questions about GRM parameters

[Pierre Michel]

Hello Phil,

I fitted a multidimensional graded response model to my data, my model is called mm, here is what I get using the function coef(mm) (for the first item)

$item1
       a1 a2 a3 a4 a5 a6 a7 a8 a9    d1   d2    d3     d4
par 3.398  0  0  0  0  0  0  0  0 3.942 1.88 0.092 -1.985

My item has 5 response categories, so it is normal to get 4 item-step parameters. My question is about the ordering of these parameters. Are the highest values correspond to the highest response categories ?

If so, I would expect an other ordering... I hope that my question is clear enough.

Thanks in advance.

Pierre

[Phil Chalmers]

Hi Pierre,

The intercepts are ordered from highest to lowest, where each corresponds to the threshold parameters. They are constrained to be ordered here because of the graded response model parameterization, and represent the threshold required to move from category 1 to 2 (d1), category 2 to 3 (d2), and so on.

You might feel more comfortable playing around with the model graphically first, which can be loaded with the `itemplot(shiny=TRUE)` interface. Cheers.

Phil

On Fri, Jan 16, 2015 at 9:20 AM, Pierre Michel <aliasj...@gmail.com> wrote:

Hello Phil,

I fitted a multidimensional graded response model to my data, my model is called mm, here is what I get using the function coef(mm) (for the first item)

$item1
       a1 a2 a3 a4 a5 a6 a7 a8 a9    d1   d2    d3     d4
par 3.398  0  0  0  0  0  0  0  0 3.942 1.88 0.092 -1.985

My item has 5 response categories, so it is normal to get 4 item-step parameters. My question is about the ordering of these parameters. Are the highest values correspond the to the highest response categories ?

If so, I would expect an other ordering... I hope that my question is clear enough.

Thanks in advance.

Pierre

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[Pierre Michel]

Thanks for the tip Phil,

I now understand better my problem. I would like to convert the slope intercept parameters into traditional IRT parameters. After "playing" with the shiny interface as you advised, it produced an error in the interface when checking both the boxes ("multidimensional" and "IRT parametrization").

As explained in the help of the function coef() it is not possible to do that when dealing with multidimensional models. Can you provide me more details about this issue ?

IRT parameters seem more intuitive to describe the item properties. For polytomous items, I am used to provide the difficulty parameters in the ascendant order (the highest category being more difficult to answer than the lowest). Moreover, in my model I fixed constraints on the discrimination parameters and I considered what is called in the literature "between-items multidimensionality", so only one discrimination parameter is estimated for one item, the others being fixed to 0. Is this still a problem to get the IRT parameters ?

Thanks

[Phil Chalmers]

On Fri, Jan 16, 2015 at 10:15 AM, Pierre Michel <aliasj...@gmail.com> wrote:

Thanks for the tip Phil,

I now understand better my problem. I would like to convert the slope intercept parameters into traditional IRT parameters. After "playing" with the shiny interface as you advised, it produced an error in the interface when checking both the boxes ("multidimensional" and "IRT parametrization").

As explained in the help of the function coef() it is not possible to do that when dealing with multidimensional models. Can you provide me more details about this issue ?

It might be possible, but I don't (and won't support) it. MIRT models make much more sense in the slope intercept form to see the connection to non-linear factor analysis: a1 * theta1 + a2 * theta2 + dk, rather than some mix of weighted minus terms. I only included the classical IRT parameterization transformations for didactic purposes, but the whole package is built on the slope-intercept parameterizations for all models. 

In many ways, I think the initial IRT models were misguided in their parameterization, because when you think that IRT is intimately connected to non-linear factor analysis then the a*(theta - b) approach seems rather counterintuitive and cumbersome (i.e., in a linear or logistic regression, you would never model your slopes and intercepts like that). 

 

IRT parameters seem more intuitive to describe the item properties. For polytomous items, I am used to provide the difficulty parameters in the ascendant order (the highest category being more difficult to answer than the lowest). Moreover, in my model I fixed constraints on the discrimination parameters and I considered what is called in the literature "between-items multidimensionality", so only one discrimination parameter is estimated for one item, the others being fixed to 0. Is this still a problem to get the IRT parameters ?

That's not a problem, but if there are several orthogonal factors you might benefit from using the bfactor() function to retain better numerical precision (or switch to the MHRM method). Cheers.

Phil

[Pierre Michel]

In fact, I already use the MH-RM method to estimate my GRM (I considered 9 factors that are correlated, not orthogonal, this is one of the asumptions of my theoretical model). Can I still use the following reparametrization to provide the IRT parameters:

bk = - ( dk / a ) or is there an issue due to the factors correlations ?

[Phil Chalmers]

On Fri, Jan 16, 2015 at 11:05 AM, Pierre Michel <aliasj...@gmail.com> wrote:

In fact, I already use the MH-RM method to estimate my GRM (I considered 9 factors that are correlated, not orthogonal, this is one of the asumptions of my theoretical model). Can I still use the following reparametrization to provide the IRT parameters:

bk = - ( dk / a ) or is there an issue due to the factors correlations ?

Excellent :-)  That approach will work if each item contains exactly 1 non-zero slope parameter, and no the correlations do not affect the transformation in this case. Cheers.

Phil

[Luis Anunciação]

Phil, I read on Reise (p.387 , link https://books.google.com.br/books?id=yDiLBQAAQBAJ&pg=PA387&lpg=PA387&dq=samejima+1+vs+2-3+threshold&source=bl&ots=Yn0K7JDW79&sig=c71oZE1Mfkb60fKUIRj6DkmHC3I&hl=pt-BR&sa=X&ved=0ahUKEwiN17Wh1M7aAhXDjZAKHeIpB9wQ6AEIKzAA#v=onepage&q&f=false image attached)

That GRM thresholds are 1 vs 2 and 3 and 4 ; then, 1 and 2, vs 3 and 4 , then 1 and 2 and 3 vs 4. 

But you said, "They are constrained to be ordered here because of the graded response model parameterization, and represent the threshold required to move from category 1 to 2 (d1), category 2 to 3 (d2), and so on."

Could you please make this point clear?

Thanks much for your always support.

[Phil Chalmers]

Reise's definition is more technically correct. I wasn't talking about the general setup in the model itself, more how to interpret the transition between categories via the ordinal intercepts. HTH.

Phil

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