Estimating true subscores using Yen's OPI
Yen.OPI.RdThis function estimates subscores using Yen's Objective Performance Index (OPI; Yen, 1987) <https://www.ets.org/research/policy_research_reports/publications/paper/1987/hrap>. Yen's OPI (Yen, 1987) is a procedure combining Bayesian method and item response theory (IRT; Embretson & Reise, 2000 <https://psycnet.apa.org/record/2000-03918-000>; Reckase, 1997 <doi: 10.1177/0146621697211002>). This method pulls an examinee's performance on a certain objective (i.e., subscale) towards his/her total test performance in order to get a more stable and precise objective subscore estimate.
References
Embretson, S. E., & Reise, S. P. (2013). "Item response theory". Mahwah, NJ: Lawrence Erlbaum Associates, Inc. https://psycnet.apa.org/record/2000-03918-000.
Reckase, M. D. (1997). "The past and future of multidimensional item response theory". Applied Psychological Measurement, 21(1), 25-36. doi: 10.1177/0146621697211002.
Yen, W. M. (1987, June). "A Bayesian/IRT index of objective performance". Paper presented at annual meeting of the Psychometric Society, Montreal, Quebec, Canada. https://www.ets.org/research/policy_research_reports/publications/paper/1987/hrap.
Examples
test.data<-data.prep(scored.data,c(3,15,15,20),
c("Algebra","Geometry","Measurement", "Math"))
Yen.OPI(test.data)
#> $summary
#> mean SD
#> OPI.Algebra 0.6558847 0.2216292
#> OPI.Geometry 0.6082498 0.2155270
#> OPI.Measurement 0.6565998 0.2071813
#>
#> $subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
#>
#> $OPI
#> OPI.Algebra OPI.Geometry OPI.Measurement
#> [1,] 0.9747709 0.9289938 0.9673208
#> [2,] 0.7096161 0.6646749 0.7016195
#> [3,] 0.9077101 0.8639275 0.9283464
#> [4,] 0.7601914 0.7408433 0.8067253
#> [5,] 0.6973147 0.6927017 0.7272270
#> [6,] 0.7714072 0.7630541 0.8054256
#> [7,] 0.7788125 0.7593592 0.8241264
#> [8,] 0.6871171 0.6560730 0.6825317
#> [9,] 0.8603797 0.7956448 0.8460538
#> [10,] 0.9067459 0.8271613 0.8998431
#> [11,] 0.8009894 0.7630916 0.7936928
#> [12,] 0.6451679 0.6140461 0.6224400
#> [13,] 0.7683511 0.7459125 0.7657678
#> [14,] 0.7193236 0.6742985 0.6874300
#> [15,] 0.7874663 0.7615548 0.7464463
#> [16,] 0.6369801 0.6059727 0.6383931
#> [17,] 0.4930852 0.4014972 0.4853637
#> [18,] 0.6724712 0.6283962 0.6919985
#> [19,] 0.6330896 0.5747003 0.6340527
#> [20,] 0.7902978 0.7780230 0.7974181
#> [21,] 0.7627935 0.7013791 0.7122521
#> [22,] 0.9378087 0.9001505 0.9305471
#> [23,] 0.9476821 0.9120805 0.9406530
#> [24,] 0.8054394 0.7924277 0.8231807
#> [25,] 0.8123140 0.7630817 0.8157811
#> [26,] 0.7430325 0.7217082 0.7429690
#> [27,] 0.8923030 0.8379405 0.8882251
#> [28,] 0.8831761 0.8032266 0.8652308
#> [29,] 0.9360361 0.8615685 0.8882762
#> [30,] 0.9456174 0.8720230 0.9103178
#> [31,] 0.8932956 0.8133949 0.8624163
#> [32,] 0.8336424 0.8050413 0.8233495
#> [33,] 0.8628196 0.8335130 0.8870010
#> [34,] 0.5731669 0.4981062 0.6037808
#> [35,] 0.8821155 0.8375360 0.8785417
#> [36,] 0.7556118 0.7454035 0.7426918
#> [37,] 0.9378390 0.8902787 0.9305779
#> [38,] 0.5265367 0.4491758 0.5614692
#> [39,] 0.9401297 0.8830060 0.9458595
#> [40,] 0.7226042 0.6637681 0.6780429
#> [41,] 0.8838827 0.8039319 0.8658883
#> [42,] 0.7851923 0.7510115 0.8045194
#> [43,] 0.9475779 0.8840804 0.9122690
#> [44,] 0.9208116 0.8457247 0.8738358
#> [45,] 0.8572600 0.7671549 0.8294315
#> [46,] 0.8827472 0.8381685 0.8791397
#> [47,] 0.8342940 0.7742921 0.8599658
#> [48,] 0.8223899 0.8087441 0.8509424
#> [49,] 0.7282583 0.6443120 0.7057902
#> [50,] 0.7647205 0.7677480 0.7992221
#> [51,] 0.8559782 0.8223226 0.8299428
#> [52,] 0.8868205 0.8169921 0.8442138
#> [53,] 0.9615742 0.8906607 0.9395669
#> [54,] 0.8444906 0.8010286 0.8195191
#> [55,] 0.8380997 0.8093240 0.8274270
