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 Nicholas Turner posted on Wednesday, June 26, 2013 - 5:54 am
I have run an IRT model using binary indicator variables using the WLSMV estimator and theta parameterization. The output gives me the difficulty and discrimination parameters. I'm now running a graded response IRT model using 3 level categorical indicator variables using the MLR estimator and I wanted to now if similarly the difficulty and discrimination parameters can be obtained?
Many thanks
 Bengt O. Muthen posted on Wednesday, June 26, 2013 - 1:05 pm
That is not automatically given, but you can do it in Model constraint by comparing (1) and (2) of the paper:

http://www.statmodel.com/download/IRT1Version2.pdf
 Nicholas Turner posted on Friday, June 28, 2013 - 6:53 am
Thanks for the reply. I've had a look at the paper and I'm not sure I follow how I can use Model constraint to get the difficulty and discrimination parameters?
If it helps here is some of the syntax for my graded response IRT model:

Analysis:
estimator = MLR;

Model:
Dep by q18_a*1 q18_c q18_d q18_e q18_f q18_g q18_i q18_j q18_l q18_m q18_n
q18_o q18_p ;

Dep@1 ;

And here it is for the model when each indicator variable was recategorised as binary:

Analysis:
estimator = WLSMV;
parameterization = theta;
Model:
Dep by q18_a*1 q18_c q18_d q18_e q18_f q18_g q18_i q18_j q18_l q18_m q18_n
q18_o q18_p ;

Dep@1 ;
 Bengt O. Muthen posted on Friday, June 28, 2013 - 4:06 pm
I actually don't think you need to translate results but stay with the Mplus parameterization for the graded response model. It seems to be the parameterization used in the IRT literature. That is, with ordinal response as opposed to binary response, they seem to switch to the Mplus factor analytic parameterization. See for example section 4.1.1.1 in the book

Reckase (2011). Multidim. IRT. Springer.

as well as eqn (6) of the Psych Method article

Cai et al (2011). Generalized full-info....

Reckase gives a discussion of interpretations. In my view, the fact that IRT makes a parameterization switch when going from binary to ordinal speaks to using the factor analytic parameterization all the time.
 Bengt O. Muthen posted on Friday, June 28, 2013 - 4:08 pm
To comment on your inputs, you can use ML or WLSMV irrespective of binary or ordinal response. With ML you can use the default logit link or you can use probit link.
 Emily posted on Monday, March 03, 2014 - 11:26 pm
I have run the following model using MLR estimation:

f1 BY U1@1 U2-U20*;
f2 BY T1-T20@-1;
f2@1;
[f2@0];
f1 on f2;

This portion of the model (f1 BY U1@1 U2-U20*;) is the 2PL IRT model.

I am wondering what the appropriate conversion formula would be to get from the MPlus parameters to the IRT parameters. Is it simply the factor loading*sqrt(f1 var) or is it more complicated because of the second factor?

Thanks!
 Bengt O. Muthen posted on Tuesday, March 04, 2014 - 7:22 pm
You use the regular formula you point to when an item loads on only one factor. It doesn't matter that you have other items loading on other factors.

For multiple factors, see a new FAQ to be posted tomorrow.
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