This level of Matrix inverse average error (MIAE) is a severe warning. For my mind, you want MIAE to be 1e-4 or less.

It is hard to diagnose the problem. The use of the undocumented '-singvals' option will print out all the singular values of the matrix; this will show how many dimensions of near singularity there are.

Determining if these dimensions are in the motion parameters or the stimulus is a little harder. The simplest thing would be to rerun the analysis with the motion parameters removed, and see if the problem disappears. If so, this means that the motion parameters are pleonastically redundant. In such a case, where it is the nuisance parameters that cause the problem, you can reduce the number of -stim_base vectors by using the program 1dsvd. For example, suppose you have the motion parameters stored in a file m.1D. Then the command

1dsvd -1Dright m.1D > ms.1D

will produce the file ms.1D, which will contain the right eigenvectors of m.1D, and the eigenvalues in a comment at the top of each column. For a trivial example:

1dsvd -1Dright '1D: 1 -1 1 2 \ 2 -2 3 4 \ 1 2 -3 3'

produces the output

# 0.25366 6.3268 4.7862
# ------------ ------------ ------------
0.092443 -0.36753 -0.16084
-0.81742 0.31918 -0.46151
-0.56573 -0.44585 0.69366
-0.056775 -0.75118 -0.52912

The second column corresponds to the largest eigenvalue, and thus accounts for the most variance. In this stupid example, you might want to keep columns '[1,2]', but not '[0]' since it has the smallest eigenvalue.

HOWEVER, if the problem of collinearity arises with your stimulus timing, then you have to rethink your analysis or experimental design; for example, you could shorten the maximum time lag for hemodynamic deconvolution (either -stim_maxlag or the 'c' parameter for -stim_times).