schluppeck · October 27, 2019 21:53
diff --git a/Readme.md b/Readme.md
diff --git a/design_contrast.txt b/design_contrast.txt
 /ContrastName1	face 
 /ContrastName2	objects 
 /ContrastName3	scenes 
 /ContrastName4	faces versus scenes 
 /ContrastName5	scenes versus faces 
 /NumWaves	6
 /NumContrasts	5
 /PPheights		8.888311e-01	8.892543e-01	8.888422e-01	8.887986e-01	8.887986e-01
 /RequiredEffect		1.092	1.077	1.083	1.139	1.139

 /Matrix
 1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00 
 1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -1.000000e+00 0.000000e+00 
 -1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00 
diff --git a/design_matrix.txt b/design_matrix.txt
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 -1.541124e-01	-1.957412e-02	-1.747192e-01	-2.997269e-03	9.300655e-02	2.004562e-01	
 -1.671890e-01	-8.872102e-03	-1.774880e-01	-3.175339e-03	3.146060e-01	2.079852e-01	
 -1.725567e-01	-2.949619e-03	-1.804367e-01	-3.360628e-03	5.087248e-01	1.671918e-01	
 -1.737901e-01	2.178767e-04	-1.835724e-01	-3.553201e-03	6.488781e-01	1.138293e-01	
 -1.728232e-01	1.919043e-03	-1.869023e-01	-3.753099e-03	7.363736e-01	3.702749e-02	
 -1.706539e-01	2.957455e-03	-1.904337e-01	-3.960348e-03	7.229867e-01	-8.147173e-02	
 -1.676095e-01	3.632612e-03	-1.941738e-01	-4.174969e-03	5.734740e-01	-1.777404e-01	
 -1.640889e-01	4.001859e-03	-1.981298e-01	-4.396996e-03	3.674413e-01	-1.959885e-01	
 -1.603049e-01	4.266785e-03	-2.023090e-01	-4.626454e-03	1.812833e-01	-1.610040e-01	
 -1.562531e-01	4.535898e-03	-2.067187e-01	-3.878823e-03	4.508447e-02	-1.116494e-01	
 -1.519296e-01	4.809095e-03	-2.093972e-01	2.878282e-02	-4.246308e-02	-6.927909e-02	
 -1.473300e-01	5.086247e-03	-1.484804e-01	1.167525e-01	-9.398481e-02	-3.978437e-02	
 -1.424506e-01	5.367184e-03	2.470499e-02	1.942373e-01	-1.225803e-01	-2.156190e-02	
 -1.372876e-01	5.651031e-03	2.403770e-01	2.017639e-01	-1.376778e-01	-1.105764e-02	
 -1.318388e-01	5.915453e-03	4.283483e-01	1.609420e-01	-1.452757e-01	-5.348930e-03	
 -1.261452e-01	6.116069e-03	5.621436e-01	1.075170e-01	-1.489613e-01	-2.406954e-03	
 -1.202933e-01	6.248579e-03	6.430994e-01	3.062274e-02	-1.506779e-01	-9.389021e-04	
 -1.143328e-01	6.356972e-03	6.230058e-01	-8.806355e-02	-1.514287e-01	-1.380204e-04	
 -1.082621e-01	6.480129e-03	4.666139e-01	-1.846651e-01	-1.515440e-01	2.974930e-04	
 -1.020533e-01	6.634810e-03	2.535110e-01	-2.033217e-01	-1.514239e-01	4.266276e-04	
 -9.567123e-02	6.853813e-03	6.006974e-02	-1.687620e-01	-1.512809e-01	4.521536e-04	
 -8.902226e-02	6.986196e-03	-8.367397e-02	-1.440022e-01	-1.511096e-01	4.662550e-04	
diff --git a/designMatrixCheck.m b/designMatrixCheck.m
 %% reality check on design matrices
 % Denis Schluppeck, 2019-10-27
 % 
 %
 % Including a quick example of 
 %
 % 1. how to load in txt files
 % 2. look at design matrix
 % 3. do some linear alebgra checks (as per question during class)
 % 4. explanation of how the temporal derivative column allows for shifts in
 %    time

 %% load in design matrix from FSL
 %
 % design.mat (chopped relevant data out renamed here to design_matrix.txt)

 X = load('design_matrix.txt');

 %% show as an image
 figure
 imagesc(X)
 colormap(gray() )
 colorbar()
 xlabel('explanatory variables')
 ylabel('Time (volumes)')


 %% plot columns 1 and 2 (EV1 and its temporal derivative)
 %
 % each TR took 1.5s (can check with |fslinfo filtered_func.nii|

 nVolumes = size(X,1); % number of rows in design matrix
 t = 1.5 .* 0:(nVolumes-1); % time in seconds

 figure
 plot(t, X(:, [1,2])); % plot only columns 1 and 2
 xlabel('Time (s)')
 ylabel('Explanatory variable, value')


 %% what happens when we mix together EV1 and EV2 in different proportions?

 response1 = X*[1; 0; zeros(4,1)];  % MATRIX multiplication ... X*beta

 response2 = X*[1; 2; zeros(4,1)];  % MATRIX multiplication ... X*beta

 response3 = X*[1; 4; zeros(4,1)];  % MATRIX multiplication ... X*beta

 response4 = X*[1; -2; zeros(4,1)];  % MATRIX multiplication ... X*beta


 figure
 p1 = plot(t, response1, 'k-', 'linewidth',2);
 hold on
 p2 = plot(t, response2, 'r-', 'linewidth',2);
 p3 = plot(t, response3, 'b-', 'linewidth',2);
 % p4 = plot(t, response4, 'm-', 'linewidth',2);

 legend([p1;p2;p3], {'no shift', '2* EV2', '4* EV2'});
 xlabel('Time (s)')
 ylabel('Explanatory variable, value')
 title('Effect of adding temporal derivative')
 pbaspect([3,1,1])


 %% linear alegbra check (answer to actual question :)

 % Q: "Is the design matrix actually ok? It looks like each EV and their
 %     temporal derivatives are quite similar... doesn't that cause
 %     problems?"

