7.3. Nonlinear Regression Analysis of FMRI Time Series Data (NLfim)

These are notes by B. Douglas Ward, written in the Good Ol’ Days.

7.3.1. Abstract

The cross-correlation coefficient has been used extensively for the detection of a given “signal” ... in FMRI time series data. This works well when the signal is completely known, or known up to a scaling constant. However, if only the functional form of the signal is known, with the signal itself being a nonlinear function fo several unknown parameters, then a different approach is required to detect the presence of the signal buried in noise.

Section 1 describes Program 3dNLfim, which was developed to provide nonlinear regression analysis of 3D+time data sets. The nonlinear regression is accomplished by calculating a least squares fit of the time series data to a user specified model of the data. Program 3dNLfim makes a separate least squares estimate of the model parameters for each voxel in the input time series data set. Program output optinos include an AFNI ‘bucket’ dataset containing the estimated model parameters, various other parameters related to the signal waveform, and the \(R^2\) and F-statistics for significance of the nonlinear model at each voxel location.

Section 2 describes Program plug_nlfit, and AFNI “plug-in”, which displays the nonlinear least squares fit of the user specified signal waveform on top of the actual time series data for voxels of interest. Program plug_nlfit is the interactive version of the batch command program 3dNLfim.

Program 3dTSgen, whcih is described in Section 3, provides a means of generating artificial time series data, and storing such data into an AFNI 3D+time dataset. The time series data is generated using the operator specified signal and noise models. Such artificial time series data is useful in several ways: 1) Testing of statistical analysis programs for significance of the result. 2) Calculation of the statistical power of a test. 3) Design of experiments.

… [end of excerpt; see below for the full document]

7.3.2. ... Full Enlightenment

For continued enjoyment of this topic, please see the complete document here: