c parameter's meaning in Rating Scale model

[와우리말]

I analyzed 5 items with a 4-point Likert scale using the RSM model in the mirt package. The analysis estimated parameters a, b1, b2, b3, and c. What does the parameter c represent? In the category characteristic curves, I observed that as c becomes smaller, the OCC curves shift to the right. Does c represent easiness?"  

[Phil Chalmers]

Yes, and this is one of the modeling benefits of the rating scale model. It's not entirely necessary to obtain such information though as generalized difficulty terms do exist (multiply by -1 to turn these into easiness estimates), and similar information comes out of observing the raw scores. See below.

####

library(mirt)
itemstats(Science)
# based on marginal scores, item easiness goes from Work -> Benefit -> Future -> Comfort

mod <- mirt(Science, itemtype = 'rsm')
coef(mod, simplify=TRUE)$items
# model-based item easiness go from Work -> Benefit -> Future -> Comfort

mod2 <- mirt(Science, itemtype = 'gpcm')
coef(mod2, simplify=TRUE)$items
gen.difficulty(mod2) *-1
# model-based generalized 'easiness' estimates go from Work -> Benefit -> Future -> Comfort

###

Phil

On Mon, Jun 16, 2025 at 10:56 AM 와우리말 <waur...@snuecse.org> wrote:

I analyzed 5 items with a 4-point Likert scale using the RSM model in the mirt package. The analysis estimated parameters a, b1, b2, b3, and c. What does the parameter c represent? In the category characteristic curves, I observed that as c becomes smaller, the OCC curves shift to the right. Does c represent easiness?"  

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