Difference between grsm and rsm model

[Irshad Mujawar]

Hello Phil,

In above shown images there are tow equations; upper one is "RSM" (Rating Scale Model ) (from CatR package) and below one is "grsm" model  form mirt package.

When I am using CatR package to simulate the RSM parameters for 6 items, I am getting parameter names as lambda and deltas

> library(catR)
> genPolyMatrix(6, 4, model = "RSM")
  lambdaj delta1 delta2 delta3
1  -0.626  0.487  0.738  0.576
2   0.184  0.487  0.738  0.576
3  -0.836  0.487  0.738  0.576
4   1.595  0.487  0.738  0.576
5   0.330  0.487  0.738  0.576
6  -0.820  0.487  0.738  0.576

whereas when I use mirt() I get for grsm as I am getting parameters as a1, di's and c

> data(Science)
> mod_grsm=mirt(Science,1,'grsm')
Iteration: 17, Log-Lik: -1621.351, Max-Change: 0.00006
> coef(mod_grsm)
$Comfort
       a1    d1    d2    d3 c
par 0.832 4.529 2.201 -1.23 0


$Work
       a1    d1    d2    d3      c
par 1.399 4.529 2.201 -1.23 -1.242


$Future
       a1    d1    d2    d3      c
par 1.671 4.529 2.201 -1.23 -0.364


$Benefit
       a1    d1    d2    d3      c
par 1.498 4.529 2.201 -1.23 -0.894


$GroupPars
    MEAN_1 COV_11
par      0      1

How can I relate here these two sets of  parameters?
 

Even the coef(mod_grsm, IRTpars=T) is returning the same output as above.




Thanking you,

Irshad

[Phil Chalmers]

These models are not the same. mirt uses the graded response model rating scale, catR uses the divide by total version, so they cannot be equated. 

But you should ask yourself, why would you want rating scale items in a CAT anyway? When you think about it, RSMs are pointless here. You could always create generalized partial credit models (or graded in mirt) from RSMs by simply adding the trailing constant term into the other intercepts. So, just translate the parameters into partial credit or graded response model variants for each item instead of trying to work with the RSMs directly.

Phil 

Thanking you,

Irshad

--
You received this message because you are subscribed to the Google Groups "mirt-package" group.
To unsubscribe from this group and stop receiving emails from it, send an email to mirt-package...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

[Irshad Mujawar]

Thank you very much for your reply.


I need Rating Scale Model because I have an item bank  where the same set of response alternatives is applied to all the items in the test and for these kind of items isn't RSM suppose to fit the best?

I am afraid if I have comprehended the part getting gpcm from RSMs . Phil, can you please give me an example?

[Phil Chalmers]

On Fri, Mar 27, 2015 at 12:33 AM, Irshad Mujawar <irshadmuj...@gmail.com> wrote:

Thank you very much for your reply.


I need Rating Scale Model because I have an item bank  where the same set of response alternatives is applied to all the items in the test and for these kind of items isn't RSM suppose to fit the best?

No, that's not what the RSM is for. What it does is assume all of the response categories are exactly equidistant, and that the items differ only in terms of their difficulty. This model rarely ever fits the data, which is why the partial credit and generalized partial credit models are used more often (or in the mirt package, it's why the graded response model is used much more often than the rating scale variant).

 

I am afraid if I have comprehended the part getting gpcm from RSMs . Phil, can you please give me an example?

Check the mirt pdf manual and study the equations; you should be able to see how the rating scale models are really just partitioned from their single item families.

Phil