cbmr.py

"""Coordinate Based Meta Regression Methods."""

import logging
import re
from functools import wraps

import nibabel as nib
import numpy as np
import pandas as pd
import scipy

try:
    import torch
except ImportError as e:
    raise ImportError(
        "Torch is required to use `CBMR` classes. Install with `pip install 'nimare[cbmr]'`."
    ) from e

from nimare import _version
from nimare.diagnostics import FocusFilter
from nimare.estimator import Estimator
from nimare.meta import models
from nimare.utils import b_spline_bases, dummy_encoding_moderators, get_masker, mm2vox

LGR = logging.getLogger(__name__)
__version__ = _version.get_versions()["version"]


class CBMREstimator(Estimator):
    """Coordinate-based meta-regression with a spatial model.

    .. versionadded:: 0.1.0

    Parameters
    ----------
    group_categories : :obj:`~str` or obj:`~list` or obj:`~None`, optional
        CBMR allows dataset to be categorized into mutiple groups, according to group categories.
        Default is one-group CBMR.
    moderators : :obj:`~str` or obj:`~list` or obj:`~None`, optional
        CBMR can accommodate study-level moderators (e.g. sample size, year of publication).
        Default is CBMR without study-level moderators.
    model : : :obj:`~nimare.meta.models.GeneralLinearModel`, optional
        Stochastic models in CBMR. The available options are

        ======================= ==================================================================
        Poisson (default)       This is the most efficient and widely used method, but slightly
                                less accurate, because Poisson model is an approximation for
                                low-rate Binomial data, but cannot account over-dispersion in
                                foci counts and may underestimate the standard error.

        NegativeBinomial        This method might be slower and less stable, but slightly more
                                accurate. Negative Binomial (NB) model asserts foci counts follow
                                a NB distribution, and allows for anticipated excess variance
                                relative to Poisson (there's an group-wise overdispersion parameter
                                shared by all studies and all voxels to index excess variance).

        ClusteredNegativeBinomial This method is also an efficient but less accurate approach.
                                Clustered NB model is "random effect" Poisson model, which asserts
                                that the random effects are latent characteristics of each study,
                                and represent a shared effect over the entire brain for a given
                                study.
        ======================= =================================================================
    penalty: :obj:`~bool`, optional
    Currently, the only available option is Firth-type penalty, which penalizes likelihood function
    by Jeffrey's invariant prior and guarantees convergent estimates.
    spline_spacing: :obj:`~int`, optional
    Spatial structure of foci counts is parameterized by coefficient of cubic B-spline bases
    in CBMR. Spatial smoothness in CBMR is determined by spline spacing, which is shared across
    x,y,z dimension.
    Default is 10 (20mm with 2mm brain atlas template).
    n_iters: :obj:`int`, optional
        Number of iterations limit in optimisation of log-likelihood function.
        Default is 10000.
    lr: :obj:`float`, optional
        Learning rate in optimization of log-likelihood function.
        Default is 1e-2 for Poisson and clustered NB model, and 1e-3 for NB model.
    lr_decay: :obj:`float`, optional
        Multiplicative factor of learning rate decay.
        Default is 0.999.
    tol: :obj:`float`, optional
        Stopping criteria w.r.t difference of log-likelihood function in two consecutive
        iterations.
        Default is 1e-2
    device: :obj:`string`, optional
        Device type ('cpu' or 'cuda') represents the device on which operations will be allocated
        Default is 'cpu'
    **kwargs
        Keyword arguments. Arguments for the Estimator can be assigned here,
        Another optional argument is ``mask``.

    Attributes
    ----------
    masker : :class:`~nilearn.input_data.NiftiMasker` or similar
        Masker object.
    inputs_ : :obj:`dict`
        Inputs to the Estimator. For CBMR estimators, there is only multiple keys:
        coordinates,
        mask_img (Niftiimage of brain mask),
        id (study id),
        studies_by_groups (study id categorized by groups),
        all_group_moderators (study-level moderators categorized by groups if exist),
        coef_spline_bases (spatial matrix of coefficient of cubic B-spline
        bases in x,y,z dimension),
        foci_per_voxel (voxelwise sum of foci count across studies, categorized by groups),
        foci_per_study (study-wise sum of foci count across space, categorized by groups).

    Notes
    -----
    Available correction methods: :meth:`~nimare.meta.cbmr.CBMRInference`.
    """

    _required_inputs = {"coordinates": ("coordinates", None)}

    def __init__(
        self,
        group_categories=None,
        moderators=None,
        mask=None,
        spline_spacing=10,
        model=models.PoissonEstimator,
        penalty=False,
        n_iter=2000,
        lr=1,
        lr_decay=0.999,
        tol=1e-9,
        device="cpu",
        **kwargs,
    ):
        super().__init__(**kwargs)
        if mask is not None:
            mask = get_masker(mask)
        self.masker = mask

        self.group_categories = group_categories
        self.moderators = moderators

        self.spline_spacing = spline_spacing
        self.model = model(
            penalty=penalty, lr=lr, lr_decay=lr_decay, n_iter=n_iter, tol=tol, device=device
        )
        self.penalty = penalty
        self.n_iter = n_iter
        self.lr = lr
        self.lr_decay = lr_decay
        self.tol = tol
        self.device = device
        if self.device == "cuda" and not torch.cuda.is_available():
            LGR.debug("cuda not found, use device cpu")
            self.device = "cpu"

        # Initialize optimisation parameters
        self.iter = 0

    def _generate_description(self):
        """Generate a description of the Estimator instance.

