Unusual results with the ggum item type

[Deon de Bruin]

Dear colleagues

I hope you will be able to shed light on some unusual results we obtained when fitting the generalized graded unfolding model (GGUM). In our example we have six items (scored on a three-point rating scale: 0 to 2). We first fitted the generalized partial credit model (GPCM) and the GGUM with mirt to five items (omitting the second item). We also fitted the GGUM with Tendeiro’s GGUM package.

The mirt GGUM analysis did not properly converge after 500 iterations, but the max-change was relatively small.

Iteration: 500, Log-Lik: -6565.962, Max-Change: 0.00031

EM cycles terminated after 500 iterations.

 

The correlations between the thetas were as follows:

mirt.GPCM and mirt.GGUM: 0.999

mirt.GGUM and Tendeiro.GGUM: 0.999

mirt.GPCM and Tendeiro.GGUM: 0.999

These results did not suggest an unfolding process.

Adding a single item (labelled Item3) yielded the following correlations between the thetas:

mirt.GPCM and mirt.GGUM: 0.125

mirt.GGUM and Tendeiro.GGUM: 0.007

mirt.GPCM and Tendeiro.GGUM: 0.999

The thetas yielded by the mirt and Tendeiro GGUM packages now were very different and this appears to be the result of including a single item. Whereas the mirt GGUM analysis suggests an unfolding process, the Tendeiro GGUM analysis does not.  

It is possible that we might be overlooking something or making an error in specifying the ggum analysis in mirt. We include our R script (below) and the data with this message. We will appreciate it very much if you could comment or advise with respect to our results. In particular we hope to understand better why the results of the GGUM analyses with the two packages first are almost identical, and then dramatically different (when an extra item is added).

Deon de Bruin

###########

library(psych)

dat <- read.csv(file.choose())

### First do the analyses without Item2 and then with Item2

## Fit the GPCM
library(mirt)
datgpcm <- mirt(dat[, -2], 1, itemtype = "gpcm")
mirt.gpcm.theta <- fscores(datgpcm)

## Fit the GGUM (takes about 105 seconds to reach max iterations)
datggum <- mirt(dat[, -2], 1, itemtype = "ggum")
mirt.ggum.theta <- fscores(datggum)

## Fit the GGUM with Tendeiro's package
library(GGUM)
datmat <- as.matrix(dat)
gwsGGUM <- GGUM(data = datmat[, -2], C = 2)
Tendeiro.ggum.theta <- Theta.EAP(gwsGGUM)

## Find the correlations of the dominance and unfolding person measures
cor(mirt.gpcm.theta, mirt.ggum.theta, use = "complete.obs")
cor(mirt.gpcm.theta, Tendeiro.ggum.theta[, 2], use = "complete.obs")
cor(mirt.ggum.theta, Tendeiro.ggum.theta[, 2], use = "complete.obs")

### Scatterplots
plot(Tendeiro.ggum.theta[, 2], mirt.ggum.theta,
     xlab = "Tendeiro GGUM theta", ylab = "mirt GGUM theta")
plot(Tendeiro.ggum.theta[, 2], mirt.gpcm.theta,
     xlab = "Tendeiro GGUM theta", ylab = "mirt GPCM theta")
plot(mirt.ggum.theta, mirt.gpcm.theta,
     xlab = "mirt GGUM theta", ylab = "mirt GPCM theta")

[Phil Chalmers]

Hi Deon de Bruin,

The GGUM is rather sensitive to starting values, so sometimes it makes sense to try a handful of random starts to see if they converge to the same solution. When I run your code with mirt(..., GenRandomPars = TRUE) the model seems to converge to something closer to the GPCM competitor. Not sure if that helps in this case as I agree item 3 seems to be causing some convergence issues.

Phil

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[Deon de Bruin]

Thank you Phil. I will try out your suggestion.

Deon