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

where df B is the number of degrees of freedom for the baseline model, and df F is thenumber of degrees of freedom for the full model. Specically, we have (assuming that thenoise model contains the two parameters for constant plus linear trend):df B = N 0 ; 2df F = N 0 ; 2 ; (p +1)so df B ; df F = p +1:where N 0 = N ; p is the number of usable data points.By the above reasoning, we see that a large value for F indicates that signal is present,whereas a small value for F suggests that only noise is present. The statistic F has theF (df B ; df F df F ) distribution under the null hypothesis (Ref. [2]).Program 3dDeconvolve calculates the F statistic for each voxel, and (if the -fout optionis used) appends these values as one of the sub-bricks of an AFNI \bucket" dataset.1.2.6 Coecient of Multiple DeterminationThe coecient ofmultiple determination, R 2 , can be used as an indicator for how well thefull model ts the data. We dene R 2 :R 2 1 ; SSE(F )SSE(B)where SSE(F ) and SSE(B) are dened above. Roughly speaking, R 2 is the proportionof the variation in the data (about the baseline) that is explained by the full regressionmodel. Note that, for every voxel, 0 R 2 1. (R 2 is a generalization of the square of thecorrelation coecient computed in the m programs).Program 3dDeconvolve calculates R 2 for each voxel, and (if the -rout option is used)appends these values as one of the sub-bricks of an AFNI \bucket" dataset.1.2.7 t-test for Signicance of Individual ParametersWhen comparing dierent impulse response functions, it is useful to know the signicanceof the individual terms that constitute the impulse response function. This may help in decidingwhether dierent impulse response functions are truly dierent, or merely reect theinuence of measurement noise. Therefore, program 3dDeconvolve provides the t-statisticsfor the individual terms in the impulse response function.For the linear regression model, the variance-covariance matrix for the regression coef-cients is given by:s 2 (b) =MSE ; X t X ;1Then, for large sample size N, dene the statistic t :t [h k ]=h ks(h k )12