README.md

Travis build status

The goal of genIRT is to generate the dichotomously scored response data from two parameter logistic model (2PL).

Installation

You can install the released version of genIRT from CRAN with:

install.packages("genIRT")

Example

This is a basic example which shows you how to generate a response data:

library(genIRT)
## basic example code
mydata=sim2pldat(10,ilocation=NULL,islope=NULL,plocation=rnorm(500,0,1),rnum=0.6)

To get parameter values and response data, separately.

  mydata$i.loc
#>  [1] -0.32656578 -0.15131579 -0.61352449  3.65778189  0.98204494  0.16446126
#>  [7]  0.57009025 -0.40364611 -1.65425126  0.01701881
  mydata$i.slp
#>  [1]  1.3136916 -2.0061764 -0.1587551  1.0372449 -0.6423504 -0.1269679
#>  [7] -1.9835610  0.7429467 -2.5241409 -1.8869301
  mydata$p.loc
#>   [1] -1.980980849  0.391201439 -0.754942930  0.130638147  1.643250802
#>   [6] -0.385699358  0.677806869  0.633767593 -0.906125276 -0.880269860
#>  [11]  1.771794273  0.499972915 -1.234652828 -0.303160175 -1.182962506
#>  [16] -1.438603843  0.230033312  0.942883982 -0.402066531 -0.045509454
#>  [21] -0.820637849  0.529312248 -0.997306661 -0.795945266 -0.018781517
#>  [26]  0.206554859  0.695032854 -0.143738546 -1.003655155 -0.524662281
#>  [31]  1.106144664 -0.921766782 -0.935545323 -0.935132851 -0.146511857
#>  [36] -1.111211854  1.368528537 -1.440063033  0.681706756  0.080508686
#>  [41] -1.240905101  1.635641558  2.261807289 -0.604253752  0.369918431
#>  [46] -1.643831303  0.475746767  1.902577281 -0.995250753  0.279718638
#>  [51]  0.953996080 -0.083738583  1.517569979  0.787659328 -1.633489038
#>  [56] -0.630508682 -0.287868444  0.080701874 -0.565814077  0.536014831
#>  [61] -0.354425429  0.781229667  0.648157615  1.024155361  0.342429845
#>  [66] -0.556461132 -0.079167809  0.824965760  0.418787712  1.031371853
#>  [71]  0.508095879  0.250939043  1.389764910  0.760912362 -0.979639362
#>  [76] -1.871147224  0.947680968  1.044112419  0.780168242 -0.602205253
#>  [81] -0.227466713 -0.184711212  0.844288348 -1.905370178 -0.985212861
#>  [86] -0.941463333 -0.699552750 -0.202727711 -0.974140215 -1.508140362
#>  [91] -1.287273416  0.866775325 -0.649556274 -1.256872046  2.002155587
#>  [96]  3.299809737 -1.042689228  2.250686643 -1.562552426  0.458759865
#> [101] -0.196041029 -1.620127191 -0.309035120 -0.336255022  0.063277435
#> [106] -1.220261544 -0.050200168  1.976545150  0.453571497  0.211012596
#> [111] -0.949162031 -0.006471972 -0.314284493 -0.686826327  2.109849260
#> [116]  0.350089417  1.065665423  0.029805785  0.272454308 -1.654232367
#> [121] -2.085913505  0.379541537 -1.027287256  0.006855363 -0.171756772
#> [126]  0.459831803  0.209612599  0.269165452  0.339194799  0.078839968
#> [131]  0.561729783 -0.697835549  1.489151398  0.597930317 -1.863731472
#> [136] -0.365934407  1.069654030 -1.001568438  0.914341488 -1.659704337
#> [141] -0.192590859 -0.017127570  0.501785776 -1.678259384 -0.135176456
#> [146] -2.370769700 -0.647478764 -0.655477916  1.212560021 -1.794257768
#> [151] -1.085009737 -0.209054408  0.332292861  1.446786461  0.095931772
#> [156]  0.425609522 -1.155971359  0.982100290 -0.822712593  1.746489697
#> [161] -0.321513150  0.273181611  0.393284287  1.398040433 -1.103873469
#> [166] -1.156799804 -0.038100467 -0.253490205 -0.437545900  1.198153225
#> [171]  0.741238483 -0.927927963 -0.388299797 -0.955279021 -0.581300795
#> [176]  0.104207542 -0.313652719  0.043363787 -0.796047133  0.789049690
#> [181]  2.704459494 -1.047911424 -1.230536854 -1.661824384 -0.760639006
#> [186]  0.384147586  0.519277633  1.055208331  0.169892673  1.860514341