        Returns
        -------
        description : :obj:`str`
            Description of the Estimator instance.
        """
        description = """CBMR is a meta-regression framework that can explicitly model
                    group-wise spatial intensity function, and consider the effect of
                    study-level moderators. It consists of two components: (1) a spatial
                    model that makes use of a spline parameterization to induce a smooth
                    response; (2) a generalized linear model (Poisson, Negative Binomial
                    (NB), Clustered NB) to model group-wise spatial intensity function).
                    CBMR is fitted via maximizing the log-likelihood function with L-BFGS
                    algorithm."""
        if self.moderators:
            moderators_str = f"""and accommodate the following study-level moderators:
                            {', '.join(self.moderators)}"""
        else:
            moderators_str = ""
        if self.model.penalty:
            penalty_str = " Firth-type penalty is applied to ensure convergence."
        else:
            penalty_str = ""

        if type(self.model).__name__ == "PoissonEstimator":
            model_str = (
                " Here, Poisson model \\citep{eisenberg1966general} is the most basic CBMR model. "
                "It's based on the assumption that foci arise from a realisation of a (continues) "
                "inhomogeneous Poisson process, so that the (discrete) voxel-wise foci counts will"
                " be independently distributed as Poisson random variables, with rate equal to the"
                " integral of (true, unobserved, continous) intensity function over each voxels"
            )
        elif type(self.model).__name__ == "NegativeBinomialEstimator":
            model_str = (
                " Negative Binomial (NB) model \\citep{barndorff1969negative} is a generalized "
                "Poisson model with over-dispersion. "
                "It's a more flexible model, but more difficult to estimate. In practice, foci"
                "counts often display over-dispersion (the variance of response variable"
                "substantially exceeeds the mean), which is not captured by Poisson model."
            )
        elif type(self.model).__name__ == "ClusteredNegativeBinomialEstimator":
            model_str = (
                " Clustered NB model \\citep{geoffroy2001poisson} can also accommodate "
                "over-dispersion in foci counts. "
                "In NB model, the latent random variable introduces indepdentent variation"
                "at each voxel. While in Clustered NB model, we assert the random effects are not "
                "independent voxelwise effects, but rather latent characteristics of each study, "
                "and represent a shared effect over the entire brain for a given study."
            )

        model_description = (
            f"CBMR is a meta-regression framework that was performed with NiMARE {__version__}. "
            f"{type(self.model).__name__} model was used to model group-wise spatial intensity "
            f"functions {moderators_str}." + model_str
        )

        optimization_description = (
            "CBMR is fitted via maximizing the log-likelihood function with L-BFGS algorithm, with"
            f" learning rate {self.lr}, learning rate decay {self.lr_decay} and "
            + "tolerance {self.tol}."
            + penalty_str
            + f" The optimization is run on {self.device}."
            f" The input dataset included {self.inputs_['coordinates'].shape[0]} foci from "
            f"{len(self.inputs_['id'])} experiments."
        )

        description = model_description + "\n" + optimization_description
        return description

    def _preprocess_input(self, dataset):
        """Mask required input images using either the Dataset's mask or the Estimator's.

        Also, categorize study id, voxelwise sum of foci counts across studies, study-wise sum of
        foci counts across space into multiple groups. And summarize study-level moderators into
        multiple groups (if exist).

        Parameters
        ----------
        dataset : :obj:`~nimare.dataset.Dataset`
            In this method, the Dataset is used to (1) select the appropriate mask image,
            (2) categorize studies into multiple groups according to group categories in
            annotations,
            (3) summarize group-wise study id, moderators (if exist), foci per voxel, foci
            per study,
            (4) extract sample size metadata and use it as one of study-level moderators.

        Attributes
        ----------
        inputs_ : :obj:`dict`
            Specifically, (1) a “mask_img” key will be added (Niftiimage of brain mask),
            (2) an 'id' key will be added (id of all studies in the dataset),
            (3) a 'coef_spline_bases' key will be added (spatial matrix of coefficient of cubic
            B-spline bases in x,y,z dimension),
            (4) an 'studies_by_group' key will be added (study id categorized by groups),
            (5) an 'moderators_by_group' key will be added (study-level moderators categorized
            by groups) if study-level moderators are considered,
            (6) an 'foci_per_voxel' key will be added (voxelwise sum of foci count across
            studies, categorized by groups),
            (7) an 'foci_per_study' key will be added (study-wise sum of foci count across
            space, categorized by groups).
        """
        masker = self.masker or dataset.masker

        mask_img = masker.mask_img or masker.labels_img
        if isinstance(mask_img, str):
            mask_img = nib.load(mask_img)
        self.inputs_["mask_img"] = mask_img