 % A: check rank of matrix...
 % .  In order for linear regression to work, X, the design matrix needs to
 %    be invertible... for this it needs to be full rank.
 %    see eg: https://en.wikipedia.org/wiki/Rank_(linear_algebra)

 fprintf('the number of EVs in X is %i, the rank(X) is %i\n', size(X,2), rank(X))
 if size(X,2) == rank(X)
    disp('rank is ok... the world is a good place')
 end

 % can also check that EV1 and its temporal derivative are not similar...
 % as that's what causes the actual problem

 % rank of the first two columns, should be 2!
 rank(X(:, [1,2]))

 % you can also check what rref() returns
 % Reduced row echelon form (Gauss-Jordan)... this underlies the
 % determination of rank... and therefore how matlab determines if a matrix
 % is invertible.
 % https://www.youtube.com/watch?v=xCIXkm3-ocQ
diff --git a/fig1.png b/fig1.png
diff --git a/fig2.png b/fig2.png
diff --git a/fig3.png b/fig3.png
	/ContrastName1 face
	/ContrastName2 objects
	/ContrastName3 scenes
	/ContrastName4 faces versus scenes
	/ContrastName5 scenes versus faces
	/NumWaves 6
	/NumContrasts 5
	/PPheights 8.888311e-01 8.892543e-01 8.888422e-01 8.887986e-01 8.887986e-01
	/RequiredEffect 1.092 1.077 1.083 1.139 1.139

	/Matrix
	1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
	0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
	0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00
	1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -1.000000e+00 0.000000e+00
	-1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00
	%% reality check on design matrices
	% Denis Schluppeck, 2019-10-27
	%
	%
	% Including a quick example of
	%
	% 1. how to load in txt files
	% 2. look at design matrix
	% 3. do some linear alebgra checks (as per question during class)
	% 4. explanation of how the temporal derivative column allows for shifts in
	% time

	%% load in design matrix from FSL
	%
	% design.mat (chopped relevant data out renamed here to design_matrix.txt)

	X = load('design_matrix.txt');

	%% show as an image
	figure
	imagesc(X)
	colormap(gray() )
	colorbar()
	xlabel('explanatory variables')
	ylabel('Time (volumes)')


	%% plot columns 1 and 2 (EV1 and its temporal derivative)
	%
	% each TR took 1.5s (can check with \|fslinfo filtered_func.nii\|

	nVolumes = size(X,1); % number of rows in design matrix
	t = 1.5 .* 0:(nVolumes-1); % time in seconds

	figure
	plot(t, X(:, [1,2])); % plot only columns 1 and 2
	xlabel('Time (s)')
	ylabel('Explanatory variable, value')


	%% what happens when we mix together EV1 and EV2 in different proportions?

	response1 = X[1; 0; zeros(4,1)]; % MATRIX multiplication ... Xbeta

	response2 = X[1; 2; zeros(4,1)]; % MATRIX multiplication ... Xbeta

	response3 = X[1; 4; zeros(4,1)]; % MATRIX multiplication ... Xbeta

	response4 = X[1; -2; zeros(4,1)]; % MATRIX multiplication ... Xbeta


	figure
	p1 = plot(t, response1, 'k-', 'linewidth',2);
	hold on
	p2 = plot(t, response2, 'r-', 'linewidth',2);
	p3 = plot(t, response3, 'b-', 'linewidth',2);
	% p4 = plot(t, response4, 'm-', 'linewidth',2);

	legend([p1;p2;p3], {'no shift', '2* EV2', '4* EV2'});
	xlabel('Time (s)')
	ylabel('Explanatory variable, value')
	title('Effect of adding temporal derivative')
	pbaspect([3,1,1])


	%% linear alegbra check (answer to actual question :)

	% Q: "Is the design matrix actually ok? It looks like each EV and their
	% temporal derivatives are quite similar... doesn't that cause
	% problems?"

	% A: check rank of matrix...
	% . In order for linear regression to work, X, the design matrix needs to
	% be invertible... for this it needs to be full rank.
	% see eg: https://en.wikipedia.org/wiki/Rank_(linear_algebra)

	fprintf('the number of EVs in X is %i, the rank(X) is %i\n', size(X,2), rank(X))
	if size(X,2) == rank(X)
	disp('rank is ok... the world is a good place')
	end

	% can also check that EV1 and its temporal derivative are not similar...
	% as that's what causes the actual problem

	% rank of the first two columns, should be 2!
	rank(X(:, [1,2]))

	% you can also check what rref() returns
	% Reduced row echelon form (Gauss-Jordan)... this underlies the
	% determination of rank... and therefore how matlab determines if a matrix
	% is invertible.
	% https://www.youtube.com/watch?v=xCIXkm3-ocQ