#> [191] -1.626945443  0.666497376  0.433135533  0.158408340 -1.782994448
#> [196] -1.098264776 -0.600786193 -0.460680737 -1.273935153  1.206995892
#> [201]  0.694004526  0.136826245  0.911208188  2.179165897  0.464062372
#> [206] -0.951471617 -2.165826854  1.793217934 -0.692548054  0.400406525
#> [211]  0.879962383 -1.756817602  0.631858424  0.689290196  0.606596386
#> [216]  0.443555026  1.034124473  0.921277069  0.980157313  0.502336115
#> [221]  1.020305257  0.857396614 -1.700080499 -0.721496784 -0.530716953
#> [226]  1.307555320  1.876240939  1.283835291  0.734389838 -1.784849102
#> [231] -1.243086152 -0.380455839  0.598799193  1.089937650  2.093046199
#> [236]  0.474766638 -0.543891718 -0.058519593 -1.673330166  0.767363593
#> [241] -0.124823637 -0.476939770 -0.306396963 -0.420365079 -0.365849166
#> [246] -0.610984053 -1.450288774 -0.085628967  0.428617904  0.334624319
#> [251] -1.067661071 -0.072732546 -0.372851843  0.142552076  0.279745038
#> [256] -0.775041038 -0.158476534  0.085043762  0.076148193  0.497739365
#> [261] -1.324549236 -2.485838330 -0.248447828  0.497416572 -0.801519173
#> [266] -0.234905701  0.772287705 -0.498880051 -0.684709795  1.848203391
#> [271] -0.806711959  0.095049328 -0.916582797 -0.398004926  0.596853290
#> [276] -1.160222434 -1.325169994 -0.849649037  0.946812864 -0.419852862
#> [281] -0.673142155  0.432797449 -0.719873963 -2.080229185  0.406742028
#> [286]  2.118940206 -0.041052557 -1.001070280  1.145373998 -0.660885281
#> [291]  0.192012220 -0.242041841  0.561458086  0.488013057  0.904800255
#> [296]  0.621623036 -1.134174214  0.092949725 -0.497522866 -0.885532381
#> [301] -0.222219710 -1.098944790  1.298848201 -0.485781220  0.842064307
#> [306] -0.717306123 -0.637449508 -0.409674485  0.230993325 -0.632296450
#> [311]  0.184886792  1.042542310 -0.870334531  0.309394058  0.293812382
#> [316] -0.920590129 -1.650006096 -0.367893525  0.689444907  1.448899354
#> [321] -1.221178350 -0.296422594 -0.098627691 -0.752208991 -0.983807485
#> [326] -0.754312271  0.042707851 -0.480355904  1.240791573  0.736438073
#> [331] -0.816476239  1.339942809 -2.026160740  0.209283366  0.228755992
#> [336]  1.781935321  1.995250876 -0.354337901 -2.111972434 -0.788677073
#> [341]  1.976106357 -0.432341530 -1.115792578 -1.745302688 -0.077901273
#> [346] -1.356187985 -1.073189893  0.911267221 -1.759778888  2.229854919
#> [351]  0.165128417  0.303547450 -1.722551802 -1.405292767  1.380188890
#> [356]  0.692809445  0.619724766 -0.969930522 -0.198828035  0.347458446
#> [361] -1.811157273 -0.421858721  1.523437326 -0.037390903  1.692972488
#> [366] -1.932406105 -0.511329713 -0.181000672 -0.063357496 -0.644138660
#> [371] -1.362138575 -0.067738168  2.437807359 -0.357666635 -0.702595892
#> [376]  0.731823934 -0.400513767 -0.401805116 -1.188651199 -1.168160360
#> [381]  1.036877314 -0.269821757  2.613027758 -0.114377490 -0.720205846
#> [386] -0.718555889  0.206032897 -0.683808051 -0.360837260  0.697000338
#> [391] -0.302717049  1.655542716  0.395499130 -0.425259280  0.080136815
#> [396]  0.305479878 -1.904189469 -0.087096180 -1.155531094  0.271074901
#> [401] -0.620719073  0.336651073 -1.339642028  1.736927351  1.732161813
#> [406] -0.910424388 -1.118237688 -0.765202604  0.881328212  1.129006253
#> [411]  0.760171760 -0.450037325  0.288172598 -1.032283315  0.307101786
#> [416] -0.257567595 -1.773919765  1.796989488  0.499320266  0.221958613
#> [421] -0.026840561  1.343335095 -0.913584036 -1.722392577  0.210582994
#> [426] -0.562803860  2.518637169 -0.009892329  0.041844506  1.097864495
#> [431]  0.809831505  1.512404106 -0.017837209  0.954447553 -0.255479982
