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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 i1i4*; ! general factor G@1; ! Variance at 1 [G@0]; ! Mean at 0 ! specific factors F1 BY i1i2*; F1@1; ! Variance at 1 [F1@0]; ! Mean at 0 F2 BY i3i4*; F2@1; ! Variance at 1 [F2@0]; ! Mean at 0 ! uncorrelated factors G with F1@0 F2@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)? Thank you. Sincerely, Arjan Berkeljon 


The implementation looks correct. You should recover the parameters you need. 

Tom Booth posted on Friday, January 23, 2015  5:56 am



Dear Linda/Bengt, I am fitting a bifactor IRT model. I would like to get a plot and associated information values for the general factor conditional on the specifics. I would just like to check that this is produced in the graphical interface using the partial test information options, with all items added, and the factor of interest (here general) selected? Would this be the correct plot and data? Thanks Tom 


Yes. 

Tom Booth posted on Monday, January 26, 2015  2:04 am



Thank you. 

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