaired.compute_contrast(
    "vertical vs horizontal", output_type="all"
)

stat_maps_paired = second_level_model_paired.compute_contrast(
    "vertical vs horizontal", output_type="all"
)

# %%
# Plot the results
# ----------------
# The two :term:`'effect_size'<Parameter Estimate>` images are essentially
# identical.
(
    stat_maps_unpaired["effect_size"].get_fdata()
    - stat_maps_paired["effect_size"].get_fdata()
).max()

# %%
# But the variance in the unpaired image is larger.
plot_glass_brain(
    stat_maps_unpaired["effect_variance"],
    vmin=0,
    vmax=6,
    cmap="inferno",
    title="vertical vs horizontal effect variance, unpaired",
)

plot_glass_brain(
    stat_maps_paired["effect_variance"],
    vmin=0,
    vmax=6,
    cmap="inferno",
    title="vertical vs horizontal effect variance, paired",
)

show()

# %%
# Together, this makes the z_scores from the paired test larger.
# We threshold the second level :term:`contrast` and plot it.
threshold = 3.1  # corresponds to  p < .001, uncorrected
plot_glass_brain(
    stat_maps_unpaired["z_score"],
    threshold=threshold,
    plot_abs=False,
    vmax=5.8,
    title="vertical vs horizontal (unc p<0.001), unpaired",
)

plot_glass_brain(
    stat_maps_paired["z_score"],
    threshold=threshold,
    plot_abs=False,
    vmax=5.8,
    title="vertical vs horizontal (unc p<0.001), paired",
)

show()

# %%
# Unsurprisingly, we see activity in the primary visual cortex, both positive
# and negative.