General Linear Model (GLM)

The general linear model (GLM) represents the observed data in a voxelwise manner, as a linear combination of independent variables in addition to an error term. The independent variables correspond to the columns of the design matrix, which in addition also include a constant regressor as the last column. The GLM represents the pattern which is expected to be observed in the data and is generated from the input onset and duration specified in the design file. Thus, it is important that it matches the timing of the stimulus presentation.

Estimation of - Values

The goal of the GLM estimation is to represent the observed data as a linear combination of the design matrix X and the estimated - values,

where an error. The - values are regression coefficients and are estimated as

where the pseudo-inverse (More-Penrose inverse) of the design matrix is estimated as

The error term is estimated as

Note that both the error term and - values are needed in for the statistical analysis of the data.

Temporal Smoothing

Temporal smoothing is done to both the image data and the design matrix. It will affect the degrees of freedom used when performing the statistical analysis of the data. Temporal smoothing is on by default and can be altered by the user in the advanced settings.

Note that the temporal smoothing is only used for statistical calculations. It will not affect the data in the image time series.