# AM Regression - modelling multiple events at the same time

Dear AFNI experts,

I have a question regarding the modelling of multiple events at the same time using amplitude modulated regression. We ran a reinforcement learning paradigm where we generated trial-by-trial estimates of expected value (EV), prediction error (PE) and learning rate (LR). We always model PE and LR at exactly the same time (and both have exactly the same duration - 1 second), but, importantly, the amplitudes are uncorrelated. When we try to run the model, AFNI gives us a collinearity error (see below). Is there any way around this? I found a handout online which stated the following: “Future directions: Allow more than one amplitude to be married to each stimulus time (insert obligatory polygamy/polyandry joke here) – this is done now” - this makes me think it SHOULD be possible.

Thanks,

Dennis Hernaus

*+ WARNING: -------------------------------------------------
*+ WARNING: Problems with the X matrix columns, listed below:
*+ WARNING: !! * Columns 16 [PE#0] and 18 [LR#0] are (nearly?) collinear!
*+ WARNING: -------------------------------------------------
*+ WARNING: !! in Signal+Baseline matrix:

• Largest singular value=1.93535
• 1 singular value is less than cutoff=1.93535e-07
• Implies strong collinearity in the matrix columns!
*+ WARNING: !! in Signal-only matrix:
• Largest singular value=1.56269
• 1 singular value is less than cutoff=1.56269e-07
• Implies strong collinearity in the matrix columns!
*+ WARNING: +++++ !! Matrix inverse average error = 0.00255102 ** BEWARE **
** ERROR: !! 3dDeconvolve: Can’t run past 4 matrix warnings without ‘-GOFORIT 4’
** ERROR: !! Currently at -GOFORIT 0
** ERROR: !! See file 3dDeconvolve.err for all WARNING and ERROR messages !!
** ERROR: !! Be sure you understand what you are doing before using -GOFORIT !!
** ERROR: !! If in doubt, consult with someone or with the AFNI message board !!
** FATAL ERROR: !! 3dDeconvolve (regretfully) shuts itself down !!

It’s difficult to make assessment about the situation since there is not enough information about the experiment. Are you modeling PE and LR as two separate regressors? But you’re also mentioning “amplitude modulation”? The error message from 3dDeconvolve indicates that the two are highly correlated with each other, but you’re saying that the two “are uncorrelated”?

hi Dennis and Gang

Is this a case where instead of having PE and LR as separate regressors, the values of PE and LR for each event should be specified using stim_times_AM2?

From the help:

-stim_times_AM1 and -stim_times_AM2 now take files with more
than 1 amplitude attached to each time; for example,
33.7*9,-2,3
indicates a stimulus at time 33.7 seconds with 3 amplitudes
attached (9 and -2 and 3). In this example, -stim_times_AM2 would
generate 4 response models: 1 for the constant response case
and 1 scaled by each of the amplitude sets.

So in this case there would be one -stim_times_AM2 argument to 3dDeconvolve with the times for each trial and the values for PE and LR would be married to them?

The collinearity error I think stems from the fact that, as Gang noted, these things are being assigned using separate -stim_times arguments.

James