M2 of bifactor models with dimensionality reduction technique

[MLee72]

Hi Phil,

Thank you for your work and this great package!

I'm employing bi-factor models with the MIRT package and trying to assess the model fit with M2. I know the 'bfactor' function converges fast due to the dimensionality reduction technique, but M2 statistics take too long to be calculated, and print message for the suggestion of QMC . Isn't the technique applied to the M2 calculation? If I have to use the QMC technique, how many nodes are appropriate to reduce the computation time but retain stability and accuracy?

Here are the model and estimation codes I'm using.

############################################################ sfac <- rep(1:4, each=5) # every 5 items are loaded on each specific factor

i20.bi.mod <- "G = 1-20 S1 = 1-5 S2 = 6-10 S3 = 11-15 S4 = 16-20

           CONSTRAIN = (1-5, a2)
           CONSTRAIN = (6-10, a3)
           CONSTRAIN = (11-15, a4)
           CONSTRAIN = (16-20, a5)

" ######## --- equality constraints on the specific factor loadings

out <- mirt::bfactor(data=res, model=sfac, model2 = i20.bi.mod, itemtype = "2PL", quadpts=21, technical = list(NCYCLES = 2000))

M2.out <- mirt::M2(out, type="M2*", quadpts=21) ##############################################################

Thank you so much! Best, Minho Lee

[philchalmers]

In principle I believe M2() and other functions can use the dimension reduction technique, though this has not been implemented yet (there are stubs in the package with #TODO tags to remind me to do this at some point...). For now I believe you're stuck with the QMC approach, though know that this feature is on the long todo list. Note that setting QMC=TRUE will use 5000 fixed quadrature by default, which should run faster than the quadpts input with many dimensions as it doesn't explode due to the curse of dimensionality.