Calculating IMV values

Here is a slightly more complex example that takes advantage of irw to easily fetch a dataset and to then compute the InterModel Vigorish contrasting predictings for the 2PL to predictions from the 1PL for an example dataset (using cross-validation across 4 folds; see also the documentation in the related imv package). Note the irw_long2resp function which is helpful for reformatting IRW data from long to wide. We have also tried to further illustrate how the IMV can be used to understand predictions here.

Code

df<-irw::irw_fetch("gilbert_meta_2")  #https://github.com/itemresponsewarehouse/Rpkg
resp<-irw::irw_long2resp(df)
resp$id<-NULL
##1pl/Rasch model
m0<-mirt::mirt(resp,1,'Rasch',verbose=FALSE)
##2pl
ni<-ncol(resp)
s<-paste("F=1-",ni,"
             PRIOR = (1-",ni,", a1, lnorm, 0.0, 1.0)",sep="")
model<-mirt::mirt.model(s)
m1<-mirt::mirt(resp,model,itemtype=rep("2PL",ni),method="EM",technical=list(NCYCLES=10000),verbose=FALSE)
##compute IMV comparing predictions from 1pl and 2pl
set.seed(8675309)
omega<-imv::imv.mirt(m0,m1) #https://github.com/intermodelvigorish/imv_R
mean(omega)

[1] 0.01415356