Deconvolution Analysis of FMRI Time Series Data - Waisman ...

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Program 3dDeconvolve Command Line for Example 1.4.5.13dDeconvolve n-input1D 'Castle.data.1D[0]' n-nfirst 0 n-polort 0 n-num stimts 6 n-stim file 1 'Castle.data.1D[1]'-stim file 2 'Castle.data.1D[2]'-stim file 3 'Castle.data.1D[3]'-stim file 4 'Castle.data.1D[4]'-stim file 5 'Castle.data.1D[5]'-stim file 6 'Castle.data.1D[6]'-stim label 1 A1B1 n-stim label 2 A1B2 n-stim label 3 A2B1 n-stim label 4 A2B2 n-stim label 5 A3B1 n-stim label 6 A3B2What is the result? This should be easy to explain, if you look at the above table.What is the column sum if you add the columns corresponding to the indicator variablesA 1 B 1 ,...,A 3 B 2 ? Remember, program 3dDeconvolve always inserts a column of all 1's as therst column of the X matrix.Example 1.4.5.2 Modied ANOVA modelTherefore, the model has to be modied (to avoid multicollinearity). There are manyways to do this. For example, if the A 1 B 1 indicator variable is left out, then we have themodel:Y = qI + rA 1 B 2 + sA 2 B 1 + tA 2 B 2 + uA 3 B 1 + vA 3 B 2where I represents the column of 1's. Now, since I = A 1 B 1 + A 1 B 2 + A 2 B 1 + A 2 B 2 +A 3 B 1 + A 3 B 2 , we can also write the above equation as:Y = qA 1 B 1 +(r + q)A 1 B 2 +(s + q)A 2 B 1 +(t + q)A 2 B 2 +(u + q)A 3 B 1 +(v + q)A 3 B 2By comparing this equation with the equation in Example 1.4.5.1, we see that:a = q b = r + q c = s + q d = t + q e = u + q f = v + qThe test for Factor A main eect is:Since the parameter vector is:a + b ; c ; d =0 () r ; s ; t =0a + b ; e ; f =0 () r ; u ; v =0 t = q r s t u v the test for Factor A main eect can be represented by the following matrix: 0 1 ;1 ;1 0 0C =0 1 0 0 ;1 ;150
Store this matrix as 2rows of ASCII numbers into le Castle.matA.The test for Factor B main eect is:a ; b + c ; d + e ; f =0 () ;r + s ; t + u ; v =0So, the test for Factor B main eect can be represented by the following matrix:C = 0 ;1 1 ;1 1 ;1 Store this matrix as 1row of ASCII numbers into le Castle.matB.Finally, thetest for AB interaction is:a ; b ; c + d =0 () ;r ; s + t =0a ; b ; e + f =0 () ;r ; u + v =0So, the test for AB interaction can be represented by the following matrix: 0 ;1 ;1 1 0 0C =0 ;1 0 0 ;1 1Store this matrix as 2rows of ASCII numbers into le Castle.matAB.That's all you will need to execute the following script:Program 3dDeconvolve Command Line for Example 1.4.5.23dDeconvolve n-input1D 'Castle.data.1D[0]' n-nfirst 0 n-polort 0 n-num stimts 5 n-stim file 1 'Castle.data.1D[2]' -stim label 1 A1B2 n-stim file 2 'Castle.data.1D[3]' -stim label 1 A2B1 n-stim file 3 'Castle.data.1D[4]' -stim label 1 A2B2 n-stim file 4 'Castle.data.1D[5]' -stim label 1 A3B1 n-stim file 5 'Castle.data.1D[6]' -stim label 1 A3B2 n-glt 2 Castle.matA -glt label 1 'Factor A' n-glt 1 Castle.matB -glt label 2 'Factor B' n-glt 2 Castle.matAB -glt label 3 'AB Interaction'This generates the following output:Program 3dDeconvolve Screen Output for Example 1.4.5.251
Page 1: Deconvolution Analysis of FMRI Time
Page 7 and 8: Since the system is linear, the ope
Page 9: the above equation can be written:Z
Page 13 and 14: where s(h k ) is the square root of
Page 15 and 16: Here, SSE(F )isthe error sum of squ
Page 17 and 18: concatenated runs, this is not the
Page 19: This equation relates the output y
Page 22 and 23: value is pnum = 1 (corresponding to
Page 24 and 25: model parameters, and P columns, ea
Page 26 and 27: Program 3dDeconvolve Command Line f
Page 28 and 29: f(t) = f 0 0 1 1 1 0 1 1 0 0 1 0 1
Page 30 and 31: If we model the measured response b
Page 32 and 33: Note that, since there is only one
Page 34 and 35: Full Model:MSE = 0.9618R^2 = 0.9835
Page 36 and 37: that are not of inherent interest,
Page 38 and 39: Program 3dDeconvolve Command Line f
Page 40 and 41: Now, model the measured data as a c
Page 42 and 43: -stim label 1 Random -stim label 2
Page 44 and 45: Note: This example is for illustrat
Page 46 and 47: The output is the same as for Examp
Page 48 and 49: After program 3dDeconvolve has nish
Page 52 and 53: Program:3dDeconvolveAuthor:B. Dougl
Page 54 and 55: cat y.1D y.1D > ycat.1DBe sure to r
Page 56 and 57: Recall that in Example 1.4.4.6, we
Page 58 and 59: and the noisy measurement data:wp(t
Page 60 and 61: The model that we will use for the
Page 62 and 63: Program 3dConvolve Command Line for
Page 64 and 65: 2 Program plug deconvolve2.1 Purpos
Page 66 and 67: voxels indicated by the crosshairs,
Page 68 and 69: Deconvolution Plugin Screen Output
Page 70 and 71: The following Random Permutation an
Page 72 and 73: Shuffled array:0 5 6 1 3 5 0 2 1 1
Page 74 and 75: Program RSFgen Command Line for Exa
Page 76 and 77: Example 3.3.3.1 Initial Random Bloc
Page 78 and 79: Compare the output for this example
Page 80 and 81: Markov chain time series:0 0 1 5 0
Page 82 and 83: (X'X) inverse matrix::065 ;:000 ;:0
Page 84 and 85: Program 3dDeconvolve Screen Output
Page 86 and 87: then the standard deviation for the
Page 88 and 89: 4 Program 3dConvolve4.1 PurposeAs t
Page 90 and 91: -input1DThe -input1D command specie
Page 92 and 93: -stim minlag k m-stim maxlag k n-st
Page 94 and 95: parameters b 0 and b 1 , and impuls
Page 96 and 97: Program 3dConvolve Command Line for
Page 98 and 99: Example 4.4.6 Single Stimulus No No
Page 100:
5 References[1 ]F.Stremler, Fourier
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