M2 system is computationally singular error

[Gareth McCray]

Dear all,

Firstly thank you, Professor Chalmers, for building and maintaining such a powerful and useful package.

I'm running MIRT Version 1.27.1.  I am trying to extract the fit statistics on a GPCM model 90 items by 269 participants.  Seventy items are binary and twenty are on three response categories.  All items have > 5 in each response category. I know the number of participants in low for fitting a GPCM but the 1) this is a preliminary analysis clearly nothing will be set in stone after it, and 2) the ability estimates look exactly as they should and behave appropriately, i.e., correlate with things they should and don't correlate with the things they shouldn't. Everything else about the analysis is great, given the fact that it is preliminary, apart from me not being able to get the fit statistics.  

I am having trouble with getting the M2 function to run. The specific error message is:

Error in solve.default(t(deltac) %*% Xi2 %*% deltac) : 
  system is computationally singular: reciprocal condition number = 2.85027e-17

I have followed the guidance on page the only other page about this problem [1].

I have tried combinations of,

1) Using QMC integration;
2) Extending the theta_lim (the data I have, by its nature, has a wide logit span);
3) The data has ~3% missingness, so I was originally imputing,  I tried manually imputing a full response sets using "imputeMissing", same issue;
4) Collapsing all 3 response category items to binary and fitting a 2pl.

Any pointers you might be able to give about what is going on and what I might be able to do to fix it would be very much appreciated and instructive.

Best,

Gareth

[1] https://groups.google.com/forum/#!searchin/mirt-package/Error$20in$20solve.default(t(deltac)$20$25*$25$20Xi2$20$25*$25$20deltac)%7Csort:date/mirt-package/7OgjjzQ6F8U/oOJoxNEzoSkJ

[Phil Chalmers]

This is tough, though I think it relates to the high-dimensional of the problem (90 items with many parameters) and the smaller sample size. I still haven't figured out the exact circumstances with which this issues comes up, and in some of my exploratory work with the C2 statistic I'm noticing similar problems. In your case, it may just be that the sample size is too small given the size of the parameter space to reliably compute the required M2 components. Sorry.

Phil

On Sat, May 19, 2018 at 5:15 AM 'Gareth McCray' via mirt-package <mirt-p...@googlegroups.com> wrote:

Dear all,

Firstly thank you, Professor Chambers, for building and maintaining such a powerful and useful package.

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