IRT with Theta/Delta parameterization PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Laura Stapleton posted on Wednesday, October 15, 2008 - 11:23 am

When modeling with variables identified as categorical, I understand that the choice of scaling of the latent item response variances (to 1.0) or the item residual variances (to 1.0) is somewhat arbitrary.

With WLSMV estimation, it appears that the delta parameterization is used as a default (latent item response variances are set to 1.0).

With ML estimation (with numerical integration), when requesting LINK=PROBIT, it appears that the theta parameterization is used (item residual variances are set to 1.0).

Is this correct?
Is there any particular reason why this is the case?
Thank you!
 Linda K. Muthen posted on Wednesday, October 15, 2008 - 3:06 pm
In maximum likelihood, scale factors are not used and residual variances are fixed to one for probit and pi squared divided by three for logit. The former is not the Theta parameterization because in multiple group or growth models, the residual variances cannot be estimated. They are fixed in all groups and at all timepoints.
 Lisa M. Yarnell posted on Friday, June 17, 2016 - 12:11 pm
Hello, I have estimated binary IRT models as factor models with categorical indicators in the past. Output automatically included the estimated parameters in both factor model parameterization (traditional factor loading and thresholds) as well as IRT parameterization.

I am now estimating an IRT model where the indicators have multiple categories (partial credit model).

Mplus is not automatically showing the IRT parameterization values as I have seen before. But the paper "IRT in Mplus" by Tihomir Asparouhov and Bengt Muthen, dated September 24, 2015, states regarding the PCM: "All of these parameters can be found in the IRT PARAMETERIZATION section of the Mplus output" (p. 8).

Is there a command I have to use, in order to see the a, b, and di through dj parameters? I am sorry for any oversight on my part. I also checked the Mplus manual and did not see this detail.

Thank you.
 Bengt O. Muthen posted on Friday, June 17, 2016 - 1:41 pm
Please send your output and license number to Support.
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