Item Response Data Parameter Estimation Techniques
Mr. Osama Alwusaidi
9/7/2019
Abstract
Comparison of the parameters of the items estimated according to classical test theory and item response theory: a simulation study By: Osama AbdulAziz Alwusaidi
There are two currently popular statistical frameworks for addressing measurement problems such as test development, test-score equating, and the identification of biased test items: Classical Test Theory (CTT) and Item Response Theory (IRT). This study is aimed empirically to examine the similarities and differences in the parameters of the items estimated using these two frameworks. and identify the statistical psychometric characteristics of the parameters of the items according to the classical theory and the item response theory, and determine the type and strength of the relationships between the estimates of the parameters of the items according to these two frameworks. In order to fulfill the objectives of the study, the descriptive methodology was used. and The population of the study was made up about a simulation study.For this purpose:
Contents
- Basic descriptive statistics
- 2PLM IRT
- 3PLM IRT
Basic descriptive statistics
summary(Data_OAlwusaidi)## Item01 Item02 Item03 Item04
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.686 Mean :0.779 Mean :0.755 Mean :0.877
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item05 Item06 Item07 Item08
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :0.000 Median :0.000
## Mean :0.733 Mean :0.784 Mean :0.426 Mean :0.381
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item09 Item10 Item11 Item12
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.00
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:0.00
## Median :1.000 Median :1.000 Median :1.000 Median :0.00
## Mean :0.509 Mean :0.704 Mean :0.753 Mean :0.48
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.00
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.00
## Item13 Item14 Item15 Item16
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.792 Mean :0.554 Mean :0.721 Mean :0.624
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item17 Item18 Item19 Item20
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.00
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:1.00
## Median :0.000 Median :1.000 Median :1.000 Median :1.00
## Mean :0.364 Mean :0.589 Mean :0.569 Mean :0.88
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.00
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.00
## Item21 Item22 Item23 Item24
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.737 Mean :0.586 Mean :0.674 Mean :0.606
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item25 Item26 Item27 Item28
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.00 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.00 Median :1.000 Median :1.000 Median :1.000
