The equateMultiple package computes:
Data preparation follows the same steps of the equateIRT package.
Load the package equateMultiple and the data
## Loading required package: equateIRTEstimate a two parameter logistic model for 5 data sets with the R package mirt
library("mirt")
m1 <- mirt(data2pl[[1]], SE = TRUE)
m2 <- mirt(data2pl[[2]], SE = TRUE)
m3 <- mirt(data2pl[[3]], SE = TRUE)
m4 <- mirt(data2pl[[4]], SE = TRUE)
m5 <- mirt(data2pl[[5]], SE = TRUE)Create an object of class modIRT
mlist<- list(m1, m2, m3, m4, m5)
test <- paste("test", 1:5, sep = "")
mods <- modIRT(est.mods = mlist, names = test, display = FALSE)The linkage plan
## [,1] [,2] [,3] [,4] [,5]
## [1,] 20 10 0 0 10
## [2,] 10 20 10 0 0
## [3,] 0 10 20 10 0
## [4,] 0 0 10 20 10
## [5,] 10 0 0 10 20Estimation of the equating coefficients using the multiple mean-mean method. Form 1 is the base form.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.84001 0.018641
## A test3 0.84285 0.021321
## A test4 0.83876 0.020682
## A test5 1.02323 0.021556
## B test1 0.00000 0.000000
## B test2 0.10723 0.022389
## B test3 0.20275 0.023998
## B test4 0.36789 0.024059
## B test5 0.50312 0.023977Estimation of the equating coefficients using the multiple mean-geometric mean method.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.83813 0.018688
## A test3 0.83986 0.021370
## A test4 0.83575 0.020736
## A test5 1.02115 0.021623
## B test1 0.00000 0.000000
## B test2 0.10726 0.022373
## B test3 0.20316 0.023898
## B test4 0.36779 0.023992
## B test5 0.50293 0.023952Estimation of the equating coefficients using the multiple item response function method.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.83588 0.018346
## A test3 0.83551 0.020907
## A test4 0.82863 0.020163
## A test5 1.01232 0.021216
## B test1 0.00000 0.000000
## B test2 0.10838 0.021732
## B test3 0.20976 0.022989
## B test4 0.37218 0.023038
## B test5 0.49821 0.023505Estimation of the equating coefficients using the multiple item response function method. The initial values are the estimates obtained with the multiple mean-geometric mean method.
## Computation of equating coefficients . . . .## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.83588 0.018346
## A test3 0.83551 0.020907
## A test4 0.82863 0.020163
## A test5 1.01232 0.021216
## B test1 0.00000 0.000000
## B test2 0.10838 0.021732
## B test3 0.20976 0.022989
## B test4 0.37218 0.023038
## B test5 0.49821 0.023505Estimation of the equating coefficients using the multiple test response function method.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.83636 0.018414
## A test3 0.83687 0.021036
## A test4 0.83097 0.020288
## A test5 1.01625 0.021242
## B test1 0.00000 0.000000
## B test2 0.10677 0.021781
## B test3 0.20626 0.023079
## B test4 0.36896 0.023105
## B test5 0.49615 0.023550Estimation of the equating coefficients using the likelihood-based method.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 1.00000 0.000000
## A test2 0.83598 0.018307
## A test3 0.83685 0.020879
## A test4 0.83112 0.020097
## A test5 1.01735 0.021281
## B test1 0.00000 0.000000
## B test2 0.10860 0.021723
## B test3 0.21062 0.022994
## B test4 0.37256 0.023027
## B test5 0.49782 0.023502It is possible to change the base form, that is the form whose item parameter estimates are left unchanged. All other item parameter estimates are converted to the scale of the base form.
## Computation of equating coefficients . . . .
## Computation of standard errors . . . .## Equating coefficients:
## EQ Form Estimate StdErr
## A test1 0.98302 0.020562
## A test2 0.82178 0.020199
## A test3 0.82268 0.020485
## A test4 0.81696 0.017662
## A test5 1.00000 0.000000
## B test1 -0.48940 0.023486
## B test2 -0.38266 0.023121
## B test3 -0.28236 0.022808
## B test4 -0.12318 0.021301
## B test5 0.00000 0.000000The package computes estimates of the item parameters on the scale of the base form, obtained using all estimates available for the same item across all the forms. Their standard errors are also computed. They can be extracted as follows (using the multiple item response function method).
