I am trying to work on how variable characteristics can help to determine variable structure and pattern. I am half way into the work though.
Are you asking can you compare the fit of the 1PL and 2PL models and use the difference to argue that that 1PL does not capture the variability in responses well? If so, yes you can. How depends on the software that you are using.
The 1-PL (Rasch) and 2-PL (Birnbaum) models of Item Response Theory (IRT) both imply that the items are unidimensional (i.e., that they measure a single underlying latent variable). Model misfit would indicate that there is a violation of the unidimensionality implication for either one of these models.
The 1-PL (Rasch) and 2-PL (Birnbaum) models of Item Response Theory (IRT) assume unidimensionality, but a misfit does not always mean unidimensionality for the item(s) is unacceptable. The Mokken Model (non parametric unidimensional model) sometimes fits when Rasch and Birnbaum does not. The Rasch and Birnbaum are very restrictive and may not fit for other reasons beside violations of unidimensionaliy. Maybe you might need a 3-Pl or 4PL model depending on your data. Or use a non parametric model to fit the data. Do you have information on the two and three way fits of your items, sometimes you might spot the problem. It can be used to detect misfitting items like you might use a residual analysis in factor analysis.
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