## Mean :0.53 Mean :0.753 Mean :0.703 Mean :0.636
## 3rd Qu.:1.00 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.00 Max. :1.000 Max. :1.000 Max. :1.000
## Item29 Item30 Item31 Item32
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :0.000
## Mean :0.805 Mean :0.715 Mean :0.729 Mean :0.349
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item33 Item34 Item35 Item36
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :0.000
## Mean :0.551 Mean :0.606 Mean :0.645 Mean :0.322
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item37 Item38 Item39 Item40
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :0.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.391 Mean :0.759 Mean :0.774 Mean :0.771
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item41 Item42 Item43 Item44
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :1.000 Median :0.000
## Mean :0.647 Mean :0.481 Mean :0.502 Mean :0.472
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item45 Item46 Item47 Item48
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.404 Mean :0.818 Mean :0.587 Mean :0.576
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item49 Item50 Item51 Item52
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.568 Mean :0.783 Mean :0.562 Mean :0.517
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item53 Item54 Item55 Item56
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :0.000
## Mean :0.958 Mean :0.774 Mean :0.548 Mean :0.496
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Item57 Item58 Item59 Item60
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000 Median :0.000 Median :1.000
## Mean :0.481 Mean :0.494 Mean :0.459 Mean :0.722
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.0002PLM IRT with R Output
summary(tplm)##
## Call:
## ltm(formula = Data_OAlwusaidi ~ z1)
##
## Model Summary:
## log.Lik AIC BIC
## -34433.95 69107.89 69696.82
##
## Coefficients:
## value std.err z.vals
## Dffclt.Item01 -0.9615 0.1097 -8.7670
## Dffclt.Item02 -2.3913 0.3819 -6.2618
## Dffclt.Item03 -1.4393 0.1558 -9.2385
## Dffclt.Item04 -2.1661 0.2293 -9.4474
## Dffclt.Item05 -1.2519 0.1335 -9.3780
## Dffclt.Item06 -1.2516 0.1035 -12.0893
## Dffclt.Item07 1.0404 0.3238 3.2128
## Dffclt.Item08 0.6325 0.0970 6.5182
## Dffclt.Item09 -0.0558 0.1076 -0.5188
## Dffclt.Item10 -1.9792 0.3621 -5.4664
## Dffclt.Item11 -1.6458 0.2034 -8.0913
## Dffclt.Item12 0.1148 0.0897 1.2804
## Dffclt.Item13 -1.6104 0.1657 -9.7169
## Dffclt.Item14 -0.2781 0.0834 -3.3335
## Dffclt.Item15 -1.0702 0.1067 -10.0302
## Dffclt.Item16 -0.7034 0.1080 -6.5154
## Dffclt.Item17 0.7322 0.1022 7.1666
## Dffclt.Item18 -0.6340 0.1343 -4.7203
## Dffclt.Item19 -0.3586 0.0860 -4.1701
## Dffclt.Item20 -2.2987 0.2598 -8.8490
## Dffclt.Item21 -1.6679 0.2234 -7.4670
## Dffclt.Item22 -0.5757 0.1227 -4.6937
## Dffclt.Item23 -1.6402 0.3009 -5.4520
## Dffclt.Item24 -0.7232 0.1337 -5.4075
## Dffclt.Item25 -0.1411 0.0724 -1.9479
## Dffclt.Item26 -1.1650 0.1052 -11.0789
## Dffclt.Item27 -1.1056 0.1255 -8.8103
## Dffclt.Item28 -0.6435 0.0852 -7.5524
## Dffclt.Item29 -1.5041 0.1360 -11.0623
## Dffclt.Item30 -1.6225 0.2359 -6.8775
## Dffclt.Item31 -1.4399 0.1760 -8.1802
## Dffclt.Item32 1.4655 0.2735 5.3589
## Dffclt.Item33 -0.2648 0.0840 -3.1527
## Dffclt.Item34 -0.5974 0.1023 -5.8416
## Dffclt.Item35 -0.6210 0.0750 -8.2837
## Dffclt.Item36 0.7874 0.0840 9.3750
## Dffclt.Item37 0.6844 0.1178 5.8122
## Dffclt.Item38 -1.4410 0.1530 -9.4185
## Dffclt.Item39 -1.8478 0.2331 -7.9288
## Dffclt.Item40 -1.4840 0.1536 -9.6595
## Dffclt.Item41 -1.0438 0.1640 -6.3629
## Dffclt.Item42 0.1323 0.1066 1.2409
## Dffclt.Item43 -0.0171 0.0634 -0.2701
## Dffclt.Item44 0.2283 0.1280 1.7841
## Dffclt.Item45 0.9978 0.2322 4.2977
## Dffclt.Item46 -1.5017 0.1290 -11.6439
## Dffclt.Item47 -0.6003 0.1279 -4.6932
## Dffclt.Item48 -0.3573 0.0765 -4.6681
## Dffclt.Item49 -0.4701 0.1218 -3.8598
## Dffclt.Item50 -2.7732 0.5052 -5.4893
## Dffclt.Item51 -0.4354 0.1223 -3.5611
## Dffclt.Item52 -0.0888 0.0829 -1.0722
## Dffclt.Item53 -2.3152 0.2174 -10.6508
## Dffclt.Item54 -1.7828 0.2176 -8.1946
## Dffclt.Item55 -0.2958 0.1024 -2.8888
## Dffclt.Item56 0.0261 0.0923 0.2832
## Dffclt.Item57 0.1398 0.1124 1.2437
## Dffclt.Item58 0.0554 0.1264 0.4377
## Dffclt.Item59 0.3704 0.1489 2.4872
## Dffclt.Item60 -1.3626 0.1649 -8.2647
## Dscrmn.Item01 0.9638 0.0997 9.6668
## Dscrmn.Item02 0.5584 0.0929 6.0099
## Dscrmn.Item03 0.9043 0.1040 8.6994
## Dscrmn.Item04 1.0735 0.1405 7.6381
## Dscrmn.Item05 0.9469 0.1032 9.1706
## Dscrmn.Item06 1.3575 0.1335 10.1669
## Dscrmn.Item07 0.2958 0.0707 4.1820
## Dscrmn.Item08 0.9034 0.0895 10.0958
## Dscrmn.Item09 0.6439 0.0795 8.1039
## Dscrmn.Item10 0.4557 0.0817 5.5807
## Dscrmn.Item11 0.7519 0.0968 7.7644
## Dscrmn.Item12 0.8135 0.0852 9.5433
## Dscrmn.Item13 0.9742 0.1130 8.6202
## Dscrmn.Item14 0.9214 0.0908 10.1434
## Dscrmn.Item15 1.0890 0.1090 9.9861
## Dscrmn.Item16 0.8211 0.0893 9.1913
## Dscrmn.Item17 0.8951 0.0895 10.0035
## Dscrmn.Item18 0.6094 0.0799 7.6223
## Dscrmn.Item19 0.9110 0.0913 9.9756
## Dscrmn.Item20 1.0078 0.1380 7.3029
## Dscrmn.Item21 0.6732 0.0917 7.3448
## Dscrmn.Item22 0.6557 0.0815 8.0426
## Dscrmn.Item23 0.4615 0.0796 5.7946
## Dscrmn.Item24 0.6459 0.0819 7.8852
## Dscrmn.Item25 1.0891 0.0987 11.0340
## Dscrmn.Item26 1.2147 0.1204 10.0903
## Dscrmn.Item27 0.9070 0.0986 9.1981
## Dscrmn.Item28 1.0704 0.1017 10.5275
## Dscrmn.Item29 1.1665 0.1256 9.2884
## Dscrmn.Item30 0.6091 0.0874 6.9710
## Dscrmn.Item31 0.7674 0.0948 8.0981
## Dscrmn.Item32 0.4482 0.0756 