Multidimensional IRT and theta scores

[William Mitchell]

Dear STATA-list,

I've got a question relating to my earlier posts regarding how to convert my individual theta scores back to standardised "expected" questionnaire scores, if someone could help?

I've run rotated promax oblique factor analysis, identified 2 factors that load ~10 questions well, and used IRT GRM models (with instruction from the Stata IRT PDF (pg 14-18)).
I've generated individual person theta estimates for each of the respondents using:

predict theta, latent se(thetaSE)

We've run linear regression models, (dependent variable = theta score; independent variable = disease type) however, found that interpreting the theta estimate might be intuitively more difficult for readers. We would like to convert the individual theta scores back into an individual factor score, using the original 5-point Likert-scale format (for a total score)

We are looking for information similar to the information on TCCs, that can show what theta level corresponds to what cumulative raw (Likert) score.
Is there a way to re-calculate estimated total questionnaire theta-scores for each participant, into estimated total (standardized) Likert-scale scores?

Any help would be really great. And happy Easter! William

[Weiwen Ng]

I proposed a solution to calculate expected total scores in a response to the same question on your other thread. We do ask people not to double-post. I'll add that, as the FAQ states, screenshots of the data usually aren't helpful.

I'll also add that it doesn't actually seem like you may have fit a multidimensional IRT model. To do that, you'd need to type something like this:

gsem (A -> q1-q5) (B -> q6-q10), ologit variance(A@1 B@1) covariance(A*B)

If you omit the covariance option, you'll constrain the latent traits to be orthogonal. Since you specified that you used an oblique factor analysis to identify the factors, you probably don't want to constrain the traits to be orthogonal. My other response mentioned that explanatory IRT models are a thing. You can extend the code there to make this a multidimensional explanatory IRT model. Be aware that as you increase the number of latent dimensions, the estimation time can climb very considerably. While fitting a multidimensional IRT model may be the 'correct' thing to do, I'm not sure that there's necessarily a strong consensus that one must do so.

[Emmanuel Estrellado]

Hello, I am quite new here but I am interested to know if there are codes that would allow me to estimate item difficulty and discrimination for polytonous items in a multidimensional IRT model? Because I can't seem to find a way to extract item difficulty and discrimination.

Thank you very much.