        # generate spatial matrix of coefficient of cubic B-spline bases in x,y,z dimension
        coef_spline_bases = b_spline_bases(
            masker_voxels=mask_img._dataobj, spacing=self.spline_spacing
        )
        self.inputs_["coef_spline_bases"] = coef_spline_bases

        for name, (type_, _) in self._required_inputs.items():
            if type_ == "coordinates":
                # remove dataset coordinates outside of mask
                focus_filter = FocusFilter(mask=masker)
                dataset = focus_filter.transform(dataset)
                valid_dset_annotations = dataset.annotations[
                    dataset.annotations["id"].isin(self.inputs_["id"])
                ]
                studies_by_group = dict()
                if self.group_categories is None:
                    studies_by_group["Default"] = (
                        valid_dset_annotations["study_id"].unique().tolist()
                    )
                    unique_groups = ["Default"]
                elif isinstance(self.group_categories, str):
                    if self.group_categories not in valid_dset_annotations.columns:
                        raise ValueError(
                            f"""Category_names: {self.group_categories} does not exist
                            in the dataset"""
                        )
                    else:
                        unique_groups = list(
                            valid_dset_annotations[self.group_categories].unique()
                        )
                        for group in unique_groups:
                            group_study_id_bool = (
                                valid_dset_annotations[self.group_categories] == group
                            )
                            group_study_id = valid_dset_annotations.loc[group_study_id_bool][
                                "study_id"
                            ]
                            studies_by_group[group.capitalize()] = group_study_id.unique().tolist()
                elif isinstance(self.group_categories, list):
                    missing_categories = set(self.group_categories) - set(
                        dataset.annotations.columns
                    )
                    if missing_categories:
                        raise ValueError(
                            f"""Category_names: {missing_categories} do/does not exist in
                            the dataset."""
                        )
                    unique_groups = (
                        valid_dset_annotations[self.group_categories]
                        .drop_duplicates()
                        .values.tolist()
                    )
                    for group in unique_groups:
                        group_study_id_bool = (
                            valid_dset_annotations[self.group_categories] == group
                        ).all(axis=1)
                        group_study_id = valid_dset_annotations.loc[group_study_id_bool][
                            "study_id"
                        ]
                        camelcase_group = "".join([g.capitalize() for g in group])
                        studies_by_group[camelcase_group] = group_study_id.unique().tolist()
                self.inputs_["studies_by_group"] = studies_by_group
                self.groups = list(self.inputs_["studies_by_group"].keys())
                # collect studywise moderators if specficed
                if self.moderators:
                    valid_dset_annotations, self.moderators = dummy_encoding_moderators(
                        valid_dset_annotations, self.moderators
                    )
                    if isinstance(self.moderators, str):
                        self.moderators = [
                            self.moderators
                        ]  # convert moderators to a single-element list if it's a string
                    moderators_by_group = dict()
                    for group in self.groups:
                        df_group = valid_dset_annotations.loc[
                            valid_dset_annotations["study_id"].isin(studies_by_group[group])
                        ]
                        group_moderators = np.stack(
                            [df_group[moderator_name] for moderator_name in self.moderators],
                            axis=1,
                        )
                        moderators_by_group[group] = group_moderators
                    self.inputs_["moderators_by_group"] = moderators_by_group

                foci_per_voxel, foci_per_study = dict(), dict()
                for group in self.groups:
                    group_study_id = studies_by_group[group]
                    group_coordinates = dataset.coordinates.loc[
                        dataset.coordinates["study_id"].isin(group_study_id)
                    ]
                    # Group-wise foci coordinates
                    # Calculate IJK matrix indices for target mask
                    # Mask space is assumed to be the same as the Dataset's space
                    group_xyz = group_coordinates[["x", "y", "z"]].values
                    group_ijk = mm2vox(group_xyz, mask_img.affine)
                    group_foci_per_voxel = np.zeros(mask_img.shape, dtype=np.int32)
                    for ijk in group_ijk:
                        group_foci_per_voxel[ijk[0], ijk[1], ijk[2]] += 1
                    # will not work with maskers that aren't NiftiMaskers
                    group_foci_per_voxel = nib.Nifti1Image(
                        group_foci_per_voxel, mask_img.affine, mask_img.header
                    )
                    group_foci_per_voxel = masker.transform(group_foci_per_voxel).transpose()
                    # number of foci per voxel/study
                    # n_group_study = len(group_study_id)
                    group_foci_per_study = group_coordinates.groupby(["study_id"]).size()
                    group_foci_per_study = group_foci_per_study.to_numpy()
                    group_foci_per_study = group_foci_per_study.reshape((-1, 1))

                    foci_per_voxel[group] = group_foci_per_voxel
                    foci_per_study[group] = group_foci_per_study

                self.inputs_["foci_per_voxel"] = foci_per_voxel
                self.inputs_["foci_per_study"] = foci_per_study

    def _fit(self, dataset):
        """Perform coordinate-based meta-regression (CBMR) on dataset.

