Difficulty switching directions when modeling independently vs. when using Multiple Group Estimation

[Daniel McKelvey]

Hi Dr. Chalmers,

I've got a 21 item polytomous (7 response cats per item) measure that I am testing for DIF in 4 groups. I first fit a graded response model to each group independently to get a since of the item properties and model fit for each. I then moved on to using Multiple Group Estimation to test invariance and everything appeared fine until I looked at the coef output. My understanding from the configural model was that I should obtain coef parameters that are pretty similar to when I modeled each group independently, but that was not the case.

Here is the first item for my referent group when modeled independently:

        a         b1      b2      b3      b4      b5      b6

par 1.985 0.349 0.783 0.938 1.386 1.599 1.895

And here it is when modeled with MGE

         a1         d1      d2       d3       d4       d5       d6

M1  1.983 -0.684 -1.545 -1.853 -2.742 -3.164 -3.752

I notice that the parameters estimated appear to have their ordering reversed (low to high vs. high to low), but taking that into account, the values appear vastly different (0.349 vs. -3.752 for the easiest threshold difficulty). Am I interpreting these values incorrectly or is this an error in my model syntax? One thing I did do differently with my MGE model when compared with examples online is that I modeled all four groups at once whereas the examples I found typically only used two groups. I'm not sure if that may have had a detrimental effect or not. 

Thanks,

Daniel

[Phil Chalmers]

On Thu, May 17, 2018 at 3:00 PM Daniel McKelvey <daniel.k...@gmail.com> wrote:

Hi Dr. Chalmers,

I've got a 21 item polytomous (7 response cats per item) measure that I am testing for DIF in 4 groups. I first fit a graded response model to each group independently to get a since of the item properties and model fit for each. I then moved on to using Multiple Group Estimation to test invariance and everything appeared fine until I looked at the coef output. My understanding from the configural model was that I should obtain coef parameters that are pretty similar to when I modeled each group independently, but that was not the case.

Here is the first item for my referent group when modeled independently:

        a         b1      b2      b3      b4      b5      b6

par 1.985 0.349 0.783 0.938 1.386 1.599 1.895

And here it is when modeled with MGE

         a1         d1      d2       d3       d4       d5       d6

M1  1.983 -0.684 -1.545 -1.853 -2.742 -3.164 -3.752

These are different parameters. By any chance, in your single group model did you pass coef(mod, IRTpars=TRUE)?  

I notice that the parameters estimated appear to have their ordering reversed (low to high vs. high to low), but taking that into account, the values appear vastly different (0.349 vs. -3.752 for the easiest threshold difficulty). Am I interpreting these values incorrectly or is this an error in my model syntax? One thing I did do differently with my MGE model when compared with examples online is that I modeled all four groups at once whereas the examples I found typically only used two groups. I'm not sure if that may have had a detrimental effect or not. 

Thanks,

Daniel

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[Daniel McKelvey]

Ah yes. I missed that. Can IRTpars = T be used for a MutipleGroupClass model? When I tried to run it now, I got this error "Error in vcov[1L, 1L] : subscript out of bounds"
Thanks for the quick reply! 

[Phil Chalmers]

It's possible that was a bug; I vaguely remember fixing that recently on the dev version on Github. If you'd like, feel free to install from there by following the OS specific instructions; otherwise, the fix should be on the next major CRAN release. 

Phil

[Daniel McKelvey]

Thanks Phil! I'll use the d parameters until the update is released.