5.9283
## Dscrmn.Item33 0.9095 0.0903 10.0681
## Dscrmn.Item34 0.8224 0.0887 9.2752
## Dscrmn.Item35 1.2681 0.1129 11.2296
## Dscrmn.Item36 1.2175 0.1066 11.4252
## Dscrmn.Item37 0.7291 0.0827 8.8165
## Dscrmn.Item38 0.9259 0.1052 8.7971
## Dscrmn.Item39 0.7351 0.0987 7.4474
## Dscrmn.Item40 0.9588 0.1086 8.8255
## Dscrmn.Item41 0.6272 0.0832 7.5400
## Dscrmn.Item42 0.6574 0.0797 8.2471
## Dscrmn.Item43 1.3329 0.1107 12.0397
## Dscrmn.Item44 0.5422 0.0760 7.1378
## Dscrmn.Item45 0.4091 0.0732 5.5889
## Dscrmn.Item46 1.2748 0.1357 9.3962
## Dscrmn.Item47 0.6324 0.0808 7.8306
## Dscrmn.Item48 1.0661 0.0984 10.8358
## Dscrmn.Item49 0.6263 0.0799 7.8430
## Dscrmn.Item50 0.4833 0.0910 5.3102
## Dscrmn.Item51 0.6131 0.0792 7.7379
## Dscrmn.Item52 0.8955 0.0892 10.0438
## Dscrmn.Item53 1.8782 0.2908 6.4593
## Dscrmn.Item54 0.7683 0.1002 7.6644
## Dscrmn.Item55 0.7159 0.0825 8.6773
## Dscrmn.Item56 0.7762 0.0840 9.2399
## Dscrmn.Item57 0.6181 0.0783 7.8922
## Dscrmn.Item58 0.5342 0.0758 7.0462
## Dscrmn.Item59 0.4787 0.0742 6.4496
## Dscrmn.Item60 0.7865 0.0948 8.2928
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): 0.026
## quasi-Newton: BFGS2PLM IRT with Plot
3PLM IRT R Output
summary(three_plm)##
## Call:
## tpm(data = Data_OAlwusaidi)
##
## Model Summary:
## log.Lik AIC BIC
## -34393.58 69147.16 70030.55
##
## Coefficients:
## value std.err z.vals
## Gussng.Item01 0.3471 0.0902 3.8466
## Gussng.Item02 0.0029 0.1604 0.0180
## Gussng.Item03 0.3090 0.1549 1.9955
## Gussng.Item04 0.3689 0.4296 0.8587
## Gussng.Item05 0.3830 0.1096 3.4942
## Gussng.Item06 0.2355 0.2234 1.0539
## Gussng.Item07 0.3229 0.0701 4.6087
## Gussng.Item08 0.1222 0.0504 2.4238
## Gussng.Item09 0.0003 0.0324 0.0086
## Gussng.Item10 0.0008 0.0507 0.0150
## Gussng.Item11 0.0001 0.0149 0.0072
## Gussng.Item12 0.2172 0.0575 3.7778
## Gussng.Item13 0.4253 0.2317 1.8356
## Gussng.Item14 0.2011 0.0747 2.6927
## Gussng.Item15 0.3277 0.0985 3.3255
## Gussng.Item16 0.2165 0.1486 1.4574
## Gussng.Item17 0.1375 0.0498 2.7597
## Gussng.Item18 0.2953 0.1465 2.0158
## Gussng.Item19 0.1422 0.0991 1.4345
## Gussng.Item20 0.0001 0.0089 0.0057
## Gussng.Item21 0.0000 0.0058 0.0069
## Gussng.Item22 0.3171 0.1063 2.9838
## Gussng.Item23 0.5037 0.0762 6.6092
## Gussng.Item24 0.1758 0.2950 0.5959
## Gussng.Item25 0.0000 0.0011 0.0083
## Gussng.Item26 0.0000 0.0039 0.0050
## Gussng.Item27 0.3592 0.1151 3.1207
## Gussng.Item28 0.3133 0.0803 3.9029
## Gussng.Item29 0.4082 0.1193 3.4218
## Gussng.Item30 0.0000 0.0058 0.0086
## Gussng.Item31 0.3208 0.2091 1.5339
## Gussng.Item32 0.1914 0.0761 2.5159
## Gussng.Item33 0.2320 0.0714 3.2475
## Gussng.Item34 0.1584 0.1681 0.9424
## Gussng.Item35 0.1110 0.1147 0.9679
## Gussng.Item36 0.0850 0.0306 2.7760
## Gussng.Item37 0.0298 0.1065 0.2796
## Gussng.Item38 0.1747 0.3235 