R irtoys

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R irtoys
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R irtoys

• For binary response data
• Provides common interface to some functions of
• ICL (external to R)
• BILOG (external to R)
• ltm (R function)
• Syntax used is simpler and consistent across
  these packages
• Other useful IRT functions NPP
• Good plotting capabilities

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Dataset

• BDI (21 items)
• 818 subjects
• See word-doc for items
• Split the items into three sets
• 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
  20 21

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Dataset 1 descript(beck,c(2,5,8,11,14,17,20))
Sample 7 items and 818 sample units 0
missing values Proportions for each level of
response 0 1 logit t1bdi1 0.7922
0.2078 -1.3381 t1bdi4 0.5538 0.4462
-0.2160 t1bdi7 0.5477 0.4523 -0.1913 t1bdi10
0.6027 0.3973 -0.4167 t1bdi13 0.4853 0.5147
0.0587 t1bdi16 0.4279 0.5721 0.2905 t1bdi19
0.4315 0.5685 0.2756 Frequencies of total
scores 0 1 2 3 4 5 6 7 Freq 133
114 91 115 103 106 91 65
Biserial correlation with Total Score
Included Excluded t1bdi1 0.6005
0.4647 t1bdi4 0.7018 0.5590 t1bdi7 0.6190
0.4513 t1bdi10 0.6565 0.5025 t1bdi13
0.7167 0.5780 t1bdi16 0.6143 0.4466 t1bdi19
0.7188 0.5824 Cronbach's alpha
value All Items 0.7861 Excluding t1bdi1
0.7680 Excluding t1bdi4 0.7494 Excluding t1bdi7
0.7708 Excluding t1bdi10 0.7607 Excluding t1bdi13
0.7454 Excluding t1bdi16 0.7716 Excluding t1bdi19
0.7446 Pairwise Associations Item i Item j
p.value 1 1 6 2e-12 2 3 6 5e-13 3
1 3 4e-14 4 3 4 5e-16 5 1 7
4e-16 6 2 4 lt2e-16 7 5 6 lt2e-16 8
4 6 lt2e-16 9 1 5 lt2e-16 10 1 4
lt2e-16 00
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-irtoys- fitting 1PL/2PL models

• irtoys_beck_1pl1 lt- est(beck,c(2,5,8,11,14,17,20)
  , model"1PL", engine"ltm")
• irtoys_beck_2pl1 lt- est(beck,c(2,5,8,11,14,17,20)
  , model"2PL", engine"ltm")

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• gt irtoys_beck_2pl1
• ,1 ,2 ,3
• t1bdi1 2.166786 1.04466980 0
• t1bdi4 2.102861 0.18276282 0
• t1bdi7 1.363356 0.19506741 0
• t1bdi10 1.727944 0.37145589 0
• t1bdi13 2.408886 -0.03577061 0
• t1bdi16 1.368479 -0.28294050 0
• t1bdi19 2.527411 -0.19989956 0
• gt irtoys_beck_1pl1
• ,1 ,2 ,3
• t1bdi1 1.860460 1.11158683 0
• t1bdi4 1.860460 0.19005034 0
• t1bdi7 1.860460 0.16912484 0
• t1bdi10 1.860460 0.35943444 0
• t1bdi13 1.860460 -0.04331848 0
• t1bdi16 1.860460 -0.24064261 0
• t1bdi19 1.860460 -0.22790729 0

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par(mfrow c(1,2)) plot(irf(irtoys_beck_1pl1),
coNA, main"1PL") plot(irf(irtoys_beck_2pl1),
coNA, main"2PL")
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Compare with Non-parametric

• Plot 1PL/2PL response functions for each item and
  compare with non-parametric curve which does not
  assume logistic function
• par(mfrow c(1,1))
• npp(beck, itemsc(2), from -2, to 4, main
  "Item 2", co3)
• plot(irf(irtoys_beck_1pl1c(1),), co"red", add
  TRUE)
• plot(irf(irtoys_beck_2pl1c(1),), co"blue", add
  TRUE)

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Estimating ability

• th.mle_1pl1 lt- mlebme(respbeck,c(2,5,8,11,14,17,
  20), ipirtoys_beck_1pl1)
• th.mle_1pl2 lt- mlebme(respbeck,c(2,5,8,11,14,17,
  20), ipirtoys_beck_2pl1)

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Patterns
Ability/SE for 1PL
Ability/SE for 2PL

• i1 i4 i7 i10 i13 i16 i19
• 793 0 1 1 1 1 1 1
• 794 1 1 1 0 1 1 1
• 795 1 1 1 1 1 1 1
• 796 1 1 1 0 1 1 1
• 797 0 1 1 1 1 1 1
• 798 1 1 0 1 1 1 1
• 799 1 1 1 1 1 1 1
• 800 0 1 1 1 1 1 1
• 801 0 1 1 1 1 1 1
• 802 1 1 0 1 1 1 0
• 803 1 1 1 1 1 1 1
• 804 1 1 1 1 1 1 1
• 805 1 1 1 1 1 1 1
• 806 1 1 1 1 1 1 1
• 807 1 1 1 0 1 1 1
• 808 1 1 1 1 1 1 1
• 809 1 1 1 1 1 1 1
• 810 0 1 1 1 1 1 1

1.276574869 0.6175342 1.276574869 0.6175342
3.999935513 5.7727585 1.276574869 0.6175342
1.276574869 0.6175342 1.276574869 0.6175342
3.999935513 5.7727585 1.276574869 0.6175342
1.276574869 0.6175342 0.734365930 0.4850223
3.999935513 5.7727585 3.999935513 5.7727585
3.999935513 5.7727585 3.999935513 5.7727585
1.276574869 0.6175342 3.999935513 5.7727585
3.999935513 5.7727585 1.276574869 0.6175342
3.999935513 5.7727585 3.999935513 5.7727585
3.999935513 5.7727585 3.999935513 5.7727585
1.276574869 0.6175342 3.999935513 5.7727585
3.999935513 5.7727585 3.999935513 5.7727585
1.171368774 0.5730090 1.327602513 0.6230293
3.999928649 5.6888878 1.327602513 0.6230293
1.171368774 0.5730090 1.482503737 0.6841684
3.999928649 5.6888878 1.171368774 0.5730090
1.171368774 0.5730090 0.713049229 0.4720853
3.999928649 5.6888878 3.999928649 5.6888878
3.999928649 5.6888878 3.999928649 5.6888878
1.327602513 0.6230293 3.999928649 5.6888878
3.999928649 5.6888878 1.171368774 0.5730090
3.999928649 5.6888878 3.999928649 5.6888878
3.999928649 5.6888878 3.999928649 5.6888878
1.327602513 0.6230293 3.999928649 5.6888878
3.999928649 5.6888878 3.999928649 5.6888878
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