        (1) Estimate group-wise spatial regression coefficients and its standard error via
        inverse of Fisher Information matrix; Similarly, estimate regression coefficient of
        study-level moderators (if exist), as well as its standard error via inverse of
        Fisher Information matrix;
        (2) Estimate standard error of group-wise log intensity, group-wise intensity via delta
        method;
        (3) For NegativeBinomial or ClusteredNegativeBinomial model, estimate regression
        coefficient of overdispersion.s

        Parameters
        ----------
        dataset : :obj:`~nimare.dataset.Dataset`
            Dataset to analyze.
        """
        init_weight_kwargs = {
            "groups": self.groups,
            "moderators": self.moderators,
            "spatial_coef_dim": self.inputs_["coef_spline_bases"].shape[1],
            "moderators_coef_dim": len(self.moderators) if self.moderators else None,
        }
        self.model.init_weights(**init_weight_kwargs)

        moderators_by_group = self.inputs_["moderators_by_group"] if self.moderators else None
        self.model.fit(
            self.inputs_["coef_spline_bases"],
            moderators_by_group,
            self.inputs_["foci_per_voxel"],
            self.inputs_["foci_per_study"],
        )

        maps, tables = self.model.summary()

        return maps, tables, self._generate_description()


class CBMRInference(object):
    """Statistical inference on outcomes of CBMR.

    .. versionadded:: 0.1.0

    (intensity estimation and study-level moderator regressors)

    Parameters
    ----------
    result : :obj:`~nimare.cbmr.CBMREstimator`
        Results of optimized regression coefficients of CBMR, as well as their
        standard error in `tables`. Results of estimated spatial intensity function
        (per study) in `maps`.
    t_con_groups : :obj:`~bool` or obj:`~list` or obj:`~None`, optional
        Contrast matrix for homogeneity test or group comparison on estimated spatial
        intensity function.
        For boolean inputs, no statistical inference will be conducted for spatial intensity
        if `t_con_groups` is False, and spatial homogeneity test for groupwise intensity
        function will be conducted if `t_con_groups` is True.
        For list inputs, generialized linear hypothesis (GLH) testing will be conducted for
        each element independently. We also allow any element of `t_con_groups` in list type,
        which represents GLH is conducted for all contrasts in this element simultaneously.
        Default is homogeneity test on group-wise estimated intensity function.
    t_con_moderators : :obj:`~bool` or obj:`~list` or obj:`~None`, optional
        Contrast matrix for testing the existence of one or more study-level moderator effects.
        For boolean inputs, no statistical inference will be conducted for study-level moderators
        if `t_con_moderatorss` is False, and statistical inference on the effect of each
        study-level moderators will be conducted if `t_con_groups` is True.
        For list inputs, generialized linear hypothesis (GLH) testing will be conducted for
        each element independently. We also allow any element of `t_con_moderatorss` in list type,
        which represents GLH is conducted for all contrasts in this element simultaneously.
        Default is statistical inference on the effect of each study-level moderators
    device: :obj:`string`, optional
        Device type ('cpu' or 'cuda') represents the device on which operations will be allocated.
        Default is 'cpu'.
    """

    def __init__(self, device="cpu"):
        self.device = device
        # device check
        if self.device == "cuda" and not torch.cuda.is_available():
            LGR.debug("cuda not found, use device 'cpu'")
            self.device = "cpu"
        self.result = None
        self.groups = None
        self.moderators = None

    def _check_fit(fn):
        """Check if CBMRInference instance has been fit."""

        @wraps(fn)
        def wrapper(self, *args, **kwargs):
            if self.result is None:
                raise ValueError("CBMRInference instance has not been fit.")
            return fn(self, *args, **kwargs)

        return wrapper

    def fit(self, result):
        """Fit CBMRInference instance.

        Parameters
        ----------
        result : :obj:`~nimare.cbmr.CBMREstimator`
            Results of optimized regression coefficients of CBMR, as well as their
            standard error in `tables`. Results of estimated spatial intensity function
            (per study) in `maps`.
        """
        self.result = result.copy()
        self.estimator = self.result.estimator
        self.groups = self.result.estimator.groups
        self.moderators = self.result.estimator.moderators

        self.create_regular_expressions()

        self.group_reference_dict, self.moderator_reference_dict = dict(), dict()
        for i in range(len(self.groups)):
            self.group_reference_dict[self.groups[i]] = i
        if self.moderators:
            for j in range(len(self.moderators)):
                self.moderator_reference_dict[self.moderators[j]] = j
                LGR.info(f"{self.moderators[j]} = index_{j}")

    @_check_fit
    def display(self):
        """Display Groups and Moderator names and order."""
        # visialize group/moderator names and their indices in contrast array
        LGR.info("Group Reference in contrast array")
        for group, index in self.group_reference_dict.items():
            LGR.info(f"{group} = index_{index}")
        if self.moderators:
            LGR.info("Moderator Reference in contrast array")
            for moderator, index in self.moderator_reference_dict.items():
                LGR.info(f"{moderator} = index_{index}")

    def create_regular_expressions(self):
        """
        Create regular expressions for parsing contrast names.

        creates the following attributes:
        self.groups_regular_expression: regular expression for parsing group names
        self.moderators_regular_expression: regular expression for parsing moderator names

        usage:
        >>> self.groups_regular_expression.match("group1 - group2").groupdict()
        """
        operator = "(\\ ?(?P<operator>[+-]?)\\ ??)"
        for attr in ["groups", "moderators"]:
            groups = getattr(self, attr)
            if groups:
                first_group, second_group = [
                    f"(?P<{order}>{'|'.join([re.escape(g) for g in groups])})"
                    for order in ["first", "second"]
                ]
                reg_expr = re.compile(first_group + "(" + operator + second_group + "?)")
            else:
                reg_expr = None

            setattr(self, "{}_regular_expression".format(attr), reg_expr)

    @_check_fit
    def create_contrast(self, contrast_name, source="groups"):
        """Create contrast matrix for generalized hypothesis testing (GLH).

