gen.difficulty {mirt}

R Documentation

Generalized item difficulty summaries

Description

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.

Usage

gen.difficulty(mod, type = "IRF", interval = c(-30, 30), ...)

Arguments

mod	a single factor model estimated by mirt
type	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	interval range to search for 'IRF' type
...	additional arguments to pass to uniroot

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

References

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

Examples

## No test: 

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

## End(No test)

---