Implement ConQuest score command in TAM

Question

in the IRT software ConQuest you can use the command "score" to model multiple dimensions/latent variables using the same manifest variable/raw data, but different coding. For example:

score (1,2,3) (0,1,2) (0,1,0) ! items(1-3);

"recodes" the original scores from 1 to 3 in 0, 1, and 2 for the first dimension and to 0, 1, 0 for the second dimension (latent variable).

Do you know any way how to implement the same in the R package TAM (using the lavaan syntax or otherwise)? I am trying to run a PCM analysis.

Great thanks in advance!

KH

Answer 1

I didn't get an answer here, but I contacted Alexander Robitzsch, the author of the TAM package, and here's what he send me (published with his permission):

data(data.gpcm)
psych::describe(data.gpcm)
resp <- data.gpcm

# define three dimensions and different loadings
# of item categories on these dimensions
I <- 3  # 3 items
D <- 3  # 3 dimensions

# define loading matrix B
# 4 categories for each item (0,1,2,3)
B <- array( 0 , dim=c(I,4,D) )
for (ii in 1:I){
    B[ ii , 1:4  , 1 ] <- 0:3
    B[ ii , 1 ,2 ] <- 1
    B[ ii , 4 ,3 ] <- 1
            }
dimnames(B)[[1]] <- colnames(resp)
B[1,,]
  ##   > B[1,,]
  ##        [,1] [,2] [,3]
  ##   [1,]    0    1    0
  ##   [2,]    1    0    0
  ##   [3,]    2    0    0
  ##   [4,]    3    0    1

# test run
mod1 <- tam.mml( resp , B = B , control=list( snodes=1000 , maxiter=5)  )
summary(mod1)

I had to edit the code for my needs, of course, but something in particular might be of interest for all of you: For some reason, the B matrix only worked if I had also defined a 0 category, although my ratings/data only included values from 1 to 5:

B <- array( 0 , dim=c(9,6,5) ) # 9 items, 5 response cat. + 1, 5 latent dimensions
for (ii in 1:I){
  B[ ii , 1:6  , 1 ] <- 0:5
  B[ ii , 2 ,2 ] <- 1
  B[ ii , 2 ,3 ] <- 1
  B[ ii , 6 ,3 ] <- 1
  B[ ii , 6 ,4 ] <- 1
  B[ ii , 4 ,5 ] <- 1
}

dimnames(B)[[1]] <- colnames(X)
B[1,,]

Cheers, KH

Answer 2

Just as an extension to the above answer with TAM, here is how to run the same code with the mirt package, except using the generalized partial credit model instead of the Rasch model (Rasch model requires an explicit model argument for proper identification).

library(mirt)
gpcm_mats <- list(B[1,,], B[2,,], B[3,,])
sv <- mirt(resp, 3, itemtype = 'gpcm', 
           gpcm_mats = gpcm_mats, pars = 'values') #starting values
mod <- mirt(resp, 3, itemtype = 'gpcm', gpcm_mats = gpcm_mats)
coef(mod, simplify=TRUE)