        (1) if `source` is "group", create contrast matrix for GLH on spatial intensity;
        if `contrast_name` begins with 'homo_test_', followed by a valid group name,
        create a contrast matrix for one-group homogeneity test on spatial intensity;
        if `contrast_name` comes in the form of "group1VSgroup2", with valid group names
        "group1" and "group2", create a contrast matrix for group comparison on estimated
        group spatial intensity;
        (2) if `source` is "moderator", create contrast matrix for GLH on study-level moderators;
        if `contrast_name` begins with 'moderator_', followed by a valid moderator name,
        we create a contrast matrix for testing if the effect of this moderator exists;
        if `contrast_name` comes in the form of "moderator1VSmoderator2", with valid moderator
        names "modeator1" and "moderator2", we create a contrast matrix for testing if the
        effect of these two moderators are different.

        Parameters
        ----------
        contrast_name : :obj:`~string`
            Name of contrast in GLH.
        """
        if isinstance(contrast_name, str):
            contrast_name = [contrast_name]
        contrast_matrix = {}
        if source == "groups":  # contrast matrix for spatial intensity
            for contrast in contrast_name:
                contrast_vector = np.zeros(len(self.groups))
                contrast_match = self.groups_regular_expression.match(contrast)
                # check validity of contrast name
                if contrast_match is None:
                    raise ValueError(f"{contrast} is not a valid contrast.")
                groups_contrast = contrast_match.groupdict()
                # create contrast matrix
                if all(groups_contrast.values()):  # group comparison
                    contrast_vector[self.group_reference_dict[groups_contrast["first"]]] = 1
                    contrast_vector[self.group_reference_dict[groups_contrast["second"]]] = int(
                        contrast_match["operator"] + "1"
                    )
                else:  # homogeneity test
                    contrast_vector[self.group_reference_dict[contrast]] = 1
                contrast_matrix[contrast] = contrast_vector

        elif source == "moderators":  # contrast matrix for moderator effect
            for contrast in contrast_name:
                contrast_vector = np.zeros(len(self.moderators))
                contrast_match = self.moderators_regular_expression.match(contrast)
                if contrast_match is None:
                    raise ValueError(f"{contrast} is not a valid contrast.")
                moderators_contrast = contrast_match.groupdict()
                if all(moderators_contrast.values()):  # moderator comparison
                    _ = list(map(moderators_contrast.get, ["first", "second"]))
                    contrast_vector[
                        self.moderator_reference_dict[moderators_contrast["first"]]
                    ] = 1
                    contrast_vector[
                        self.moderator_reference_dict[moderators_contrast["second"]]
                    ] = int(moderators_contrast["operator"] + "1")
                else:  # moderator effect
                    contrast_vector[self.moderator_reference_dict[contrast]] = 1
                contrast_matrix[contrast] = contrast_vector

        return contrast_matrix

    @_check_fit
    def transform(self, t_con_groups=None, t_con_moderators=None):
        """Conduct generalized linear hypothesis (GLH) testing on CBMR estimates.

        Estimate group-wise spatial regression coefficients and its standard error via inverse
        Fisher Information matrix, estimate standard error of group-wise log intensity,
        group-wise intensity via delta method.  For NB or clustered model, estimate regression
        coefficient of overdispersion. Similarly, estimate regression coefficient of study-level
        moderators (if exist), as well as its standard error via Fisher Information matrix.
        Save these outcomes in `tables`. Also, estimate group-wise spatial intensity (per study)
        and save the results in `maps`.

        Parameters
        ----------
        t_con_groups : :obj:`~list`, optional
            Contrast matrix for GLH on group-wise spatial intensity estimation.
            Default is None (group-wise homogeneity test for all groups).
        t_con_moderators : :obj:`~list`, optional
            Contrast matrix for GLH on moderator effects.
            Default is None (tests if moderator effects exist for all moderators).
        """
        self.t_con_groups = t_con_groups
        self.t_con_moderators = t_con_moderators

        if self.t_con_groups:
            # preprocess and standardize group contrast
            self.t_con_groups, self.t_con_groups_name = self._preprocess_t_con_regressor(
                source="groups"
            )
            # GLH test for group contrast
            self._glh_con_group()
        if self.t_con_moderators:
            # preprocess and standardize moderator contrast
            self.t_con_moderators, self.t_con_moderators_name = self._preprocess_t_con_regressor(
                source="moderators"
            )
            # GLH test for moderator contrast
            self._glh_con_moderator()

        return self.result

    def fit_transform(self, result, t_con_groups=None, t_con_moderators=None):
        """Fit and transform."""
        self.fit(result)
        return self.transform(t_con_groups, t_con_moderators)

    @_check_fit
    def _preprocess_t_con_regressor(self, source):
        """Preprocess contrast vector/matrix for GLH testing.

