CTT dan IRT DICHOTOMOUS
Heru Wiryanto
August 4, 2016
CTT punya Analisa
Ini hasil analisa data ujian matematika (benar/salah) yang diikuti 7130 orang dan 10 soal
## Loading required package: multilevel## Loading required package: nlme## Loading required package: MASS## Warning in read.spss("mathg6.sav", to.data.frame = TRUE): mathg6.sav:
## Unrecognized record type 7, subtype 18 encountered in system file## re-encoding from CP1252## Warning in cor(x, TOT, use = "complete"): the standard deviation is zero## Warning in cor(x, TOT.woi, use = "complete"): the standard deviation is
## zero## Sample.SD Item.total Item.Tot.woi Difficulty Discrimination
## V1 0.3722668 0.3856870 0.2304420 0.834 0.2942943
## V2 0.4544508 0.4822591 0.3026286 0.709 0.4774775
## V3 0.4511624 0.5212417 0.3497617 0.716 0.5315315
## V4 0.4420853 0.5516544 0.3898520 0.734 0.5345345
## V5 0.4977427 0.5613090 0.3778609 0.550 0.6516517
## V6 0.4539891 0.5835584 0.4235215 0.710 0.5915916
## V7 0.4950364 0.4840760 0.2865799 0.572 0.5555556
## V8 0.4549098 0.5610327 0.3957490 0.708 0.5615616
## V9 0.4506818 0.5894298 0.4320636 0.717 0.6036036
## V10 0.2159760 0.3702086 0.2821553 0.951 0.1201201
## filter_. 0.0000000 NA NA 1.000 0.0000000
## Item.Criterion Item.Reliab Item.Rel.woi Item.Validity
## V1 NA 0.1435067 0.08574299 NA
## V2 NA 0.2190534 0.13746102 NA
## V3 NA 0.2350471 0.15772043 NA
## V4 NA 0.2437564 0.17226164 NA
## V5 NA 0.2792477 0.18798344 NA
## V6 NA 0.2647967 0.19217800 NA
## V7 NA 0.2395154 0.14179653 NA
## V8 NA 0.2550916 0.17994009 NA
## V9 NA 0.2655125 0.19462581 NA
## V10 NA 0.0799162 0.06090832 NA
## filter_. NA NA NA NA## [1] 0.6784851## LCL ALPHA UCL
## 1 0.7148683 0.7245 0.7339356Analisa Rasch Model
## Loading required package: msm## Loading required package: polycor## Loading required package: mvtnorm## Loading required package: sfsmisc## Warning: glm.fit: algorithm did not converge##
## Call:
## rasch(data = mathg6, constraint = cbind(ncol(mathg6) + 1, 1))
##
## Model Summary:
## log.Lik AIC BIC
## -5213.032 10448.06 10502.05
##
## Coefficients:
## value std.err z.vals
## Dffclt.V1 -1.9386 0.0972 -19.9344
## Dffclt.V2 -1.0845 0.0830 -13.0694
## Dffclt.V3 -1.1256 0.0834 -13.4883
## Dffclt.V4 -1.2338 0.0848 -14.5535
## Dffclt.V5 -0.2437 0.0773 -3.1510
## Dffclt.V6 -1.0903 0.0830 -13.1294
## Dffclt.V7 -0.3534 0.0777 -4.5500
## Dffclt.V8 -1.0786 0.0829 -13.0093
## Dffclt.V9 -1.1315 0.0835 -13.5480
## Dffclt.V10 -3.4361 0.1555 -22.0901
## Dffclt.filter_. -26.5661 14120.6008 -0.0019
## Dscrmn 1.0000 NA NA
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): 7.5e-06
## quasi-Newton: BFGS
##
## Call:
## rasch(data = mathg6, constraint = cbind(ncol(mathg6) + 1, 1))
##
## Total Information = 10
## Information in (-10, 10) = 10 (100%)
## Based on all the items
##
## Item-Fit Statistics and P-values
##
## Call:
## rasch(data = mathg6, constraint = cbind(ncol(mathg6) + 1, 1))
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## V1 22.4174 0.001
