Re: Compensatory Between-Item MIRT

[Phil Chalmers]

On Tue, Oct 31, 2023 at 1:11 PM Hanif Akhtar <hanif.a...@gmail.com> wrote:

Dear all,

This thread is not specifically about the package, but I hope you can give me more insight regarding the theoretical issue of compensatory between-item MIRT. 

In literature, when talking about compensatory and non-compensatory models, mostly explains that "In the compensatory model, if an item on a test requires two different abilities, a person’s high abilities on the first dimension may compensate for the lack of ability on the second (or vice versa), thus making it still somewhat probable that the person will respond correctly to the item". Most literature only gives examples like this, when a single item measures two abilities, which implies a within-item model. In many papers, researchers often used a compensatory between-item model. However, only a few provide justification for why they use a compensatory model, instead of a non-compensatory one.

When you say compensatory between-item model that seems to be a bit of a misnomer. If the factor structure is that of a simple structure, where one and only one factor explains the manifest response variation, then there is no compensation going on at all. 

 

I want to use compensatory between-item MIRT. I develop reasoning tasks measuring two dimensions (let's say verbal and quantitative), and each item only loads on a single dimension. Theoretically, they are separate but highly correlated, so I want to use a between-item model. My supervisor challenged me: "If one task requires only verbal reasoning, then why does quantitative reasoning help solve it, and vice versa?"  His question implied that the compensatory model is only relevant to within-item model. 

There wouldn't be any compensation going on there though. There likely would be a relationship between verbal and quantitative, which is what appears in the interfactor structure (correlations), but someone's verbal skill doesn't necessarily tell you anything about their quantitative skills unless there happens to be a correlation --- in which case knowledge of one tells you something about the likely intensity of the other trait. So yes, compensatory models only apply to within-item structures. 

 

Is it true that the between-item model is non-compensatory in nature? If not, I hope someone could give a plausible explanation of how compensatory between-item works. What is the justification if I want to use a compensatory between-item MIRT?  

I wouldn't use the classification compensatory/non-compensatory for any between item models as they only apply to within item models where you're describing how the latent variables interact. HTH.

Phil

P.S. Note that the classical linear factor analysis model has the same 'compensatory' problem, which is why Thurstone and other psychometricians strongly encouraged finding the  'simple structure' as this removes the issue of how to model the interaction of multiple traits on single items. 

 

I appreciate it if anyone could share anything about this.

Best,

Hanif

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