Computes profiled-likelihood based confidence intervals. Supports the inclusion of equality constraints. Object returns the confidence intervals and whether the respective interval could be found.
Usage
PLCI.mirt(
mod,
parnum = NULL,
alpha = 0.05,
search_bound = TRUE,
step = 0.5,
lower = TRUE,
upper = TRUE,
inf2val = 30,
NealeMiller = FALSE,
verbose = TRUE,
...
)Arguments
- mod
a converged mirt model
- parnum
a numeric vector indicating which parameters to estimate. Use
mod2valuesto determine parameter numbers. IfNULL, all possible parameters are used- alpha
two-tailed alpha critical level
- search_bound
logical; use a fixed grid of values around the ML estimate to determine more suitable optimization bounds? Using this has much better behaviour than setting fixed upper/lower bound values and searching from more extreme ends
- step
magnitude of steps used when
search_boundisTRUE. Smaller values create more points to search a suitable bound for (up to the lower bound value visible withmod2values). When upper/lower bounds are detected this value will be adjusted accordingly- lower
logical; search for the lower CI?
- upper
logical; search for the upper CI?
- inf2val
a numeric used to change parameter bounds which are infinity to a finite number. Decreasing this too much may not allow a suitable bound to be located. Default is 30
- NealeMiller
logical; use the Neale and Miller 1997 approximation? Default is
FALSE- verbose
logical; include additional information in the console?
- ...
additional arguments to pass to the estimation functions
References
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
Chalmers, R. P., Pek, J., & Liu, Y. (2017). Profile-likelihood Confidence Intervals in Item Response Theory Models. Multivariate Behavioral Research, 52, 533-550. doi:10.1080/00273171.2017.1329082
Neale, M. C. & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113-120.
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
# \donttest{
if(interactive()) mirtCluster() #use all available cores to estimate CI's in parallel
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
result <- PLCI.mirt(mod)
result
#> Item class parnam parnum value lower_2.5 upper_97.5 lower_conv
#> 1 Item.1 dich a1 1 0.9879254 0.6705382 1.3819761 TRUE
#> 2 Item.1 dich d 2 1.8560605 1.6203325 2.1474211 TRUE
#> 3 Item.2 dich a1 5 1.0808847 0.7816287 1.4614714 TRUE
#> 4 Item.2 dich d 6 0.8079786 0.6373152 0.9994390 TRUE
#> 5 Item.3 dich a1 9 1.7058006 1.1965700 2.6063138 TRUE
#> 6 Item.3 dich d 10 1.8042187 1.4754050 2.3765517 TRUE
#> 7 Item.4 dich a1 13 0.7651853 0.5211915 1.0554405 TRUE
#> 8 Item.4 dich d 14 0.4859966 0.3417041 0.6365806 TRUE
#> 9 Item.5 dich a1 17 0.7357980 0.4551545 1.0555079 TRUE
#> 10 Item.5 dich d 18 1.8545127 1.6438380 2.0976038 TRUE
#> upper_conv
#> 1 TRUE
#> 2 TRUE
#> 3 TRUE
#> 4 TRUE
#> 5 TRUE
#> 6 TRUE
#> 7 TRUE
#> 8 TRUE
#> 9 TRUE
#> 10 TRUE
mod2 <- 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
result2 <- PLCI.mirt(mod2)
result2
#> Item class parnam parnum value lower_2.5 upper_97.5 lower_conv
#> 1 Comfort graded a1 1 1.0417547 0.7008509 1.453043 TRUE
#> 2 Comfort graded d1 2 4.8641542 4.0112194 5.966782 TRUE
#> 3 Comfort graded d2 3 2.6399417 2.2332766 3.115799 TRUE
#> 4 Comfort graded d3 4 -1.4660135 -1.7996417 -1.171326 TRUE
#> 5 Work graded a1 5 1.2259618 0.8942261 1.620993 TRUE
#> 6 Work graded d1 6 2.9240027 2.4851419 3.430756 TRUE
#> 7 Work graded d2 7 0.9011651 0.6307977 1.195238 TRUE
#> 8 Work graded d3 8 -2.2665647 -2.6975967 -1.893557 TRUE
#> 9 Future graded a1 9 2.2933717 1.5687257 3.986967 TRUE
#> 10 Future graded d1 10 5.2339928 4.1279881 7.822343 TRUE
#> 11 Future graded d2 11 2.2137728 1.6589420 3.416513 TRUE
#> 12 Future graded d3 12 -1.9637062 -3.0256934 -1.453916 TRUE
#> 13 Benefit graded a1 13 1.0949151 0.7659052 1.501997 TRUE
#> 14 Benefit graded d1 14 3.3479196 2.8453841 3.940600 TRUE
#> 15 Benefit graded d2 15 0.9916289 0.7267311 1.282508 TRUE
#> 16 Benefit graded d3 16 -1.6882599 -2.0443917 -1.375841 TRUE
#> upper_conv
#> 1 TRUE
#> 2 TRUE
#> 3 TRUE
#> 4 TRUE
#> 5 TRUE
#> 6 TRUE
#> 7 TRUE
#> 8 TRUE
#> 9 TRUE
#> 10 TRUE
#> 11 TRUE
#> 12 TRUE
#> 13 TRUE
#> 14 TRUE
#> 15 TRUE
#> 16 TRUE
# only estimate CI's slopes
sv <- mod2values(mod2)
parnum <- sv$parnum[sv$name == 'a1']
result3 <- PLCI.mirt(mod2, parnum)
result3
#> Item class parnam parnum value lower_2.5 upper_97.5 lower_conv
#> 1 Comfort graded a1 1 1.041755 0.7008509 1.453043 TRUE
#> 2 Work graded a1 5 1.225962 0.8942261 1.620993 TRUE
#> 3 Future graded a1 9 2.293372 1.5687257 3.986967 TRUE
#> 4 Benefit graded a1 13 1.094915 0.7659052 1.501997 TRUE
#> upper_conv
#> 1 TRUE
#> 2 TRUE
#> 3 TRUE
#> 4 TRUE
# }