## V2 32.2738 <0.0001
## V3 61.1025 <0.0001
## V4 66.4189 <0.0001
## V5 86.0035 <0.0001
## V6 89.5578 <0.0001
## V7 40.9280 <0.0001
## V8 70.7723 <0.0001
## V9 91.7241 <0.0001
## V10 58.0512 <0.0001
## filter_. 0.0000 1## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.4970 -1.1510 -0.5207 -0.6412 -0.1848 1.0680## [1] 0.6120304
1PL Analisa
## Warning: glm.fit: algorithm did not converge##
## Call:
## rasch(data = mathg6)
##
## Model Summary:
## log.Lik AIC BIC
## -5205.218 10434.44 10493.33
##
## Coefficients:
## value std.err z.vals
## Dffclt.V1 -1.7117 0.1006 -17.0209
## Dffclt.V2 -0.9612 0.0790 -12.1658
## Dffclt.V3 -0.9974 0.0798 -12.4999
## Dffclt.V4 -1.0928 0.0820 -13.3286
## Dffclt.V5 -0.2189 0.0692 -3.1618
## Dffclt.V6 -0.9663 0.0791 -12.2138
## Dffclt.V7 -0.3159 0.0698 -4.5267
## Dffclt.V8 -0.9561 0.0789 -12.1174
## Dffclt.V9 -1.0026 0.0799 -12.5471
## Dffclt.V10 -3.0156 0.1663 -18.1324
## Dffclt.filter_. -22.6163 11233.0602 -0.0020
## Dscrmn 1.1746 0.0470 24.9953
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): 0.0098
## quasi-Newton: BFGS
##
## Call:
## rasch(data = mathg6)
##
## Total Information = 11.75
## Information in (-10, 10) = 11.75 (100%)
## Based on all the items##
## Call:
## rasch(data = mathg6)
##
## Total Information = 11.75
## Information in (0, 10) = 2.83 (24.13%)
## Based on all the items
##
## Item-Fit Statistics and P-values
##
## Call:
## rasch(data = mathg6, constraint = cbind(ncol(mathg6) + 1, 1))
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## V1 22.4174 0.001
## V2 32.2738 <0.0001
## V3 61.1025 <0.0001
## V4 66.4189 <0.0001
## V5 86.0035 <0.0001
## V6 89.5578 <0.0001
## V7 40.9280 <0.0001
## V8 70.7723 <0.0001
## V9 91.7241 <0.0001
## V10 58.0512 <0.0001
## filter_. 0.0000 1## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.4230 -1.1010 -0.5135 -0.6247 -0.1990 1.05102PL
## Warning: glm.fit: algorithm did not converge##
## Call:
## ltm(formula = mathg6 ~ z1)
##
## Coefficients:
## Dffclt Dscrmn
## V1 -2.355000e+00 0.762
## V2 -1.176000e+00 0.879
## V3 -1.035000e+00 1.111
## V4 -9.880000e-01 1.392
## V5 -2.160000e-01 1.219
## V6 -8.300000e-01 1.533
## V7 -4.130000e-01 0.805
## V8 -8.810000e-01 1.348
## V9 -8.390000e-01 1.614
## V10 -2.272000e+00 1.896
## filter_. 2.498988e+11 0.000
##
## Log.Lik: -5179.223
##
## Call:
## ltm(formula = mathg6 ~ z1)
##
## Total Information = 12.56
## Information in (-10, 10) = 12.56 (100%)
## Based on all the items
##
## Item-Fit Statistics and P-values
##
## Call:
## ltm(formula = mathg6 ~ z1)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## V1 12.3701 0.1354
## V2 19.1640 0.014
## V3 30.0788 0.0002
## V4 30.7628 0.0002
## V5 52.0632 <0.0001
## V6 33.9417 <0.0001
## V7 21.4155 0.0061
## V8 36.9559 <0.0001
## V9 37.8002 <0.0001
## V10 44.1856 <0.0001
## filter_. 0.0000 1
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.4060 -1.0190 -0.5808 -0.6387 -0.2343 1.02203PL Analisa