        Follow the steps below:
        (1) Remove groups not involved in contrast;
        (2) Standardize contrast matrix (row sum to 1);
        (3) Remove duplicate rows in contrast matrix.

        Parameters
        ----------
        source : :obj:`~string`
            Source of contrast matrix, either "groups" or "moderators".

        Returns
        -------
        t_con_regressor : :obj:`~list`
            Preprocessed contrast vector/matrix for inference on
            spatial intensity or study-level moderators.
        t_con_regressor_name : :obj:`~list`
            Name of contrast vector/matrix for spatial intensity
        """
        # regressor can be either groups or moderators
        t_con_regressor = getattr(self, f"t_con_{source}")
        n_regressors = len(getattr(self, f"{source}"))
        # if contrast matrix is a dictionary, convert it to list
        if isinstance(t_con_regressor, dict):
            t_con_regressor_name = list(t_con_regressor.keys())
            t_con_regressor = list(t_con_regressor.values())
        elif isinstance(t_con_regressor, (list, np.ndarray)):
            for i in range(len(t_con_regressor)):
                self.result.metadata[f"GLH_{source}_{i}"] = t_con_regressor[i]
            t_con_regressor_name = None
        # Conduct group-wise spatial homogeneity test by default
        t_con_regressor = (
            [np.eye(n_regressors)]
            if t_con_regressor is None
            else [np.array(con_regressor) for con_regressor in t_con_regressor]
        )
        # make sure contrast matrix/vector is 2D
        t_con_regressor = [
            con_regressor.reshape((1, -1)) if len(con_regressor.shape) == 1 else con_regressor
            for con_regressor in t_con_regressor
        ]
        # raise error if dimension of contrast matrix/vector doesn't match with number of groups
        if np.any([con_regressor.shape[1] != n_regressors for con_regressor in t_con_regressor]):
            wrong_con_regressor_idx = np.where(
                [con_regressor.shape[1] != n_regressors for con_regressor in t_con_regressor]
            )[0].tolist()
            raise ValueError(
                f"""The shape of {str(wrong_con_regressor_idx)}th contrast vector(s) in contrast
                matrix doesn't match with {source}."""
            )
        # remove zero rows in contrast matrix (if exist)
        con_regressor_zero_row = [
            np.where(np.sum(np.abs(con_regressor), axis=1) == 0)[0]
            for con_regressor in t_con_regressor
        ]
        if np.any([len(zero_row) > 0 for zero_row in con_regressor_zero_row]):
            t_con_regressor = [
                np.delete(t_con_regressor[i], con_regressor_zero_row[i], axis=0)
                for i in range(len(t_con_regressor))
            ]
            if np.any([con_regressor.shape[0] == 0 for con_regressor in t_con_regressor]):
                raise ValueError(
                    f"""One or more of contrast vector(s) in {source} contrast matrix are
                    all zeros."""
                )
        # standardization (row sum 1)
        t_con_regressor = [
            con_regressor / np.sum(np.abs(con_regressor), axis=1).reshape((-1, 1))
            for con_regressor in t_con_regressor
        ]
        # remove duplicate rows in contrast matrix (after standardization)
        uniq_con_regressor_idx = np.unique(t_con_regressor, axis=0, return_index=True)[1].tolist()
        t_con_regressor = [t_con_regressor[i] for i in uniq_con_regressor_idx[::-1]]

        return t_con_regressor, t_con_regressor_name

    @_check_fit
    def _glh_con_group(self):
        """Conduct GLH testing for group-wise spatial intensity estimation.

        GLH testing allows flexible hypothesis testings on spatial
        intensity, including group-wise spatial homogeneity test and
        group comparison test.
        """
        X = self.estimator.inputs_["coef_spline_bases"]
        n_brain_voxel, spatial_coef_dim = X.shape
        con_group_count = 0
        for con_group in self.t_con_groups:
            con_group_involved_index = np.where(np.any(con_group != 0, axis=0))[0].tolist()
            con_group_involved = [self.groups[i] for i in con_group_involved_index]
            n_con_group_involved = len(con_group_involved)
            # Simplify contrast matrix by removing irrelevant columns
            simp_con_group = con_group[:, ~np.all(con_group == 0, axis=0)]
            # Covariance of involved group-wise spatial coef (either one or multiple groups)
            moderators_by_group = (
                self.estimator.inputs_["moderators_by_group"] if self.moderators else None
            )
            f_spatial_coef = self.estimator.model.fisher_info_multiple_group_spatial(
                con_group_involved,
                self.estimator.inputs_["coef_spline_bases"],
                moderators_by_group,
                self.estimator.inputs_["foci_per_voxel"],
                self.estimator.inputs_["foci_per_study"],
            )
            cov_spatial_coef = np.linalg.inv(f_spatial_coef)
            # compute numerator: contrast vector * group-wise log spatial intensity
            involved_log_intensity_per_voxel = list()
            for group in con_group_involved:
                group_log_intensity_per_voxel = np.log(
                    self.result.maps["spatialIntensity_group-" + group]
                )
                if np.all(np.count_nonzero(con_group, axis=1) == 1):  # GLH: homogeneity test
                    group_foci_per_voxel = self.estimator.inputs_["foci_per_voxel"][group]
                    group_foci_per_study = self.estimator.inputs_["foci_per_study"][group]
                    n_voxels, n_study = (
                        group_foci_per_voxel.shape[0],
                        group_foci_per_study.shape[0],
                    )
                    group_null_log_spatial_intensity = np.log(
                        np.sum(group_foci_per_voxel) / (n_voxels * n_study)
                    )
                    group_log_intensity_per_voxel -= group_null_log_spatial_intensity
                involved_log_intensity_per_voxel.append(group_log_intensity_per_voxel)
            involved_log_intensity_per_voxel = np.stack(involved_log_intensity_per_voxel, axis=0)
            contrast_log_intensity = np.matmul(simp_con_group, involved_log_intensity_per_voxel)