#> [436] -0.754902308  0.969539627  0.011660560 -0.639846068  0.727983013
#> [441] -0.517774016  1.711088797 -0.865861647 -1.149278789  0.409390868
#> [446] -0.610287096 -1.123339667 -0.728378947 -0.400428098  1.871575330
#> [451] -0.282316206 -0.466109332 -0.209668963  1.268339240  1.189279910
#> [456] -0.945253804 -0.933836631 -0.302763914  0.233580959 -0.413331535
#> [461] -0.128403563 -0.246468320 -1.176737835 -0.246918636  0.160172895
#> [466] -1.570836655  0.101079690 -0.083195644 -0.206555958  1.005255786
#> [471]  1.460731036  1.144289725 -0.373961942 -1.587415730 -1.397211923
#> [476]  1.349286255  0.878192214 -0.799218147 -0.286819938 -1.482030665
#> [481]  0.026537205  1.303547510 -1.408110091  0.202817070  2.131728179
#> [486] -0.246311708  0.808639875 -0.751830105 -0.246221715  1.086116419
#> [491] -1.377712474 -1.512098918 -1.120376334  0.537641415 -1.493455054
#> [496]  0.348941963 -1.576394615  1.360429034  0.085539808  0.854671156
  mydata$resp
#>        [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#>   [1,]    0    1    0    0    1    0    1    0    1     1
#>   [2,]    1    0    0    0    0    0    0    1    0     0
#>   [3,]    0    1    0    0    1    0    1    0    0     1
#>   [4,]    1    0    0    0    1    0    1    0    0     0
#>   [5,]    1    0    0    0    0    0    0    1    0     0
#>   [6,]    0    1    0    0    1    0    1    0    0     1
#>   [7,]    1    0    0    0    0    0    0    1    0     0
#>   [8,]    1    0    0    0    0    0    0    1    0     0
#>   [9,]    0    1    0    0    1    0    1    0    0     1
#>  [10,]    0    1    0    0    1    0    1    0    0     1
#>  [11,]    1    0    0    0    0    0    0    1    0     0
#>  [12,]    1    0    0    0    0    0    0    1    0     0
#>  [13,]    0    1    0    0    1    0    1    0    0     1
#>  [14,]    0    0    0    0    1    0    1    0    0     1
#>  [15,]    0    1    0    0    1    0    1    0    0     1
#>  [16,]    0    1    0    0    1    0    1    0    0     1
#>  [17,]    1    0    0    0    1    0    1    1    0     0
#>  [18,]    1    0    0    0    0    0    0    1    0     0
#>  [19,]    0    1    0    0    1    0    1    0    0     1
#>  [20,]    0    0    0    0    1    0    1    0    0     0
#>  [21,]    0    1    0    0    1    0    1    0    0     1
#>  [22,]    1    0    0    0    0    0    0    1    0     0
#>  [23,]    0    1    0    0    1    0    1    0    0     1
#>  [24,]    0    1    0    0    1    0    1    0    0     1
#>  [25,]    0    0    0    0    1    0    1    0    0     0
#>  [26,]    1    0    0    0    1    0    1    1    0     0
#>  [27,]    1    0    0    0    0    0    0    1    0     0
#>  [28,]    0    0    0    0    1    0    1    0    0     0
#>  [29,]    0    1    0    0    1    0    1    0    0     1
#>  [30,]    0    1    0    0    1    0    1    0    0     1
#>  [31,]    1    0    0    0    0    0    0    1    0     0
#>  [32,]    0    1    0    0    1    0    1    0    0     1
#>  [33,]    0    1    0    0    1    0    1    0    0     1
#>  [34,]    0    1    0    0    1    0    1    0    0     1
#>  [35,]    0    0    0    0    1    0    1    0    0     0
#>  [36,]    0    1    0    0    1    0    1    0    0     1
#>  [37,]    1    0    0    0    0    0    0    1    0     0
#>  [38,]    0    1    0    0    1    0    1    0    0     1
#>  [39,]    1    0    0    0    0    0    0    1    0     0
#>  [40,]    1    0    0    0    1    0    1    0    0     0
#>  [41,]    0    1    0    0    1    0    1    0    0     1
#>  [42,]    1    0    0    0    0    0    0    1    0     0
#>  [43,]    1    0    0    0    0    0    0    1    0     0
