There’s been a little bit of discussion regarding this warning in this thread, and while I’ve contemplated making changes to the relevant code, I’m still not confident in exactly how I want to classify these things.
Firstly, the design matrix condition number is wholly independent of the data being provided as input to the command; it depends solely on the design matrix.
The purpose of this warning is that it can identify cases where there has been an outright error in construction of the design matrix. However it seems that it can also flag cases where the design matrix is maybe not optimal, but is nevertheless functional. Hence I’m trying to decide whether I should revise the rules around when a warning is or is not issued.
In your case:
My design matrix is very simple, one column of 1s and one column of behavioral measurements.
, my best guess is that you have entered your behavioural measurements as-is (in whatever units they are quantified), and have not demeaned the data. The consequence of this is that the model will “have a hard time” determining, based on the input data values, what to ascribe to the first explanatory variable (the column of ones) and what to ascribe to the second explanatory variable (the behavioural measurements). You could think of this “difficulty” as being quantified via the condition number.
Alternatively, the condition number can be large when the magnitudes of values within different columns of the design matrix vary substantially. E.g. If you had two behavioural measures, but one was quantified in the range [0.0, 1.0] and the other in the range [0, 1,000,000], the condition number would be similarly high, because the model “has difficulty” calculating both the very small rate of change of the input values as a function of the first measure and the very large rate of change of the input values as a function of the second measure.
If my hunch is right, demeaning the behavioural data (and possibly also scaling to unit variance if necessary) should yield a drastically reduced condition number. If that’s the case, please report back to us with your results, as this will hopefully be a good reference for others.