Testing for Nonuniform Differential Item Functioning With Multiple Indicator Multiple Cause Models
Carol M. Woods and Kevin J. Grimm
In 2009, Woods used multiple indicator multiple cause (MIMIC) models to indentify items that display uniform DIF. This paper is the expanding of the former paper. One interaction variable was added to the MIMIC model to test nonuniform DIF. The new model with the interaction was compared with the MIMIC model without interaction and IRT-LR-DIF. Two simulated studies and one empirical study were used to demonstrate the effect. The result shows the MIMIC model with interaction can be used to detect nonuniform DIF, however the Type I error is severely inflated. The LMS method in Mplus may be one of the cause.
Simulation is the same with the former article:
Sample size: 25, 50,100, 200, or 400
q~N (0, 1)
a~N (1.7, 0.3)
b~N (0, 1)
Number of items: 6, 12, or 24
Reference-group:
Sample size: 500 or 1,000
q~N (0.4, 1)
Ordinal:
Focal-group:
Sample size: 50, 100, 200, or 400
q~N (0, 1)
Reference-group:
Sample size: 500 or 1,000
q~N (0.4, 1)
a~N (1.7, 0.6)
b~N (-0.4, 0.9) (The first R-group threshold)
Results：
False-Positive Rates：
Rates for MIMIC-interaction models were unacceptably high, whereas the rates for MIMIC and IRT-LR-DIF were near the nominal level.
Hit Rates:
MIMIC-interaction models often had the most power but recall that Type I error was unacceptably high for these models.
Estimates of Mean Difference:
For binary responses, estimated mean differences were almost exactly the same with and without the interaction.
Item Parameter Estimates:
Bias in the F-group parameters was larger than what is reported here for MIMIC-interaction models.
For both binary and ordinal responses, bias in item parameter estimates for anchor items was similar with and without the interaction in the model.
For both binary and ordinal responses, bias in aiF and aiR for items with uniform DIF was previously low for IRT-LR-DIF and MIMIC models without the interaction. Adding an interaction to the MIMIC models tended to decrease the bias in bijR for items with nonuniform DIF.
The empirical study found that only one item was identified as DIF comparing to 4 DIF items in the former study.
Comments:
1 The MIMIC model does offer a method to detect uniform and nonuniform DIF which can be directly used in our own research. However the LMS method should be improved to overcome the estimation problem.
2 Generally speaking, it seems the IRT-LR-DIF is better than the other two method.Though we have learnt there are under different theory assumption.
3 Some samll mistakes have been found in the paper.