I would like to fit a bifactor IRT model in Mplus. I have come up with the following syntax which, I believe, is a bifactor implementation of the Graded Response Model (Samejima, 1969; 1996):
** I simplified the syntax for posting MODEL: G by i1-i4*; ! general factor G@1; ! Variance at 1 [G@0]; ! Mean at 0 ! specific factors F1 BY i1-i2*; F1@1; ! Variance at 1 [F1@0]; ! Mean at 0 F2 BY i3-i4*; F2@1; ! Variance at 1 [F2@0]; ! Mean at 0 ! uncorrelated factors G with F1@0F2@0; F1 with F2@0; ! Item thresholds free ! First threshold [i1$1]; [i2$1]; [i3$1]; [i4$1]; ! Second threshold [i1$2]; [i2$2]; [i3$2]; [i4$2];
Does this implementation seem sound or do I need to place additional constraints? Also, in a correctly specified bifactor IRT model, would recovery of IRT parameters be the same as in the single factor case (i.e. a standard IRT model specification)?
I am running a bifactor IRT model in mplus. I would like to examine the information curves for both the general and specific factors, but after I ran the model, the plots were not generated. I used this syntax to generate a plot: PLOT: type is plot2;
I also received the following error: WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE DAPS11.
I attempted to re-run the model without the identified problem variable, but then the error indicated that there was a problem with a different variable.
It would be very helpful if you could provide some guidance on if the problem with the plot is due to the warning message or if I am using the incorrect syntax for the plot.