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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. 


Dear Linda/Bengt: I would like to fit a bifactor IRT model in Mplus. I specified the model with the following syntax: Analysis: model: Yans BY y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 y17 y18 y19; Yans By y1y19*; [y1$1y19$1*]; [y1$2y19$2*]; [y1$3y19$3*]; Yans@1; [Yans@0]; Factor1 BY y1 y4 y6 y9 y10 y12 y15; Factor1@1; [Factor1@0]; Factor2 BY y2 y5 y8; Factor2@1; [Factor2@0]; Factor3 BY y14 y16 y17; Factor3@1; [Factor3@0]; Factor4 BY y3 y7 y11 y13 y18 y19; Factor4@1; [Factor4@0]; Yans with Factor1@0 Factor2@0 Factor3@0 Factor4@0; Factor1 with Factor2@0 Factor3@0 Factor4@0; Factor2 with Factor3@0 Factor4@0; Factor3 with Factor4@0; OUTPUT: STDYX Residual; how to recover the parameters in the model? Thanks 


What happens when you run the input file in Mplus? 


Dear Linda: I can see goodnessoffit indexes, STDYX Standardization and RSquare, but can´t find "Item Discriminations" nor "Item Difficulties". Thanks 


Please send the output and your license number to support@statmodel.com. 


Hello, 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 rerun 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. Thank you for your help! 


You need to resolve the problem before you get plots and results that can be interpreted. Please send the output and your license number to support@statmodel.com. 

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