## Item Estimate StdErr
## 1 Dscrmn.I1 1.02652530 0.03495975
## 2 Dscrmn.I10 1.31948324 0.04191803
## 3 Dscrmn.I11 1.06342212 0.04224192
## 4 Dscrmn.I12 1.10845097 0.04290795
## 5 Dscrmn.I13 1.37885644 0.04903040
## 6 Dscrmn.I14 1.18555992 0.04467058
## 7 Dscrmn.I15 1.08034189 0.04233749
## 8 Dscrmn.I16 1.37261998 0.04859053
## 9 Dscrmn.I17 1.25174298 0.04602021
## 10 Dscrmn.I18 1.14803194 0.04332686
## 11 Dscrmn.I19 1.31580738 0.04872432
## 12 Dscrmn.I2 1.13822432 0.03720922
## 13 Dscrmn.I20 1.00764475 0.03982246
## 14 Dscrmn.I21 1.19507601 0.04486314
## 15 Dscrmn.I22 1.24082387 0.04649240
## 16 Dscrmn.I23 1.29795840 0.04916097
## 17 Dscrmn.I24 1.04197007 0.04135682
## 18 Dscrmn.I25 1.28124101 0.04707868
## 19 Dscrmn.I26 1.33037490 0.04829875
## 20 Dscrmn.I27 1.31366426 0.04847777
## 21 Dscrmn.I28 1.15439454 0.04383667
## 22 Dscrmn.I29 1.10637354 0.04397104
## 23 Dscrmn.I3 1.07855018 0.03598696
## 24 Dscrmn.I30 1.30604236 0.04850613
## 25 Dscrmn.I31 1.46888755 0.04241811
## 26 Dscrmn.I32 1.36995941 0.04104517
## 27 Dscrmn.I33 1.33421246 0.03937279
## 28 Dscrmn.I34 1.40114311 0.04123979
## 29 Dscrmn.I35 1.29815213 0.03835338
## 30 Dscrmn.I36 1.05179536 0.03409166
## 31 Dscrmn.I37 1.26979112 0.03774838
## 32 Dscrmn.I38 1.47862668 0.04232501
## 33 Dscrmn.I39 1.38810080 0.04052315
## 34 Dscrmn.I4 1.31548168 0.04116937
## 35 Dscrmn.I40 1.45854135 0.04347621
## 36 Dscrmn.I41 1.19020293 0.04362829
## 37 Dscrmn.I42 1.20045309 0.04252692
## 38 Dscrmn.I43 1.18295833 0.04270864
## 39 Dscrmn.I44 1.14471888 0.04116369
## 40 Dscrmn.I45 1.39705107 0.04621696
## 41 Dscrmn.I46 1.35358270 0.04673421
## 42 Dscrmn.I47 1.26265214 0.04281988
## 43 Dscrmn.I48 1.15607873 0.04036263
## 44 Dscrmn.I49 0.98071137 0.03644209
## 45 Dscrmn.I5 1.02766152 0.03506514
## 46 Dscrmn.I50 1.23335941 0.04212137
## 47 Dscrmn.I6 0.94149371 0.03479529
## 48 Dscrmn.I7 1.00568277 0.03460417
## 49 Dscrmn.I8 1.18404445 0.03821698
## 50 Dscrmn.I9 1.00420319 0.03477178
## 51 Dffclt.I1 0.04729781 0.02626137
## 52 Dffclt.I10 0.67038640 0.02732356
## 53 Dffclt.I11 0.93113357 0.03786443
## 54 Dffclt.I12 0.79050080 0.03394265
## 55 Dffclt.I13 0.43713941 0.02580696
## 56 Dffclt.I14 0.75476773 0.03217098
## 57 Dffclt.I15 0.82963371 0.03520837
## 58 Dffclt.I16 0.11717165 0.02454754
## 59 Dffclt.I17 0.59912678 0.02880217
## 60 Dffclt.I18 0.57943272 0.02960223
## 61 Dffclt.I19 0.89351648 0.03337780
## 62 Dffclt.I2 0.01210300 0.02491868
## 63 Dffclt.I20 0.07415299 0.02822900
## 64 Dffclt.I21 0.23688948 0.02654187
## 65 Dffclt.I22 -0.09924292 0.02835816
## 66 Dffclt.I23 -0.41499245 0.03312636
## 67 Dffclt.I24 0.62596997 0.03080688
## 68 Dffclt.I25 0.39511469 0.02610118
## 69 Dffclt.I26 0.28096278 0.02541336
## 70 Dffclt.I27 0.74521506 0.02949214
## 71 Dffclt.I28 0.38465839 0.02720872
## 72 Dffclt.I29 -0.41131364 0.03550641
## 73 Dffclt.I3 0.04689779 0.02558258
## 74 Dffclt.I30 0.81859219 0.03083072
## 75 Dffclt.I31 0.52979689 0.02372639
## 76 Dffclt.I32 0.80606548 0.02743385
## 77 Dffclt.I33 0.55956721 0.02498080
## 78 Dffclt.I34 -0.36526934 0.02563614
## 79 Dffclt.I35 0.45865817 0.02460116
## 80 Dffclt.I36 0.85492089 0.03189395
## 81 Dffclt.I37 0.48778059 0.02493596
## 82 Dffclt.I38 -0.12764922 0.02319156
## 83 Dffclt.I39 0.51879390 0.02436926
## 84 Dffclt.I4 0.38880128 0.02448540