0.5400
## Gussng.Item39 0.0003 0.0256 0.0111
## Gussng.Item40 0.0000 0.0028 0.0052
## Gussng.Item41 0.0000 0.0026 0.0063
## Gussng.Item42 0.2944 0.0652 4.5164
## Gussng.Item43 0.1324 0.0501 2.6436
## Gussng.Item44 0.2029 0.1378 1.4723
## Gussng.Item45 0.0754 0.2536 0.2975
## Gussng.Item46 0.3333 0.1429 2.3316
## Gussng.Item47 0.1602 0.2687 0.5961
## Gussng.Item48 0.1986 0.0828 2.3987
## Gussng.Item49 0.1027 0.2575 0.3990
## Gussng.Item50 0.0011 0.0819 0.0139
## Gussng.Item51 0.1726 0.2477 0.6968
## Gussng.Item52 0.0000 0.0012 0.0070
## Gussng.Item53 0.0001 0.0167 0.0046
## Gussng.Item54 0.5671 0.0659 8.6122
## Gussng.Item55 0.2041 0.1169 1.7463
## Gussng.Item56 0.1924 0.0801 2.4020
## Gussng.Item57 0.3127 0.0423 7.4014
## Gussng.Item58 0.0001 0.0039 0.0141
## Gussng.Item59 0.0044 0.1347 0.0327
## Gussng.Item60 0.2259 0.2849 0.7930
## Dffclt.Item01 -0.0638 0.2632 -0.2425
## Dffclt.Item02 -2.4242 0.6384 -3.7972
## Dffclt.Item03 -0.6673 0.4668 -1.4298
## Dffclt.Item04 -1.5176 1.1684 -1.2988
## Dffclt.Item05 -0.2589 0.3376 -0.7670
## Dffclt.Item06 -0.8466 0.4676 -1.8107
## Dffclt.Item07 2.2051 0.4251 5.1866
## Dffclt.Item08 0.8898 0.1359 6.5470
## Dffclt.Item09 -0.0510 0.1529 -0.3338
## Dffclt.Item10 -2.0524 0.4361 -4.7068
## Dffclt.Item11 -1.6751 0.2087 -8.0265
## Dffclt.Item12 0.6990 0.1657 4.2180
## Dffclt.Item13 -0.5662 0.7549 -0.7501
## Dffclt.Item14 0.2513 0.2031 1.2372
## Dffclt.Item15 -0.3126 0.2607 -1.1993
## Dffclt.Item16 -0.0847 0.4455 -0.1902
## Dffclt.Item17 1.0034 0.1299 7.7245
## Dffclt.Item18 0.4407 0.5392 0.8174
## Dffclt.Item19 0.0206 0.2691 0.0765
## Dffclt.Item20 -2.3849 0.2614 -9.1227
## Dffclt.Item21 -1.6841 0.2230 -7.5534
## Dffclt.Item22 0.5055 0.3662 1.3804
## Dffclt.Item23 0.7913 0.3857 2.0518
## Dffclt.Item24 -0.1207 1.0540 -0.1145
## Dffclt.Item25 -0.1284 0.0728 -1.7638
## Dffclt.Item26 -1.1941 0.1097 -10.8822
## Dffclt.Item27 -0.1405 0.3623 -0.3876
## Dffclt.Item28 0.1164 0.2115 0.5503
## Dffclt.Item29 -0.6441 0.3272 -1.9686
## Dffclt.Item30 -1.6345 0.2350 -6.9539
## Dffclt.Item31 -0.4990 0.7295 -0.6841
## Dffclt.Item32 1.8858 0.2785 6.7722
## Dffclt.Item33 0.3507 0.1966 1.7841
## Dffclt.Item34 -0.1487 0.4956 -0.3001
## Dffclt.Item35 -0.3894 0.2478 -1.5715
## Dffclt.Item36 0.9115 0.0891 10.2328
## Dffclt.Item37 0.7669 0.3175 2.4155
## Dffclt.Item38 -1.0608 0.8443 -1.2564
## Dffclt.Item39 -1.9134 0.2506 -7.6358
## Dffclt.Item40 -1.5363 0.1607 -9.5609
## Dffclt.Item41 -1.0431 0.1636 -6.3776
## Dffclt.Item42 1.0086 0.1904 5.2961
## Dffclt.Item43 0.2683 0.1135 2.3632
## Dffclt.Item44 0.9849 0.4741 2.0773
## Dffclt.Item45 1.3544 1.1254 1.2035
## Dffclt.Item46 -0.8965 0.3359 -2.6692
## Dffclt.Item47 -0.0412 0.9788 -0.0421
## Dffclt.Item48 0.1229 0.2084 0.5900
## Dffclt.Item49 -0.1087 0.9135 -0.1189
## Dffclt.Item50 -2.8487 0.5943 -4.7934
