fitting "rating scale model"...

[KwonHyun Kim]

  Hello,

  Is mirt able to fit "RSM; rating scale model" which is a constrained model of pcm..?

  I see "rsm" in 02-item_methods.R but it's commented in LoadPars.R

  So I wonder if it's okay to uncomment it to fit "RSM" (using Numerical Derivation) ?

  or is there any other convenient way to fit "RSM"? 

  If it's not possible in mirt, is there any other packages fitting RSM?

  I tried TAM, but the results are quite confusing, I seriously think it's not working because the estimation is not

  accurate even though N is 1e6

  

a = matrix(1, 4, 1)

d = matrix(seq(-2,2,len=4),4, 1)

d = cbind(0,d,d)

d = d+matrix(c(0,-1, 1), byrow=T, nrow=4, ncol=3)

d[,1]=0

dat <- mirt::simdata(a=a, d=d, N=100000, itemtype="gpcm")

mod1a <- TAM::tam.mml( resp=dat, control=list(maxiter=5000, progress=F, nodes=seq(-6,6,len=61),

                                              convD = .0001), irtmodel="RSM" )

summary(mod1a)

mod1a$item

  The result is

Item Parameters Xsi

          xsi se.xsi

Item_1  0.511  0.004

Item_2 -0.181  0.004

Item_3 -0.822  0.005

Item_4 -1.382  0.005

Cat1    1.400  0.006

  Could you tell us what's the problem of derivation in RSM so that we can look into it to see if I can solve it?

  

  

  

[robi...@ipn.uni-kiel.de]

I am not sure whether you really simulated from a rating scale model. Does not mirt parametrize d as "item intercepts"? Then, your code

d = matrix(seq(-2,2,len=4),4, 1)

would not be appropriate. I guess it should be rather

d <- outer( seq(-2,2,len=4) , 0:2 )

Alexander 

[Phil Chalmers]

I imagine mirt just parametrizes the model differently. They should give the same results after some linear transformation (log-likelihoods should match though). The difference probably is that mirt sets the first item's rating scale coefficient to 0 rather than using the typical sum to 0 constraint for these models. 

So, to obtain the generalized partial credit models, just add the rating intercept to the respective category intercepts.

> mod <- mirt(Science, 1, 'grsm')

Iteration: 20, Log-Lik: -1621.351, Max-Change: 0.00009

> (items <- coef(mod, simplify=TRUE)$items)

                   a1   d1    d2    d3      c

Comfort 0.832 4.53 2.201 -1.23  0.000

Work    1.399 4.53 2.201 -1.23 -1.242

Future  1.672 4.53 2.201 -1.23 -0.364

Benefit 1.499 4.53 2.201 -1.23 -0.895

> (graded_ds <- items[,2:4] + items[,5])

                  d1    d2     d3

Comfort 4.530 2.201 -1.230

Work    3.288 0.959 -2.472

Future  4.166 1.837 -1.594

Benefit 3.635 1.306 -2.125

Of course, this is for the graded rating scale model, but the idea is the same for the rsm (the rsm itemtype is currently offline and commented out due to an unfinished/slow derivative term that is currently being evaluated numerically. I haven't gotten around to fixing yet). Cheers. 

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