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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.
 Alvin  posted on Thursday, August 14, 2014 - 10:20 pm
Hi Dr Muthen,

I ran a two-parameter IRT model - with four factors. Given the number of integration points, it seems to take a long time for estimation ... My question is, in addition to using monte carlo integration (is this recommended?), are there alternative estimator methods (e.g. Bayesian) that may reduce computational time? Or does it make sense to run separate models for each component of the measure? but I am interested in the item response properties as well as the structure of this psychiatric construct. Also, the other question, in IRT models, is factor variance always fixed to 1, as demonstrated in mplus users guide?
 Bengt O. Muthen posted on Friday, August 15, 2014 - 7:51 am
With four factors you can use integration = montecarlo(5000). You can also use Bayes.

Factor variances are often fixed at 1 in IRT, but you can set the metric differently (e.g. fixing the first loading) in Mplus.
 Alvin  posted on Wednesday, August 20, 2014 - 1:30 am
Thanks Dr Muthen - I ran a 2-parameter LRT with a four-factor model with binary variables using Monte Carlo (5000) - mplus says I need to increase miterations which I did up to 1000 but still couldn't get the parameter estimates?
 Linda K. Muthen posted on Wednesday, August 20, 2014 - 5:58 am
Please send the output and your license number to support@statmodel.com.
 Alvin  posted on Saturday, August 30, 2014 - 7:22 pm
Hi Dr muthen can I clarify - in my 2-parameter binary IRT output, the discrimination parameters for some of my items are not significant with a high SE, is it correct to interprete this as evidence of the items not being able to statistically discriminate positive from negative cases? The threshold parameters however are significant. The other question is re multidimensional IRT, parameterization switches around automatically when a model of this kind is estimated? Many thanks
 Bengt O. Muthen posted on Sunday, August 31, 2014 - 11:03 am
Q1. That's right.

Q2. I think you are saying that with a single factor Mplus offers additional output with a re-parameterization into IRT parameters, but with multiple factors Mplus does not offer re-parameterized output. The reason is given in the FAQ:

IRT parameterization using Mplus thresholds

I recommend always using the default Mplus parameterization of thresholds and factor loadings.
 Alvin  posted on Sunday, August 31, 2014 - 11:02 pm
Thanks Dr Muthen - When running a multidimensional version of the 2PL model (with two factors), factor loadings can be interpreted as discrimination parameters? is the key distinction between multi- and unidimensional 2-PL that in a multidimensional model, the probability of endorsing a positive response depends on M latent variables and that item responses can be plotted against different latent variables (in this case severity based two sets of symptoms or factors)? when plotting CCIs one has to look at item charateristics as a function factor 1 and factor 2?
 Bengt O. Muthen posted on Monday, September 01, 2014 - 3:18 pm
Q1. The factor loadings are simply slopes in a logit or probit regression, so the interpretation is just like for such regression (see our Topic 2 handout or standard textbooks).

Q2. You want to plot against one factor holding other factors constant at for example their means (typically zero).
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