## 85 Dffclt.I40 0.85877342 0.02694958
## 86 Dffclt.I41 -0.58159689 0.03787620
## 87 Dffclt.I42 -0.28819961 0.03160015
## 88 Dffclt.I43 1.26082476 0.03757152
## 89 Dffclt.I44 1.12148675 0.03504277
## 90 Dffclt.I45 0.56097371 0.02531162
## 91 Dffclt.I46 -0.31006416 0.03034852
## 92 Dffclt.I47 0.47890518 0.02583944
## 93 Dffclt.I48 0.20248015 0.02675857
## 94 Dffclt.I49 0.28033084 0.02880551
## 95 Dffclt.I5 0.01797425 0.02628429
## 96 Dffclt.I50 0.34072018 0.02579272
## 97 Dffclt.I6 -0.77064798 0.03742373
## 98 Dffclt.I7 0.14049864 0.02665738
## 99 Dffclt.I8 0.33649415 0.02530837
## 100 Dffclt.I9 -0.17811176 0.02743718Equated scores with the true score equating method
## The following scores are not attainable: 0## theta test1 test2.as.test1 StdErr_test2.as.test1 test3.as.test1
## 1 -2.344 1 1.073 0.027 0.783
## 2 -1.661 2 2.072 0.034 1.651
## 3 -1.242 3 3.041 0.039 2.551
## 4 -0.929 4 3.992 0.041 3.469
## 5 -0.672 5 4.933 0.042 4.402
## 6 -0.449 6 5.870 0.042 5.346
## 7 -0.248 7 6.806 0.041 6.301
## 8 -0.060 8 7.743 0.040 7.264
## 9 0.119 9 8.682 0.040 8.236
## 10 0.293 10 9.626 0.041 9.217
## 11 0.467 11 10.576 0.043 10.208
## 12 0.642 12 11.534 0.047 11.209
## 13 0.825 13 12.501 0.052 12.222
## 14 1.018 14 13.481 0.058 13.249
## 15 1.230 15 14.476 0.062 14.293
## 16 1.472 16 15.491 0.065 15.358
## 17 1.764 17 16.532 0.065 16.450
## 18 2.152 18 17.611 0.060 17.578
## 19 2.781 19 18.746 0.044 18.753
## 20 35.212 20 20.000 0.000 20.000
## StdErr_test3.as.test1 test4.as.test1 StdErr_test4.as.test1 test5.as.test1
## 1 0.041 0.932 0.050 0.750
## 2 0.060 1.967 0.071 1.633
## 3 0.070 3.016 0.080 2.562
## 4 0.074 4.061 0.082 3.516
## 5 0.074 5.096 0.080 4.486
## 6 0.071 6.116 0.076 5.467
## 7 0.067 7.124 0.070 6.456
## 8 0.063 8.118 0.065 7.453
## 9 0.060 9.102 0.061 8.456
## 10 0.060 10.075 0.059 9.466
## 11 0.063 11.041 0.059 10.483
## 12 0.068 12.002 0.061 11.508
## 13 0.074 12.961 0.065 12.540
## 14 0.081 13.920 0.069 13.580
## 15 0.087 14.884 0.073 14.629
## 16 0.091 15.858 0.074 15.688
## 17 0.089 16.848 0.073 16.756
## 18 0.081 17.861 0.066 17.836
## 19 0.059 18.909 0.049 18.926
## 20 0.000 20.000 0.000 20.000
## StdErr_test5.as.test1
## 1 0.034
## 2 0.047
## 3 0.052
## 4 0.052
## 5 0.050
## 6 0.047
## 7 0.045
## 8 0.043
## 9 0.041
## 10 0.040
## 11 0.041
## 12 0.042
## 13 0.044
## 14 0.047
## 15 0.050
## 16 0.051
## 17 0.051
## 18 0.047
## 19 0.036
## 20 0.000Equated scores with the observed score equating method, avoiding computation of standard errors
## test1 test2.as.test1 test3.as.test1 test4.as.test1 test5.as.test1
## 1 0 0.031 -0.164 -0.025 -0.158
## 2 1 1.032 0.714 0.983 0.725
## 3 2 2.014 1.611 2.013 1.639
## 4 3 2.982 2.524 3.048 2.576
## 5 4 3.941 3.444 4.079 3.531
## 6 5 4.893 4.379 5.102 4.498
## 7 6 5.841 5.327 6.115 5.475
## 8 7 6.788 6.285 7.117 6.460
## 9 8 7.735 7.252 8.110 7.453
## 10 9 8.683 8.227 9.094 8.453
## 11 10 9.635 9.211 10.070 9.458
## 12 11 10.590 10.203 11.041 10.470
## 13 12 11.551 11.203 12.007 11.489
## 14 13 12.519 12.214 12.971 12.515
## 15 14 13.497 13.235 13.935 13.547
## 16 15 14.487 14.269 14.902 14.588
## 17 16 15.489 15.317 15.875 15.637
## 18 17 16.507 16.378 16.858 16.693
## 19 18 17.551 17.451 17.854 17.757
## 20 19 18.626 18.548 18.868 18.829
## 21 20 19.742 19.703 19.906 19.907