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Function to calculate expected value of item

Source: R/expected.item.R
expected.item.Rd

Given an internal mirt object extracted from an estimated model compute the expected value for an item given the ability parameter(s).

Usage

expected.item(x, Theta, min = 0, include.var = FALSE)

Arguments

x

an extracted internal mirt object containing item information (see extract.item)

Theta

a vector (unidimensional) or matrix (multidimensional) of latent trait values

min

a constant value added to the expected values indicating the lowest theoretical category. Default is 0

include.var

logical; include the model-implied variance of the expected scores as well? When TRUE will return a list containing the expected values (E) and variances (VAR)

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

See also

extract.item, expected.test

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


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
extr.2 <- extract.item(mod, 2)
Theta <- matrix(seq(-6,6, length.out=200))
expected <- expected.item(extr.2, Theta, min(Science[,1])) #min() of first item
head(data.frame(expected, Theta=Theta))
#>   expected     Theta
#> 1 1.013391 -6.000000
#> 2 1.014407 -5.939698
#> 3 1.015498 -5.879397
#> 4 1.016672 -5.819095
#> 5 1.017933 -5.758794
#> 6 1.019289 -5.698492

expected.item(extr.2, Theta, min(Science[,1]), include.var=TRUE)
#> $E
#>   [1] 1.013391 1.014407 1.015498 1.016672 1.017933 1.019289 1.020744 1.022308
#>   [9] 1.023988 1.025791 1.027727 1.029805 1.032035 1.034427 1.036992 1.039742
#>  [17] 1.042690 1.045848 1.049231 1.052853 1.056729 1.060875 1.065309 1.070047
#>  [25] 1.075108 1.080511 1.086276 1.092422 1.098971 1.105943 1.113361 1.121247
#>  [33] 1.129622 1.138510 1.147932 1.157911 1.168469 1.179625 1.191402 1.203817
#>  [41] 1.216889 1.230634 1.245068 1.260201 1.276046 1.292610 1.309898 1.327913
#>  [49] 1.346654 1.366117 1.386296 1.407180 1.428756 1.451008 1.473916 1.497459
#>  [57] 1.521611 1.546346 1.571635 1.597448 1.623754 1.650519 1.677712 1.705300
#>  [65] 1.733251 1.761532 1.790113 1.818965 1.848058 1.877365 1.906859 1.936516
#>  [73] 1.966312 1.996222 2.026225 2.056299 2.086421 2.116571 2.146726 2.176865
#>  [81] 2.206964 2.237001 2.266952 2.296794 2.326501 2.356050 2.385416 2.414575
#>  [89] 2.443504 2.472180 2.500583 2.528693 2.556494 2.583970 2.611109 2.637904
#>  [97] 2.664348 2.690439 2.716178 2.741571 2.766624 2.791350 2.815763 2.839881
#> [105] 2.863722 2.887310 2.910668 2.933821 2.956795 2.979616 3.002311 3.024906
#> [113] 3.047424 3.069889 3.092321 3.114739 3.137157 3.159587 3.182039 3.204516
#> [121] 3.227018 3.249541 3.272079 3.294617 3.317140 3.339628 3.362056 3.384398
#> [129] 3.406624 3.428701 3.450594 3.472269 3.493688 3.514816 3.535615 3.556050
#> [137] 3.576087 3.595693 3.614838 3.633495 3.651638 3.669246 3.686301 3.702787
#> [145] 3.718692 3.734007 3.748728 3.762852 3.776380 3.789316 3.801665 3.813436
#> [153] 3.824638 3.835286 3.845391 3.854970 3.864039 3.872615 3.880715 3.888358
#> [161] 3.895562 3.902347 3.908731 3.914733 3.920370 3.925662 3.930626 3.935280
#> [169] 3.939639 3.943720 3.947540 3.951112 3.954452 3.957572 3.960487 3.963208
#> [177] 3.965749 3.968118 3.970329 3.972390 3.974312 3.976102 3.977771 3.979325
#> [185] 3.980773 3.982120 3.983375 3.984543 3.985630 3.986642 3.987583 3.988458
#> [193] 3.989273 3.990030 3.990735 3.991390 3.991999 3.992565 3.993092 3.993581
#> 
#> $VAR
#>   [1] 1.016618 1.017866 1.019207 1.020645 1.022188 1.023843 1.025618 1.027521
#>   [9] 1.029559 1.031743 1.034082 1.036585 1.039263 1.042127 1.045188 1.048457
#>  [17] 1.051948 1.055673 1.059644 1.063876 1.068380 1.073172 1.078265 1.083673
#>  [25] 1.089410 1.095488 1.101921 1.108722 1.115902 1.123471 1.131439 1.139814
#>  [33] 1.148602 1.157807 1.167431 1.177473 1.187930 1.198794 1.210054 1.221698
#>  [41] 1.233706 1.246057 1.258724 1.271677 1.284881 1.298297 1.311884 1.325594
#>  [49] 1.339380 1.353188 1.366966 1.380659 1.394211 1.407567 1.420673 1.433478
#>  [57] 1.445931 1.457987 1.469604 1.480744 1.491375 1.501468 1.511003 1.519961
#>  [65] 1.528331 1.536103 1.543274 1.549843 1.555812 1.561184 1.565964 1.570157
#>  [73] 1.573769 1.576804 1.579266 1.581159 1.582485 1.583244 1.583437 1.583064
#>  [81] 1.582126 1.580625 1.578563 1.575947 1.572785 1.569088 1.564875 1.560165
#>  [89] 1.554985 1.549365 1.543342 1.536957 1.530255 1.523285 1.516100 1.508754
#>  [97] 1.501305 1.493809 1.486322 1.478902 1.471600 1.464468 1.457551 1.450890
#> [105] 1.444522 1.438478 1.432779 1.427443 1.422479 1.417891 1.413671 1.409809
#> [113] 1.406285 1.403072 1.400140 1.397448 1.394955 1.392612 1.390368 1.388168
#> [121] 1.385957 1.383677 1.381273 1.378688 1.375872 1.372773 1.369347 1.365556
#> [129] 1.361365 1.356749 1.351687 1.346169 1.340189 1.333753 1.326870 1.319558
#> [137] 1.311842 1.303752 1.295323 1.286593 1.277605 1.268404 1.259035 1.249544
#> [145] 1.239978 1.230381 1.220797 1.211267 1.201828 1.192517 1.183365 1.174401
#> [153] 1.165650 1.157134 1.148870 1.140874 1.133157 1.125728 1.118592 1.111753
#> [161] 1.105213 1.098969 1.093021 1.087362 1.081989 1.076893 1.072068 1.067505
#> [169] 1.063195 1.059129 1.055297 1.051689 1.048296 1.045106 1.042112 1.039302
#> [177] 1.036667 1.034199 1.031887 1.029723 1.027699 1.025807 1.024039 1.022387
#> [185] 1.020845 1.019406 1.018063 1.016810 1.015642 1.014553 1.013539 1.012593
#> [193] 1.011713 1.010892 1.010129 1.009418 1.008756 1.008140 1.007567 1.007034
#>