Function provides the four generalized item difficulty representations for polytomous response models described by Ali, Chang, and Anderson (2015). These estimates are used to gauge how difficult a polytomous item may be.
gen.difficulty(mod, type = "IRF", interval = c(-30, 30), ...)a single factor model estimated by mirt
type of generalized difficulty parameter to report.
Can be 'IRF' to use the item response function (default),
'mean' to find the average of the difficulty estimates,
'median' the median of the difficulty estimates, and
'trimmed' to find the trimmed mean after removing the first
and last difficulty estimates
interval range to search for 'IRF' type
additional arguments to pass to uniroot
Ali, U. S., Chang, H.-H., & Anderson, C. J. (2015). Location indices for ordinal polytomous items based on item response theory (Research Report No. RR-15-20). Princeton, NJ: Educational Testing Service. http://dx.doi.org/10.1002/ets2.12065
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
# \donttest{
mod <- mirt(Science, 1)
coef(mod, simplify=TRUE, IRTpars = TRUE)$items
#> a b1 b2 b3
#> Comfort 1.041755 -4.669193 -2.5341299 1.4072541
#> Work 1.225962 -2.385068 -0.7350678 1.8488053
#> Future 2.293372 -2.282226 -0.9652918 0.8562529
#> Benefit 1.094915 -3.057698 -0.9056673 1.5419094
gen.difficulty(mod)
#> Comfort Work Future Benefit
#> -2.3089094 -0.5741303 -0.9207845 -0.8530161
gen.difficulty(mod, type = 'mean')
#> Comfort Work Future Benefit
#> -1.9320231 -0.4237770 -0.7970883 -0.8071519
# also works for dichotomous items (though this is unnecessary)
dat <- expand.table(LSAT7)
mod <- mirt(dat, 1)
coef(mod, simplify=TRUE, IRTpars = TRUE)$items
#> a b g u
#> Item.1 0.9879254 -1.8787456 0 1
#> Item.2 1.0808847 -0.7475160 0 1
#> Item.3 1.7058006 -1.0576962 0 1
#> Item.4 0.7651853 -0.6351358 0 1
#> Item.5 0.7357980 -2.5204102 0 1
gen.difficulty(mod)
#> Item.1 Item.2 Item.3 Item.4 Item.5
#> -1.8787448 -0.7475182 -1.0576961 -0.6351601 -2.5204127
gen.difficulty(mod, type = 'mean')
#> Item.1 Item.2 Item.3 Item.4 Item.5
#> -1.8787456 -0.7475160 -1.0576962 -0.6351358 -2.5204102
# }