            # check if a single hypothesis is tested or GLH tests
            # (with multiple contrasts) are conducted
            m, _ = con_group.shape
            if m == 1:  # a single contrast vector, use Wald test
                var_log_intensity = []
                for k in range(n_con_group_involved):
                    cov_spatial_coef_k = cov_spatial_coef[
                        k * spatial_coef_dim : (k + 1) * spatial_coef_dim,
                        k * spatial_coef_dim : (k + 1) * spatial_coef_dim,
                    ]
                    var_log_intensity_k = np.sum(np.multiply(X @ cov_spatial_coef_k, X), axis=1)
                    var_log_intensity.append(var_log_intensity_k)
                var_log_intensity = np.stack(var_log_intensity, axis=0)
                involved_var_log_intensity = simp_con_group**2 @ var_log_intensity
                involved_std_log_intensity = np.sqrt(involved_var_log_intensity)
                # Conduct Wald test (Z test)
                z_stats_spatial = contrast_log_intensity / involved_std_log_intensity
                if n_con_group_involved == 1:  # one-tailed test
                    p_vals_spatial = scipy.stats.norm.sf(z_stats_spatial)  # shape: (1, n_voxels)
                else:  # two-tailed test
                    p_vals_spatial = (
                        scipy.stats.norm.sf(abs(z_stats_spatial)) * 2
                    )  # shape: (1, n_voxels)
            else:  # GLH tests (with multiple contrasts)
                cov_log_intensity = np.empty(shape=(0, n_brain_voxel))
                for k in range(n_con_group_involved):
                    for s in range(n_con_group_involved):
                        cov_beta_ks = cov_spatial_coef[
                            k * spatial_coef_dim : (k + 1) * spatial_coef_dim,
                            s * spatial_coef_dim : (s + 1) * spatial_coef_dim,
                        ]
                        cov_group_log_intensity = (
                            (X.dot(cov_beta_ks) * X).sum(axis=1).reshape((1, -1))
                        )
                        cov_log_intensity = np.concatenate(
                            (cov_log_intensity, cov_group_log_intensity), axis=0
                        )  # (m^2, n_voxels)
                # GLH on log_intensity (eta)
                chi_sq_spatial = self._chi_square_log_intensity(
                    m,
                    n_brain_voxel,
                    n_con_group_involved,
                    simp_con_group,
                    cov_log_intensity,
                    contrast_log_intensity,
                )
                p_vals_spatial = 1 - scipy.stats.chi2.cdf(chi_sq_spatial, df=m)
                # convert p-values to z-scores for visualization
                if np.all(np.count_nonzero(con_group, axis=1) == 1):  # GLH: homogeneity test
                    z_stats_spatial = scipy.stats.norm.isf(p_vals_spatial)
                    z_stats_spatial[z_stats_spatial < 0] = 0
                else:
                    z_stats_spatial = scipy.stats.norm.isf(p_vals_spatial / 2)
                    if con_group.shape[0] == 1:  # GLH one test: Z statistics are signed
                        z_stats_spatial *= np.sign(contrast_log_intensity.flatten())
                z_stats_spatial = np.clip(z_stats_spatial, a_min=-10, a_max=10)
            #  save results
            if self.t_con_groups_name:
                if m > 1:  # GLH tests (with multiple contrasts)
                    self.result.maps[
                        f"chiSquare_group-{self.t_con_groups_name[con_group_count]}"
                    ] = chi_sq_spatial
                self.result.maps[
                    f"p_group-{self.t_con_groups_name[con_group_count]}"
                ] = p_vals_spatial
                self.result.maps[
                    f"z_group-{self.t_con_groups_name[con_group_count]}"
                ] = z_stats_spatial
            else:
                if m > 1:  # GLH tests (with multiple contrasts)
                    self.result.maps[f"chiSquare_GLH_groups_{con_group_count}"] = chi_sq_spatial
                self.result.maps[f"p_GLH_groups_{con_group_count}"] = p_vals_spatial
                self.result.maps[f"z_GLH_groups_{con_group_count}"] = z_stats_spatial
            con_group_count += 1

    def _chi_square_log_intensity(
        self,
        m,
        n_brain_voxel,
        n_con_group_involved,
        simp_con_group,
        cov_log_intensity,
        contrast_log_intensity,
    ):
        """
        Calculate chi-square statistics for GLH on group-wise log intensity function.