## Dffclt.Item51 0.1866 0.9092 0.2052
## Dffclt.Item52 -0.0791 0.0821 -0.9627
## Dffclt.Item53 -2.5418 0.2401 -10.5882
## Dffclt.Item54 0.0921 0.2783 0.3309
## Dffclt.Item55 0.3503 0.3743 0.9360
## Dffclt.Item56 0.5790 0.2349 2.4647
## Dffclt.Item57 1.0617 0.1472 7.2135
## Dffclt.Item58 0.0566 0.1273 0.4446
## Dffclt.Item59 0.3899 0.6092 0.6401
## Dffclt.Item60 -0.7442 0.8992 -0.8277
## Dscrmn.Item01 1.4468 0.2984 4.8478
## Dscrmn.Item02 0.5496 0.0941 5.8418
## Dscrmn.Item03 1.1013 0.2239 4.9194
## Dscrmn.Item04 1.1573 0.3621 3.1964
## Dscrmn.Item05 1.3676 0.3017 4.5332
## Dscrmn.Item06 1.5472 0.3742 4.1344
## Dscrmn.Item07 0.8972 0.5248 1.7097
## Dscrmn.Item08 1.3087 0.2572 5.0879
## Dscrmn.Item09 0.6485 0.0830 7.8180
## Dscrmn.Item10 0.4384 0.0798 5.4946
## Dscrmn.Item11 0.7371 0.0931 7.9176
## Dscrmn.Item12 1.3152 0.2643 4.9768
## Dscrmn.Item13 1.3066 0.4841 2.6992
## Dscrmn.Item14 1.2781 0.2337 5.4692
## Dscrmn.Item15 1.5133 0.2831 5.3453
## Dscrmn.Item16 1.0462 0.2643 3.9585
## Dscrmn.Item17 1.4133 0.3184 4.4385
## Dscrmn.Item18 0.9198 0.3287 2.7986
## Dscrmn.Item19 1.0992 0.2022 5.4362
## Dscrmn.Item20 0.9694 0.1273 7.6128
## Dscrmn.Item21 0.6667 0.0884 7.5416
## Dscrmn.Item22 1.0754 0.3246 3.3133
## Dscrmn.Item23 1.0014 0.3370 2.9712
## Dscrmn.Item24 0.7678 0.3167 2.4246
## Dscrmn.Item25 1.0805 0.0978 11.0517
## Dscrmn.Item26 1.1646 0.1134 10.2729
## Dscrmn.Item27 1.2899 0.3095 4.1678
## Dscrmn.Item28 1.7069 0.3773 4.5238
## Dscrmn.Item29 1.5561 0.3086 5.0420
## Dscrmn.Item30 0.6047 0.0847 7.1395
## Dscrmn.Item31 0.9633 0.2781 3.4636
## Dscrmn.Item32 0.8653 0.3680 2.3515
## Dscrmn.Item33 1.3537 0.2696 5.0209
## Dscrmn.Item34 0.9657 0.2417 3.9949
## Dscrmn.Item35 1.4018 0.2340 5.9901
## Dscrmn.Item36 1.7716 0.2806 6.3133
## Dscrmn.Item37 0.7810 0.1935 4.0371
## Dscrmn.Item38 0.9926 0.2589 3.8343
## Dscrmn.Item39 0.7065 0.0940 7.5171
## Dscrmn.Item40 0.9168 0.1027 8.9295
## Dscrmn.Item41 0.6270 0.0815 7.6943
## Dscrmn.Item42 1.3778 0.4378 3.1468
## Dscrmn.Item43 1.7833 0.2735 6.5212
## Dscrmn.Item44 0.7816 0.3101 2.5203
## Dscrmn.Item45 0.4645 0.2603 1.7848
## Dscrmn.Item46 1.5233 0.2704 5.6338
## Dscrmn.Item47 0.7351 0.2837 2.5913
## Dscrmn.Item48 1.4201 0.2715 5.2306
## Dscrmn.Item49 0.6999 0.2362 2.9634
## Dscrmn.Item50 0.4699 0.0882 5.3263
## Dscrmn.Item51 0.7450 0.3062 2.4331
## Dscrmn.Item52 0.9058 0.0894 10.1324
## Dscrmn.Item53 1.6708 0.2507 6.6646
## Dscrmn.Item54 1.5409 0.3779 4.0774
## Dscrmn.Item55 0.9581 0.2467 3.8842
## Dscrmn.Item56 1.1119 0.2457 4.5256
## Dscrmn.Item57 1.4862 0.3529 4.2113
## Dscrmn.Item58 0.5337 0.0758 7.0428
## Dscrmn.Item59 0.4800 0.1126 4.2641
## Dscrmn.Item60 0.9007 0.2687 3.3524
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Optimizer: optim (BFGS)
## Convergence: 0
## max(|grad|): 0.0623PLM IRT with Plot