#>  [44,]    0    1    0    0    1    0    1    0    0     1
#>  [45,]    1    0    0    0    0    0    0    1    0     0
#>  [46,]    0    1    0    0    1    0    1    0    0     1
#>  [47,]    1    0    0    0    0    0    0    1    0     0
#>  [48,]    1    0    0    0    0    0    0    1    0     0
#>  [49,]    0    1    0    0    1    0    1    0    0     1
#>  [50,]    1    0    0    0    1    0    1    1    0     0
#>  [51,]    1    0    0    0    0    0    0    1    0     0
#>  [52,]    0    0    0    0    1    0    1    0    0     0
#>  [53,]    1    0    0    0    0    0    0    1    0     0
#>  [54,]    1    0    0    0    0    0    0    1    0     0
#>  [55,]    0    1    0    0    1    0    1    0    0     1
#>  [56,]    0    1    0    0    1    0    1    0    0     1
#>  [57,]    0    0    0    0    1    0    1    0    0     1
#>  [58,]    1    0    0    0    1    0    1    0    0     0
#>  [59,]    0    1    0    0    1    0    1    0    0     1
#>  [60,]    1    0    0    0    0    0    0    1    0     0
#>  [61,]    0    1    0    0    1    0    1    0    0     1
#>  [62,]    1    0    0    0    0    0    0    1    0     0
#>  [63,]    1    0    0    0    0    0    0    1    0     0
#>  [64,]    1    0    0    0    0    0    0    1    0     0
#>  [65,]    1    0    0    0    1    0    1    1    0     0
#>  [66,]    0    1    0    0    1    0    1    0    0     1
#>  [67,]    0    0    0    0    1    0    1    0    0     0
#>  [68,]    1    0    0    0    0    0    0    1    0     0
#>  [69,]    1    0    0    0    0    0    0    1    0     0
#>  [70,]    1    0    0    0    0    0    0    1    0     0
#>  [71,]    1    0    0    0    0    0    0    1    0     0
#>  [72,]    1    0    0    0    1    0    1    1    0     0
#>  [73,]    1    0    0    0    0    0    0    1    0     0
#>  [74,]    1    0    0    0    0    0    0    1    0     0
#>  [75,]    0    1    0    0    1    0    1    0    0     1
#>  [76,]    0    1    0    0    1    0    1    0    1     1
#>  [77,]    1    0    0    0    0    0    0    1    0     0
#>  [78,]    1    0    0    0    0    0    0    1    0     0
#>  [79,]    1    0    0    0    0    0    0    1    0     0
#>  [80,]    0    1    0    0    1    0    1    0    0     1
#>  [81,]    0    0    0    0    1    0    1    0    0     1
#>  [82,]    0    0    0    0    1    0    1    0    0     0
#>  [83,]    1    0    0    0    0    0    0    1    0     0
#>  [84,]    0    1    0    0    1    0    1    0    1     1
#>  [85,]    0    1    0    0    1    0    1    0    0     1
#>  [86,]    0    1    0    0    1    0    1    0    0     1
#>  [87,]    0    1    0    0    1    0    1    0    0     1
#>  [88,]    0    0    0    0    1    0    1    0    0     1
#>  [89,]    0    1    0    0    1    0    1    0    0     1
#>  [90,]    0    1    0    0    1    0    1    0    0     1
#>  [91,]    0    1    0    0    1    0    1    0    0     1
#>  [92,]    1    0    0    0    0    0    0    1    0     0
#>  [93,]    0    1    0    0    1    0    1    0    0     1
#>  [94,]    0    1    0    0    1    0    1    0    0     1
#>  [95,]    1    0    0    0    0    0    0    1    0     0
#>  [96,]    1    0    0    0    0    0    0    1    0     0
#>  [97,]    0    1    0    0    1    0    1    0    0     1
#>  [98,]    1    0    0    0    0    0    0    1    0     0
#>  [99,]    0    1    0    0    1    0    1    0    0     1
#> [100,]    1    0    0    0    0    0    0    1    0     0
#> [101,]    0    0    0    0    1    0    1    0    0     0
#> [102,]    0    1    0    0    1    0    1    0    0     1
#> [103,]    0    0    0    0    1    0    1    0    0     1
