Operating Characteristic Curve

[BE PE]

Hi,

First I'd like to say thanks for a terrific R package!

I wonder if it's possible, in some way, to plot so called OCCs. It's possible in the package ltm, but for various reasons I'd prefer to do it in mirt. My understanding is that trace lines show each category with adjacent categories subtracted (relative probabilities, I guess), whereas OCCs are absolute probabilities (please correct me if I'm wrong).

I also have a general IRT question: Is it possible to correlate residuals? (Why not?)

Cheers!

[Phil Chalmers]

On Thu, Mar 30, 2017 at 5:16 PM, BE PE <perss...@gmail.com> wrote:

Hi,

First I'd like to say thanks for a terrific R package!

I wonder if it's possible, in some way, to plot so called OCCs. It's possible in the package ltm, but for various reasons I'd prefer to do it in mirt. My understanding is that trace lines show each category with adjacent categories subtracted (relative probabilities, I guess), whereas OCCs are absolute probabilities (please correct me if I'm wrong).

See the plot() generic, particularly the 'type' input, as well as itemplot(). There are numerous examples of this through the help files as well.  

I also have a general IRT question: Is it possible to correlate residuals? (Why not?)

What's a residual for a categorical variable? That should answer you question.  

Cheers!

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[BE PE]

Hi,

I have to return to this. Maybe I used inappropriate terminology. What I'm looking for is cumulative response curves, and I can't find any examples of that in the documentation. Please point me in the right direction.

Cheers!

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[Phil Chalmers]

On Tue, May 9, 2017 at 5:54 PM, BE PE <perss...@gmail.com> wrote:

Hi,

I have to return to this. Maybe I used inappropriate terminology. What I'm looking for is cumulative response curves,

I'm not familiar with that term. If you know how to do it in ltm then please post that code and we can help you figure out how to do it in mirt.

 

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[BP]

OK, so what I want is called "OCCu" in ltm (item operation characteristic curves) in ltm. What I find in mirt is ICCs (category characteristic curves).

library(mirt)
library(ltm)

test <- ltm::grm(Science)
ltm::plot.grm(test, type = "OCCu")
#ltm::plot.grm(test, type = "ICC") is the same as itemplot(x, type="trace") in mirt

I've seen these described as cumulative response curves as well, although IRT terminology can get quite confusing, as many things seem to have multiple names. My understand is that each ICC is calculated by subtracting adjacent probabilities, and OCCs are curves for each response category or higher.

 

[Phil Chalmers]

I see. No, those don't exist in mirt (they are kind of weird, no? I don't see why they are more useful than the probability plots themselves.....). You could of course build them up manually, but I don't really have any interest in adding these in natively. 

#-------------------------------------------------------------------------------------------

library(mirt)

mod <- mirt(Science, 1)

Theta <- matrix(seq(-4,4,length.out=1000))

ii <- extract.item(mod, 1)

P <- probtrace(ii, Theta)

cP <- t(apply(P, 1, cumsum))[,-4]

cPdf <- data.frame(p = 1 - as.numeric(cP), q = as.numeric(cP), 

                   Theta=Theta, cat = rep(1:3, each = nrow(cP)))

xyplot(p ~ Theta, cPdf, group = cPdf$cat, type = 'l', auto.key = TRUE) # type = 'OCCu'

xyplot(q ~ Theta, cPdf, group = cPdf$cat, type = 'l', auto.key = TRUE) # type = 'OCCl'

# compare

dat <- Science

library(ltm)

lmod <- ltm::grm(dat)

plot.grm(lmod, type = 'OCCu')

plot.grm(lmod, type = 'OCCl')

Phil

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[BP]

Weird or not, I actually think they're simpler to understand. Thanks a lot for the code (and your, usual, quick help)!