        It is an intermediate steps for GLH testings.

        Parameters
        ----------
        m : :obj:`int`
            Number of independent GLH tests.
        n_brain_voxel : :obj:`int`
            Number of voxels within the brain mask.
        n_con_group_involved : :obj:`int`
            Number of groups involved in the GLH test.
        simp_con_group : :obj:`numpy.ndarray`
            Simplified contrast matrix for the GLH test.
        cov_log_intensity : :obj:`numpy.ndarray`
            Covariance matrix of log intensity estimation.
        contrast_log_intensity : :obj:`numpy.ndarray`
            The product of contrast matrix and log intensity estimation.

        Returns
        -------
        chi_sq_spatial : :obj:`numpy.ndarray`
            Voxel-wise chi-square statistics for GLH tests on group-wise spatial
            intensity estimations.
        """
        chi_sq_spatial = np.empty(shape=(0,))
        for j in range(n_brain_voxel):
            contrast_log_intensity_j = contrast_log_intensity[:, j].reshape(m, 1)
            v_j = cov_log_intensity[:, j].reshape((n_con_group_involved, n_con_group_involved))
            cv_jc = simp_con_group @ v_j @ simp_con_group.T
            cv_jc_inv = np.linalg.inv(cv_jc)
            chi_sq_spatial_j = contrast_log_intensity_j.T @ cv_jc_inv @ contrast_log_intensity_j
            chi_sq_spatial = np.concatenate(
                (
                    chi_sq_spatial,
                    chi_sq_spatial_j.reshape(
                        1,
                    ),
                ),
                axis=0,
            )
        return chi_sq_spatial

    @_check_fit
    def _glh_con_moderator(self):
        """Conduct Generalized linear hypothesis (GLH) testing for study-level moderators.

        GLH testing allows flexible hypothesis testings on regression
        coefficients of study-level moderators, including testing for
        the existence of moderator effects and difference in moderator
        effects across multiple moderator effects.
        """
        con_moderator_count = 0
        for con_moderator in self.t_con_moderators:
            m_con_moderator, _ = con_moderator.shape
            moderator_coef = self.result.tables["moderators_regression_coef"].to_numpy().T
            contrast_moderator_coef = np.matmul(con_moderator, moderator_coef)

            moderators_by_group = (
                self.estimator.inputs_["moderators_by_group"] if self.moderators else None
            )
            f_moderator_coef = self.estimator.model.fisher_info_multiple_group_moderator(
                self.estimator.inputs_["coef_spline_bases"],
                moderators_by_group,
                self.estimator.inputs_["foci_per_voxel"],
                self.estimator.inputs_["foci_per_study"],
            )

            cov_moderator_coef = np.linalg.inv(f_moderator_coef)
            if m_con_moderator == 1:  # a single contrast vector, use Wald test
                var_moderator_coef = np.diag(cov_moderator_coef)
                involved_var_moderator_coef = con_moderator**2 @ var_moderator_coef
                involved_std_moderator_coef = np.sqrt(involved_var_moderator_coef)
                # Conduct Wald test (Z test)
                z_stats_moderator = contrast_moderator_coef / involved_std_moderator_coef
                p_vals_moderator = (
                    scipy.stats.norm.sf(abs(z_stats_moderator)) * 2
                )  # two-tailed test
            else:  # GLH test (multiple contrast vectors)
                chi_sq_moderator = (
                    contrast_moderator_coef.T
                    @ np.linalg.inv(con_moderator @ cov_moderator_coef @ con_moderator.T)
                    @ contrast_moderator_coef
                )
                p_vals_moderator = 1 - scipy.stats.chi2.cdf(chi_sq_moderator, df=m_con_moderator)
                z_stats_moderator = scipy.stats.norm.isf(p_vals_moderator / 2)

            if self.t_con_moderators_name:  # None?
                if m_con_moderator > 1:
                    self.result.tables[
                        f"chi_square_{self.t_con_moderators_name[con_moderator_count]}"
                    ] = pd.DataFrame(data=np.array(chi_sq_moderator), columns=["chi_square"])
                self.result.tables[
                    f"p_{self.t_con_moderators_name[con_moderator_count]}"
                ] = pd.DataFrame(data=np.array(p_vals_moderator), columns=["p"])
                self.result.tables[
                    f"z_{self.t_con_moderators_name[con_moderator_count]}"
                ] = pd.DataFrame(data=np.array(z_stats_moderator), columns=["z"])
            else:
                if m_con_moderator > 1:
                    self.result.tables[
                        f"chi_square_GLH_moderators_{con_moderator_count}"
                    ] = pd.DataFrame(data=np.array(chi_sq_moderator), columns=["chi_square"])
                self.result.tables[f"p_GLH_moderators_{con_moderator_count}"] = pd.DataFrame(
                    data=np.array(p_vals_moderator), columns=["p"]
                )
                self.result.tables[f"z_GLH_moderators_{con_moderator_count}"] = pd.DataFrame(
                    data=np.array(z_stats_moderator), columns=["z"]
                )
            con_moderator_count += 1