#> [56,] 0.8588278 0.7898130 0.8069233
#> [57,] 1.0000000 0.5333333 0.9000000
#> [58,] 0.9371865 0.8895266 0.9428127
#> [59,] 0.8709771 0.8265097 0.8558503
#> [60,] 0.9606316 0.8895046 0.9385713
#> [61,] 0.9264199 0.8676517 0.9191124
#> [62,] 0.7216016 0.6765576 0.7123071
#> [63,] 0.6242834 0.5104367 0.5919295
#> [64,] 0.5784113 0.5454905 0.5973781
#> [65,] 0.1906052 0.1726266 0.2249631
#> [66,] 0.4055373 0.3542395 0.3718285
#> [67,] 0.5457678 0.4705334 0.4992610
#> [68,] 0.9510841 0.8979828 0.9157802
#> [69,] 0.4282175 0.4040660 0.4623470
#> [70,] 0.8192142 0.7553527 0.7849904
#> [71,] 0.3472033 0.2463014 0.3404995
#> [72,] 0.4500291 0.3714389 0.4351536
#> [73,] 0.7692988 0.7096150 0.7536192
#> [74,] 0.5413467 0.4794363 0.5407023
#> [75,] 0.6688481 0.6531002 0.7252898
#> [76,] 0.4415938 0.3216595 0.4273325
#> [77,] 0.6420840 0.5974642 0.6309072
#> [78,] 0.4302709 0.4194571 0.4761764
#> [79,] 0.2982796 0.2526038 0.2855097
#> [80,] 0.8251755 0.7757241 0.8394951
#> [81,] 0.4086730 0.4110829 0.4800140
#> [82,] 0.7832315 0.7325539 0.7184296
#> [83,] 0.4966478 0.4184758 0.4781546
#> [84,] 0.5965252 0.5918711 0.6596165
#> [85,] 0.5073580 0.4854997 0.5223168
#> [86,] 0.1572398 0.1567912 0.2325771
#> [87,] 0.5433582 0.4950133 0.5432098
#> [88,] 0.2629665 0.2221087 0.3393462
#> [89,] 0.5984459 0.6074085 0.6501740
#> [90,] 0.4131396 0.4161913 0.4151958
#> [91,] 0.1868098 0.1918947 0.1962412
#> [92,] 0.2864278 0.2676828 0.3603094
#> [93,] 0.3438552 0.2816577 0.3269145
#> [94,] 0.3291122 0.2937929 0.3615837
#> [95,] 0.5900429 0.5718042 0.5513248
#> [96,] 0.8349064 0.7705738 0.8227641
#> [97,] 0.3281942 0.2167978 0.2987576
#> [98,] 0.1964994 0.1890309 0.2554595
#> [99,] 0.5379707 0.5171154 0.5613514
#> [100,] 0.6793605 0.6483043 0.6868983
#> [101,] 0.6639039 0.6196713 0.6617090
#> [102,] 0.3039304 0.2454620 0.3514813
#> [103,] 0.3236138 0.2376969 0.3683811
#> [104,] 0.6096822 0.5783580 0.5683154
#> [105,] 0.9166729 0.8572425 0.8843761
#> [106,] 0.5662848 0.5329053 0.5640365
#> [107,] 0.7502175 0.7309665 0.7741639
#> [108,] 0.4207601 0.3411731 0.4441807
#> [109,] 0.6453024 0.6145181 0.6571678
#> [110,] 0.8602208 0.8057700 0.8459074
#> [111,] 0.6207016 0.5484799 0.6685226
#> [112,] 0.4692806 0.3899026 0.4989363
#> [113,] 0.7640203 0.7162241 0.7258004
#> [114,] 0.7665261 0.7049306 0.7269992
#> [115,] 0.7637056 0.6901552 0.7130443
#> [116,] 0.2843615 0.2913142 0.3473830
#> [117,] 0.3412216 0.2922307 0.3726233
#> [118,] 0.5198229 0.4288080 0.5211015
#> [119,] 0.7801701 0.7432982 0.7516604
#> [120,] 0.2386862 0.2248594 0.2565780
#> [121,] 0.5308431 0.4809848 0.6002589
#> [122,] 0.2665435 0.2497635 0.2825775
#> [123,] 0.4772174 0.4545328 0.4610864
#> [124,] 0.3209536 0.2734307 0.3304749
#> [125,] 0.5728288 0.4985017 0.5239307
#> [126,] 0.8802513 0.7901022 0.8625138
#> [127,] 0.9109194 0.8413779 0.9038849
#> [128,] 0.4956214 0.3906674 0.4528807
#> [129,] 0.8250473 0.7718889 0.7901779
#> [130,] 0.8982062 0.8183845 0.9039674
#> [131,] 0.6885618 0.6980749 0.7436539
#> [132,] 0.2777890 0.2225284 0.3157506
#> [133,] 0.8336188 0.7840797 0.8353293
#> [134,] 0.6367037 0.6056890 0.6606243
#> [135,] 0.7632973 0.6776592 0.7126897
#> [136,] 0.5984459 0.6074085 0.6501740
#> [137,] 0.6339278 0.5894456 0.5781619
#> [138,] 0.7083014 0.6773048 0.7015439
#> [139,] 0.3197013 0.3241781 0.3665622
#> [140,] 0.3514310 0.3412224 0.3469286
#> [141,] 0.4313427 0.4486381 0.4771427
#> [142,] 0.2969851 0.2637291 0.2962713
#> [143,] 0.2833235 0.2899612 0.3337657
#> [144,] 0.4248287 0.4145458 0.4023084
#> [145,] 0.7088135 0.7162024 0.7262824
#> [146,] 0.3418789 0.3057267 0.3974012
#> [147,] 0.7528457 0.7545565 0.7286387
#> [148,] 0.4582772 0.4477691 0.5127134
#> [149,] 0.4604972 0.3270218 0.4553031
#> [150,] 0.9016064 0.8318132 0.8701643
#>