Depending on what software you use for analysis, you have to specify relationship(covariance) between latent constructs. Otherwise, IRT's conditional independence assumption may be reason for 'no relationship'.
Hope this helps
Matt
Hi, Matthew,
Thank you for your interest in this topic.
(1) In MIRT, all the latent variables represent the scores associated with sub-scales, but no latent variable is for Overall scale. Further, the covariance between sub-scales is the linear part of the mutual relations between subscales, the mutual infomation beyond the linear part and those interactions associated with more than two sub-scales are totally missing in MIRT. Again, key argument is that, in MIRT, there is no way to represent the Overall Score.
(2) In multivariate statistics, the ONLY reason to put all the variables into a single system is that they are interactive, otherwise, those (jointly) independent variables should be studied individually (and therefore, easily). In IRT, the assumption of conditional independence shouldn't be there because, in real world, it is rare to be true. Now, issue is that, without any unrealistic precondition, why IRT can not express its OVERALL score in terms of its sub-scores, i.e. Does IRT have its OVERALL score and what latent variable (theta-parameter) in IRT stands for?
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