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
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
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
# \donttest{
mod <- mirt(Science, 1)
#>
Iteration: 1, Log-Lik: -1629.361, Max-Change: 0.50660
Iteration: 2, Log-Lik: -1617.374, Max-Change: 0.25442
Iteration: 3, Log-Lik: -1612.894, Max-Change: 0.16991
Iteration: 4, Log-Lik: -1610.306, Max-Change: 0.10461
Iteration: 5, Log-Lik: -1609.814, Max-Change: 0.09162
Iteration: 6, Log-Lik: -1609.534, Max-Change: 0.07363
Iteration: 7, Log-Lik: -1609.030, Max-Change: 0.03677
Iteration: 8, Log-Lik: -1608.988, Max-Change: 0.03200
Iteration: 9, Log-Lik: -1608.958, Max-Change: 0.02754
Iteration: 10, Log-Lik: -1608.878, Max-Change: 0.01443
Iteration: 11, Log-Lik: -1608.875, Max-Change: 0.00847
Iteration: 12, Log-Lik: -1608.873, Max-Change: 0.00515
Iteration: 13, Log-Lik: -1608.872, Max-Change: 0.00550
Iteration: 14, Log-Lik: -1608.872, Max-Change: 0.00318
Iteration: 15, Log-Lik: -1608.871, Max-Change: 0.00462
Iteration: 16, Log-Lik: -1608.871, Max-Change: 0.00277
Iteration: 17, Log-Lik: -1608.870, Max-Change: 0.00145
Iteration: 18, Log-Lik: -1608.870, Max-Change: 0.00175
Iteration: 19, Log-Lik: -1608.870, Max-Change: 0.00126
Iteration: 20, Log-Lik: -1608.870, Max-Change: 0.00025
Iteration: 21, Log-Lik: -1608.870, Max-Change: 0.00285
Iteration: 22, Log-Lik: -1608.870, Max-Change: 0.00108
Iteration: 23, Log-Lik: -1608.870, Max-Change: 0.00022
Iteration: 24, Log-Lik: -1608.870, Max-Change: 0.00059
Iteration: 25, Log-Lik: -1608.870, Max-Change: 0.00014
Iteration: 26, Log-Lik: -1608.870, Max-Change: 0.00068
Iteration: 27, Log-Lik: -1608.870, Max-Change: 0.00065
Iteration: 28, Log-Lik: -1608.870, Max-Change: 0.00019
Iteration: 29, Log-Lik: -1608.870, Max-Change: 0.00061
Iteration: 30, Log-Lik: -1608.870, Max-Change: 0.00012
Iteration: 31, Log-Lik: -1608.870, Max-Change: 0.00012
Iteration: 32, Log-Lik: -1608.870, Max-Change: 0.00058
Iteration: 33, Log-Lik: -1608.870, Max-Change: 0.00055
Iteration: 34, Log-Lik: -1608.870, Max-Change: 0.00015
Iteration: 35, Log-Lik: -1608.870, Max-Change: 0.00052
Iteration: 36, Log-Lik: -1608.870, Max-Change: 0.00010
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)
#>
Iteration: 1, Log-Lik: -2668.786, Max-Change: 0.18243
Iteration: 2, Log-Lik: -2663.691, Max-Change: 0.13637
Iteration: 3, Log-Lik: -2661.454, Max-Change: 0.10231
Iteration: 4, Log-Lik: -2659.430, Max-Change: 0.04181
Iteration: 5, Log-Lik: -2659.241, Max-Change: 0.03417
Iteration: 6, Log-Lik: -2659.113, Max-Change: 0.02911
Iteration: 7, Log-Lik: -2658.812, Max-Change: 0.00456
Iteration: 8, Log-Lik: -2658.809, Max-Change: 0.00363
Iteration: 9, Log-Lik: -2658.808, Max-Change: 0.00273
Iteration: 10, Log-Lik: -2658.806, Max-Change: 0.00144
Iteration: 11, Log-Lik: -2658.806, Max-Change: 0.00118
Iteration: 12, Log-Lik: -2658.806, Max-Change: 0.00101
Iteration: 13, Log-Lik: -2658.805, Max-Change: 0.00042
Iteration: 14, Log-Lik: -2658.805, Max-Change: 0.00025
Iteration: 15, Log-Lik: -2658.805, Max-Change: 0.00026
Iteration: 16, Log-Lik: -2658.805, Max-Change: 0.00023
Iteration: 17, Log-Lik: -2658.805, Max-Change: 0.00023
Iteration: 18, Log-Lik: -2658.805, Max-Change: 0.00021
Iteration: 19, Log-Lik: -2658.805, Max-Change: 0.00019
Iteration: 20, Log-Lik: -2658.805, Max-Change: 0.00017
Iteration: 21, Log-Lik: -2658.805, Max-Change: 0.00017
Iteration: 22, Log-Lik: -2658.805, Max-Change: 0.00015
Iteration: 23, Log-Lik: -2658.805, Max-Change: 0.00015
Iteration: 24, Log-Lik: -2658.805, Max-Change: 0.00013
Iteration: 25, Log-Lik: -2658.805, Max-Change: 0.00013
Iteration: 26, Log-Lik: -2658.805, Max-Change: 0.00011
Iteration: 27, Log-Lik: -2658.805, Max-Change: 0.00011
Iteration: 28, Log-Lik: -2658.805, Max-Change: 0.00010
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
# }