#> [104,]    0    0    0    0    1    0    1    0    0     1
#> [105,]    1    0    0    0    1    0    1    0    0     0
#> [106,]    0    1    0    0    1    0    1    0    0     1
#> [107,]    0    0    0    0    1    0    1    0    0     0
#> [108,]    1    0    0    0    0    0    0    1    0     0
#> [109,]    1    0    0    0    0    0    0    1    0     0
#> [110,]    1    0    0    0    1    0    1    1    0     0
#> [111,]    0    1    0    0    1    0    1    0    0     1
#> [112,]    1    0    0    0    1    0    1    0    0     0
#> [113,]    0    0    0    0    1    0    1    0    0     1
#> [114,]    0    1    0    0    1    0    1    0    0     1
#> [115,]    1    0    0    0    0    0    0    1    0     0
#> [116,]    1    0    0    0    1    0    1    1    0     0
#> [117,]    1    0    0    0    0    0    0    1    0     0
#> [118,]    1    0    0    0    1    0    1    0    0     0
#> [119,]    1    0    0    0    1    0    1    1    0     0
#> [120,]    0    1    0    0    1    0    1    0    0     1
#> [121,]    0    1    0    0    1    0    1    0    1     1
#> [122,]    1    0    0    0    0    0    0    1    0     0
#> [123,]    0    1    0    0    1    0    1    0    0     1
#> [124,]    1    0    0    0    1    0    1    0    0     0
#> [125,]    0    0    0    0    1    0    1    0    0     0
#> [126,]    1    0    0    0    0    0    0    1    0     0
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#> [212,]    0    1    0    0    1    0    1    0    0     1
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#> [223,]    0    1    0    0    1    0    1    0    0     1
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#> [406,]    0    1    0    0    1    0    1    0    0     1
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#> [412,]    0    1    0    0    1    0    1    0    0     1
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#> [414,]    0    1    0    0    1    0    1    0    0     1
#> [415,]    1    0    0    0    1    0    1    1    0     0
#> [416,]    0    0    0    0    1    0    1    0    0     1
#> [417,]    0    1    0    0    1    0    1    0    0     1
#> [418,]    1    0    0    0    0    0    0    1    0     0
#> [419,]    1    0    0    0    0    0    0    1    0     0
#> [420,]    1    0    0    0    1    0    1    1    0     0
#> [421,]    0    0    0    0    1    0    1    0    0     0
#> [422,]    1    0    0    0    0    0    0    1    0     0
#> [423,]    0    1    0    0    1    0    1    0    0     1
#> [424,]    0    1    0    0    1    0    1    0    0     1
#> [425,]    1    0    0    0    1    0    1    1    0     0
#> [426,]    0    1    0    0    1    0    1    0    0     1
#> [427,]    1    0    0    0    0    0    0    1    0     0
#> [428,]    1    0    0    0    1    0    1    0    0     0
#> [429,]    1    0    0    0    1    0    1    0    0     0
#> [430,]    1    0    0    0    0    0    0    1    0     0
#> [431,]    1    0    0    0    0    0    0    1    0     0
#> [432,]    1    0    0    0    0    0    0    1    0     0
#> [433,]    1    0    0    0    1    0    1    0    0     0
#> [434,]    1    0    0    0    0    0    0    1    0     0
#> [435,]    0    0    0    0    1    0    1    0    0     1
#> [436,]    0    1    0    0    1    0    1    0    0     1
#> [437,]    1    0    0    0    0    0    0    1    0     0
#> [438,]    1    0    0    0    1    0    1    0    0     0
#> [439,]    0    1    0    0    1    0    1    0    0     1
#> [440,]    1    0    0    0    0    0    0    1    0     0
#> [441,]    0    1    0    0    1    0    1    0    0     1
#> [442,]    1    0    0    0    0    0    0    1    0     0
#> [443,]    0    1    0    0    1    0    1    0    0     1
#> [444,]    0    1    0    0    1    0    1    0    0     1
#> [445,]    1    0    0    0    0    0    0    1    0     0
#> [446,]    0    1    0    0    1    0    1    0    0     1
#> [447,]    0    1    0    0    1    0    1    0    0     1
#> [448,]    0    1    0    0    1    0    1    0    0     1
#> [449,]    0    1    0    0    1    0    1    0    0     1
#> [450,]    1    0    0    0    0    0    0    1    0     0
#> [451,]    0    0    0    0    1    0    1    0    0     1
#> [452,]    0    1    0    0    1    0    1    0    0     1
#> [453,]    0    0    0    0    1    0    1    0    0     1
#> [454,]    1    0    0    0    0    0    0    1    0     0
#> [455,]    1    0    0    0    0    0    0    1    0     0
#> [456,]    0    1    0    0    1    0    1    0    0     1
#> [457,]    0    1    0    0    1    0    1    0    0     1
#> [458,]    0    0    0    0    1    0    1    0    0     1
#> [459,]    1    0    0    0    1    0    1    1    0     0
#> [460,]    0    1    0    0    1    0    1    0    0     1
#> [461,]    0    0    0    0    1    0    1    0    0     0
#> [462,]    0    0    0    0    1    0    1    0    0     1
#> [463,]    0    1    0    0    1    0    1    0    0     1
#> [464,]    0    0    0    0    1    0    1    0    0     1
#> [465,]    1    0    0    0    1    0    1    1    0     0
#> [466,]    0    1    0    0    1    0    1    0    0     1
#> [467,]    1    0    0    0    1    0    1    0    0     0
#> [468,]    0    0    0    0    1    0    1    0    0     0
#> [469,]    0    0    0    0    1    0    1    0    0     1
#> [470,]    1    0    0    0    0    0    0    1    0     0
#> [471,]    1    0    0    0    0    0    0    1    0     0
#> [472,]    1    0    0    0    0    0    0    1    0     0
#> [473,]    0    1    0    0    1    0    1    0    0     1
#> [474,]    0    1    0    0    1    0    1    0    0     1
#> [475,]    0    1    0    0    1    0    1    0    0     1
#> [476,]    1    0    0    0    0    0    0    1    0     0
#> [477,]    1    0    0    0    0    0    0    1    0     0
#> [478,]    0    1    0    0    1    0    1    0    0     1
#> [479,]    0    0    0    0    1    0    1    0    0     1
#> [480,]    0    1    0    0    1    0    1    0    0     1
#> [481,]    1    0    0    0    1    0    1    0    0     0
#> [482,]    1    0    0    0    0    0    0    1    0     0
#> [483,]    0    1    0    0    1    0    1    0    0     1
#> [484,]    1    0    0    0    1    0    1    1    0     0
#> [485,]    1    0    0    0    0    0    0    1    0     0
#> [486,]    0    0    0    0    1    0    1    0    0     1
#> [487,]    1    0    0    0    0    0    0    1    0     0
#> [488,]    0    1    0    0    1    0    1    0    0     1
#> [489,]    0    0    0    0    1    0    1    0    0     1
#> [490,]    1    0    0    0    0    0    0    1    0     0
#> [491,]    0    1    0    0    1    0    1    0    0     1
#> [492,]    0    1    0    0    1    0    1    0    0     1
#> [493,]    0    1    0    0    1    0    1    0    0     1
#> [494,]    1    0    0    0    0    0    0    1    0     0
#> [495,]    0    1    0    0    1    0    1    0    0     1
#> [496,]    1    0    0    0    1    0    1    1    0     0
#> [497,]    0    1    0    0    1    0    1    0    0     1
#> [498,]    1    0    0    0    0    0    0    1    0     0
#> [499,]    1    0    0    0    1    0    1    0    0     0
#> [500,]    1    0    0    0    0    0    0    1    0     0


alanbio/genIRT documentation built on Aug. 4, 2020, 7:51 p.m.