philchalmers
commented
4 years ago There's a google forum called mirt-package where questions like these are generally more appropriate (Github is reserved for actual coding problems/feature requests). Nevertheless, I'll try and answer your question.
Currently, the mirt package does not reflect any error-in-variables method directly as was discussed by Schonfield, but that's not to say close approximations are not possible. Mislevy's work in the 1990s discusses such methods via plausible-value imputations for the theta values, where the uncertainty in the trait estimates is imputed stochastically. This is then repeated a number of times and averaged over using Rubin's formula to obtain the estimates + SEs. That should be fairly close to estimation the full joint distribution, though of course estimating everything at once has some efficiency benefits. HTH.
Not sure whether to ask here, but here goes. I read a series of papers by Lynne Steuerle Schofield, who argues for a modeling approach (Mixed Effects Structural Equations (MESE)) that takes into account the measurement error in trait estimates when estimating regression models (i.e. kind of error-in-variables approach). This relies on some of the data from the IRT model fit. I was unable to find any R package that can accomplish this. Is this something one could accomplish with mirt, perhaps in conjunction with another package? I am thinking one would first fit the mirt IRT model, and then input this to some function that wraps the usual modeling functions in R and uses the IRT information from the mirt fit object.
The current formula interface in mirt() seems to only be able adding explanatory covariates, i.e. covariates that predict theta but aren't items/indicators of the trait as such (say, age).
Refs (there are more):