Chi-square for IRT
Message/Author
 delphine courvoisier posted on Thursday, April 26, 2007 - 11:32 am
hello,

I estimated an IRT model on 14 items measured on a 5-point likert scale
using MLR. M+ indicates that THE CHI-SQUARE TEST IS NOT COMPUTED BECAUSE
THE FREQUENCY TABLE FOR THE LATENT CLASS INDICATOR MODEL PART IS TOO LARGE.
However, other programs do compute chi-square for this model. Is there a
way to bypass this problem and obtain chi-squares?

Another problem:
I estimate several different models. In each of these models, there are 8
items on a 5-point scale. The degree of freedom for each chi-square differ
because M+ delete a certain number of "cells in the latent class indicator
table" "due to extreme value". Could you please indicate a reference that
justifies this deletion?

 Linda K. Muthen posted on Friday, April 27, 2007 - 8:16 am
When the frequency table for chi-square is very large as in your situation, there are too many cells ( 5*5*5*etc.) to make the test meaningful. We don't recommend using it with over 8 binary indicators. I think you can find a discussion of this in the Agresti book.
 delphine courvoisier posted on Wednesday, May 02, 2007 - 12:54 am
thank you for your prompt answer. I would just like to ask some precisions. I know that the frequency table for a questionnaire with 14 questions and 5 modalities per question is 5^14. However, is there another goodness of fit statistic, given by Mplus, that could help to estimate if the model fits (i.e. absolute fit and not relative fit like AIC)? Second question: concerning the deletion of extreme value, I wish to publish examining several 8 items scales. The degrees of freedom should be the same. However, since the deletion is not always the same, the df differ. I am sure that the reviewers will ask why and I would like to cite a reference explaining the deletion and thus the difference in df.

thank you.
 Linda K. Muthen posted on Wednesday, May 02, 2007 - 8:52 am
I would look at the bivariate standardized residuals in TECH10.

You may find what you want in the Agresti book regarding deleted cells.