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)?