problems with iteminfo for multidimensional model?

[Jay Verkuilen]

Dear Phil,

My grad student Peter Johnson (who is a group member) and I are running some multidimensional models and want to get item information functions in directions. iteminfo seems to be able to do this but I'm not sure it's doing things correctly. This code is lightly adapted from the iteminfo help file. 

## Customized test information plot dat <- expand.table(LSAT7)

# multidimensional mod <- mirt(dat, 2, TOL=1e-2) ii <- extract.item(mod, 1) Theta <- as.matrix(expand.grid(-4:4, -4:4)) ii45 <- iteminfo(ii, Theta, degrees=c(45,45)) # equal angle ii90 <- iteminfo(ii, Theta, degrees=c(90,0)) # first dimension only

ii0 <- iteminfo(ii, Theta, degrees=c(0,0)) # ??

plot(ii45)

points(ii90,col="blue")

points(ii45,col="red")

When these are plotted they end up generating different curves but they are perfectly

correlated. The look like bouncy balls, not at all what I'd expect a 2PL2D information curve

to look like. It seems like the function is plotting the item information for one dimension

at a time—generating values for one dimension before moving to the second, following the theta

grid—instead of generating the values in the order they should be to suggest a unimodal curve

in the direction of the angles chosen. It also doesn't make sense to me that the first dimension

angle would be 90, but perhaps I'm not understanding something or multiple somethings.

We can send additional code and examples if that would be helpful.

Thanks,

Jay

[Phil Chalmers]

Hi Jay,

The degrees input ultimate gets changed into radians first, after which it is cos()-ed to reflect the angular property. So 90 would drop a specific dimension, while 0 would include it (think 90 degrees as orthogonal), and these are used as weights when summing the information contribution (see Reckase, 2009). Here's what is happening internally:

cos(mirt:::d2r(90))  # numerically 0, so excluded
cos(mirt:::d2r(0))    # numerically 1, so completely included

I think your code should look something like this if you want to drop the information from both dimensions (see changes to last few lines). HTH for now.

## Customized test information plot
dat <- expand.table(LSAT7)

# multidimensional
mod <- mirt(dat, 2, TOL=1e-2)
ii <- extract.item(mod, 1)
Theta <- as.matrix(expand.grid(-4:4, -4:4))

ii45 <- iteminfo(ii, Theta, degrees=c(45,45)) # equal angle

ii90 <- iteminfo(ii, Theta, degrees=c(90,0)) # *second* dimension only
ii0 <- iteminfo(ii, Theta, degrees=c(90,90)) # drop both

plot(ii45)
points(ii90,col="blue")
points(ii0,col="red")

###

Phil

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