run splithalf correlationsΒΆ

Matlab output: run_splithalf_correlations

%% roi-based MVPA with group-analysis
%
% Load t-stat data from all subjects, apply 'vt' mask, compute difference
% of (fisher-transformed) between on- and off diagonal split-half
% correlation values, and perform a random effects analysis.
%
% #   For CoSMoMVPA's copyright information and license terms,   #
% #   see the COPYING file distributed with CoSMoMVPA.           #

%% Set analysis parameters
subject_ids={'s01','s02','s03','s04','s05','s06','s07','s08'};
rois={'ev'; 'vt'; 'brain'};
labels = {'monkey'; 'lemur'; 'mallard'; 'warbler'; 'ladybug'; 'lunamoth'};

nsubjects=numel(subject_ids);

% allocate space for output
sum_weighted_zs_all=zeros(nsubjects,1);

config=cosmo_config();
study_path=fullfile(config.tutorial_data_path,'ak6');


%% Loop over rois
nrois=numel(rois);
for i_roi = 1:nrois

    % pre-allocate space weighted correlation difference
    % in each subject
    sum_weighted_zs_all=zeros(nsubjects,1);

    %% Computations for each subject
    for i_subj=1:nsubjects
        subject_id=subject_ids{i_subj};

        data_path=fullfile(study_path, subject_id);

        % file locations for both halves
        half1_fn=fullfile(data_path,'glm_T_stats_odd.nii');
        half2_fn=fullfile(data_path,'glm_T_stats_even.nii');

        %mask name for given subject and roi
        mask_fn=fullfile(data_path,[rois{i_roi},'_mask.nii']);

        % load two halves as CoSMoMVPA dataset structs.
        half1_ds=cosmo_fmri_dataset(half1_fn,'mask',mask_fn);
        half2_ds=cosmo_fmri_dataset(half2_fn,'mask',mask_fn);

        % get the sample data
        % each half has six samples:
        % monkey, lemur, mallard, warbler, ladybug, lunamoth.
        half1_samples=half1_ds.samples;
        half2_samples=half2_ds.samples;

        % compute all correlation values between the two halves, resulting
        % in a 6x6 matrix. Store this matrix in a variable 'rho'.
        % Hint: use cosmo_corr
        rho=cosmo_corr(half1_samples',half2_samples');

        % for the advanced exercise ('compute the average of all individual
        % correlation matrices'): if the first subject and roi,
        % allocate space for a 'rho_sum' array with three dimensions;
        % the first two dimensions for the two halves, the third
        % one for different rois.
        % Then add 'rho' to 'rho_sum'
        %
        % (If you don't want to do the advanced
        % exercise, yo don't have to do anything here.)
        if i_subj == 1 && i_roi == 1
            % first correlation was just computed, and we now know
            % the number of conditions through the size of rho.
            %
            % allocate space for sum over subjects
            nclasses=size(rho,1);
            rho_sum=zeros([nclasses,nclasses,nrois]);
        end
        rho_sum(:, :, i_roi)=rho_sum(:, :, i_roi)+rho;


        % To make these correlations more 'normal', apply a Fisher
        % transformation and store this in a variable 'z' (use atanh).
        z=atanh(rho);

        % visualize the matrix 'z'
        subplot(3,3,i_subj);
        imagesc(z);
        colorbar()
        title([subject_id ' ' rois{i_roi}]);

        % define in a variable 'contrast_matrix' how correlations values
        % are going to be weighted.
        % The matrix must have a mean of zero, positive values on diagonal,
        % negative elsewhere.

        nclasses=size(rho,1);
        % sanity check; in this example there are 6 conditions
        assert(nclasses==6);

        % set contrast matrix. It has a mean of zero, the diagonal elements
        % sum to 1, and the non-diagonal element sum to -1
        contrast_matrix=(eye(nclasses)-1/nclasses)/(nclasses-1);

        if abs(mean(contrast_matrix(:)))>1e-14
            error('illegal contrast matrix');
        end

        % Weigh the values in the matrix 'z' by those in the
        % contrast_matrix and then sum them (hint: use the '.*'
        % operator for element-wise multiplication). Store the results in
        % a variable 'sum_weighted_z'.
        weighted_z=z.*contrast_matrix;

        sum_weighted_z=sum(weighted_z(:));

        % store the result for this subject in sum_weighted_zs_all
        % (at the i_subj-th position), so that
        % group statistics can be computed
        sum_weighted_zs_all(i_subj)=sum_weighted_z;
    end

    %% compute t statistic and print the result
    % run one-sample t-test again zero

    % Using matlab's stat toolbox (if present)
    if cosmo_check_external('@stats',false)

        [h,p,ci,stats]=ttest(sum_weighted_zs_all);
        fprintf(['correlation difference in %s at group level: '...
            '%.3f +/- %.3f, t_%d=%.3f, p=%.5f (using matlab stats '...
            'toolbox)\n'],...
            rois{i_roi},mean(sum_weighted_zs_all),...
                        std(sum_weighted_zs_all),...
            stats.df,stats.tstat,p);
    else
        fprintf('Matlab stats toolbox not available\n');
    end

    % Apart from using the 'ttest' function (if available), one can
    % also use 'cosmo_stat' for univaraite statistics.
    % For this approach, data must be represented in a dataset struct.
    %
    % The targets are chunks are set to indicate that all samples are from
    % the same class (condition), and each observation is independent from
    % the others
    sum_weighted_zs_ds=struct();
    sum_weighted_zs_ds.samples=sum_weighted_zs_all;
    sum_weighted_zs_ds.sa.targets=ones(nsubjects,1);
    sum_weighted_zs_ds.sa.chunks=(1:nsubjects)';

    ds_t=cosmo_stat(sum_weighted_zs_ds,'t');     % t-test against zero
    ds_p=cosmo_stat(sum_weighted_zs_ds,'t','p'); % convert to p-value

    fprintf(['correlation difference in %s at group level: '...
        '%.3f +/- %.3f, %s=%.3f, p=%.5f (using cosmo_stat)\n'],...
        rois{i_roi},mean(sum_weighted_zs_all),std(sum_weighted_zs_all),...
        ds_t.sa.stats{1},ds_t.samples,ds_p.samples);

end

%% advanced exercise

% plot an image of the correlation matrix averaged over
% participants (one for each roi)

% allocate space for axis handles, so that later all plots can be set to
% have the same color limits
ax_handles=zeros(nrois,1);
col_limits=zeros(nrois,2);

for i_roi = 1:nrois
    figure

    % store axis handle for current figure
    ax_handles(i_roi) = gca;

    % compute the average correlation matrix using 'rho_sum', and store the
    % result in a variable 'rho_mean'. Note that the number of subjects is
    % stored in a variable 'nsubjects'
    rho_mean=rho_sum(:, :, i_roi)/nsubjects;

    % visualize the rho_mean matrix using imagesc
    imagesc(rho_mean);

    % set labels, colorbar and title
    set(gca, 'xtick', 1:numel(labels), 'xticklabel', labels)
    set(gca, 'ytick', 1:numel(labels), 'yticklabel', labels)

    colorbar
    desc=sprintf(['Average splithalf correlation across subjects '...
                    'in mask ''%s'''], rois{i_roi});
    title(desc)


    col_limits(i_roi,:) = get(gca, 'clim');
end

% give all figures the same color limits such that correlations can be
% compared visually
set(ax_handles, 'clim', [min(col_limits(:)), max(col_limits(:))])