IRT vs. Normal Score with Prelis? PreviousNext
Mplus Discussion > Categorical Data Modeling >
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 Jeehoon Kim posted on Saturday, February 26, 2011 - 11:14 pm
Dear Professors:

I've once asked you if IRT might be used to measure 9 binary indicators as an endogenous mediating variable in my path model and got confirmed.I've tested a measurement only model and final structural model, and got those fit indices.

For IRT measurement only model, overall fit indices are not good except RMSEA (CFI:.865, TLI: .819, RMSEA: .049, WRMR: 1.602). For my final structural model, fit indices are acceptable although WRMR is still high (CFI:.972, TLI: .963, RMSEA: .035, WRMR: 1.302).

The reason for poor fit indices in measurement only model is those variables are services utilized by caregivers, so some services are quite related.

Because a measurement only model was not good fitted to the data, I'd like to know if I need to find alternative or if it is fine to use.

A summed score was range of 0 to 8, and skewness is 1.08 and kurtosis is 1.34. If I can't use IRT measure in my structural model, can I use this summed score as a continuous variable? Or can I use a transformed score by normal score transformation with Prelis? For both models, treating it as continuous variable and with a normal score transformed variable, model fit indices are almost identical like CFI: .987, TLI: .971, RMSEA: .047, and WRMR: .961.

Any advice would be greatly appreciated.

Regards,
Jeehoon
 Jeehoon Kim posted on Sunday, February 27, 2011 - 1:16 pm
Or what if I can treat this summed score variable as a categorical variable? Thank you for your any advice or suggestion.
 Linda K. Muthen posted on Monday, February 28, 2011 - 5:06 pm
I would not inlcude an ill-fitting IRT model as part of a larger model. I would instead include the needed residual covariances using the weighted least squares estimator. Summing the categorical variables ignores the fact that the model does not fit.
 Jeehoon Kim posted on Tuesday, March 01, 2011 - 7:18 pm
Thank you for your suggestion. I, however, wonder if including residual covariates would violate local independence assumption with IRT measure.
I'm a beginner to use IRT, so I might be wrong, but want to make sure of it.

Also, if I will be fine to include residual covariates, and I would like to do multiple group analysis further, how can I handle with residual covariates then? Any advice will be greatly appreciated. Thanks again!

Jeehoon
 Bengt O. Muthen posted on Tuesday, March 01, 2011 - 9:31 pm
Having correlated residuals violates the local independence assumption of IRT. But you have to make a distinction here - this violation is only a problem if your model does not include the correlated residuals. Including the correlated residuals, you are no longer assuming the standard IRT, so you are ok.

Multiple-group analysis can also handle correlated residuals.
 Jeehoon Kim posted on Tuesday, March 01, 2011 - 9:37 pm
Thank you so much for clarifying this issue. I now can move it forward.

Many thanks,
Jeehoon
 Jeehoon Kim posted on Tuesday, March 01, 2011 - 10:43 pm
Dear Bengt,

Could you let me know any paper have allowed residual covariates with IRT measure? Thanks.

Jeehoon
 Bengt O. Muthen posted on Wednesday, March 02, 2011 - 12:25 am
None comes to mind off hand - you may want to ask on SEMNET. But bi-factor modeling can be seen as a version of this where a group of items correlate beyond what a single factor can explain.
 Jeehoon Kim posted on Wednesday, March 02, 2011 - 12:54 am
Thank you for the information. I will ask on SEMNET. I have one more question though.

For multiple group analysis for a path model with two latent variables, should I test measurement invariance with only measurement model separately or with my whole model? If it is latter, after checking measurement invariance, can I compare path coefficients with all free model and equality constraints model?
Again, thanks for your valuable advice.

Jeehoon
 Bengt O. Muthen posted on Wednesday, March 02, 2011 - 4:47 pm
Those are questions with too long answers which are covered in our courses. Briefly:

You have to make that decision and it depends on the circumstances.

You can compare path coefficients when the measurement models have a sufficient degree of invariance.
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