Hi there,
Usually this error means one of two things:
1) There are linearly dependent or extremely highly correlated variables in your dataset.
2) The imputation model isn't identified because you have more parameters than observations. Note that you need far more observations than in a typical regression because you need to run regressions for each column with missing data.
Note that you have turned off the internal Amelia error checking, which should give you an informative error message if there is an obvious problem with the data. Use "incheck = TRUE" to get that. Either way, you should probably start with a couple of variable to see if Amelia runs then and then try to remove any highly correlated (rho > 0.95 or so) variables from the data. You can also use the "empri" argument to stabilize the computation. See the manual for more details on this.
Cheers,
Matt
~~~~~~~~~~~
Matthew Blackwell
Assistant Professor of Government
Harvard University