## Warning: glm.fit: algorithm did not converge##
## Call:
## tpm(data = mathg6)
##
## Model Summary:
## log.Lik AIC BIC
## -5178.772 10423.54 10585.5
##
## Coefficients:
## value std.err z.vals
## Gussng.V1 1.700000e-03 4.600000e-02 0.0370
## Gussng.V2 1.000000e-04 7.100000e-03 0.0128
## Gussng.V3 3.672000e-01 9.450000e-02 3.8850
## Gussng.V4 1.700000e-01 1.733000e-01 0.9808
## Gussng.V5 0.000000e+00 3.800000e-03 0.0095
## Gussng.V6 6.490000e-02 1.643000e-01 0.3949
## Gussng.V7 1.127000e-01 1.953000e-01 0.5772
## Gussng.V8 0.000000e+00 1.000000e-03 0.0034
## Gussng.V9 3.854000e-01 3.530000e-02 10.9150
## Gussng.V10 1.000000e-03 2.710000e-02 0.0385
## Gussng.filter_. 5.000000e-02 NaN NaN
## Dffclt.V1 -2.297900e+00 3.243000e-01 -7.0859
## Dffclt.V2 -1.161400e+00 1.426000e-01 -8.1459
## Dffclt.V3 -1.690000e-01 2.458000e-01 -0.6875
## Dffclt.V4 -6.732000e-01 3.499000e-01 -1.9238
## Dffclt.V5 -2.149000e-01 7.050000e-02 -3.0480
## Dffclt.V6 -7.244000e-01 3.031000e-01 -2.3900
## Dffclt.V7 -8.840000e-02 5.687000e-01 -0.1555
## Dffclt.V8 -8.650000e-01 8.630000e-02 -10.0186
## Dffclt.V9 -3.130000e-02 NaN NaN
## Dffclt.V10 -2.299500e+00 2.107000e-01 -10.9138
## Dffclt.filter_. 2.843882e+09 5.868059e+21 0.0000
## Dscrmn.V1 7.834000e-01 1.207000e-01 6.4906
## Dscrmn.V2 8.895000e-01 1.108000e-01 8.0270
## Dscrmn.V3 1.870200e+00 5.234000e-01 3.5728
## Dscrmn.V4 1.606600e+00 3.819000e-01 4.2075
## Dscrmn.V5 1.172100e+00 1.240000e-01 9.4550
## Dscrmn.V6 1.569500e+00 3.210000e-01 4.8897
## Dscrmn.V7 9.198000e-01 2.866000e-01 3.2091
## Dscrmn.V8 1.368100e+00 1.452000e-01 9.4198
## Dscrmn.V9 1.724840e+01 NaN NaN
## Dscrmn.V10 1.865600e+00 3.060000e-01 6.0977
## Dscrmn.filter_. 0.000000e+00 1.927519e+04 0.0000
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Optimizer: optim (BFGS)
## Convergence: 0
## max(|grad|): 0.028
##
## Call:
## tpm(data = mathg6)
##
## Total Information = 16.73
## Information in (-10, 10) = 16.73 (100%)
## Based on all the items##
## Call:
## tpm(data = mathg6)
##
## Total Information = 16.73
## Information in (0, 10) = 6.29 (37.58%)
## Based on all the items
##
## Item-Fit Statistics and P-values
##
## Call:
## tpm(data = mathg6)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## V1 28.0417 0.0002
## V2 44.1994 <0.0001
## V3 51.9982 <0.0001
## V4 83.2102 <0.0001
## V5 73.5609 <0.0001
## V6 75.5793 <0.0001
## V7 38.7992 <0.0001
## V8 58.3654 <0.0001
## V9 123.9174 <0.0001
## V10 84.8073 <0.0001
## filter_. 0.0000 1
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.26500 -0.94930 -0.25520 -0.46950 0.05524 0.99970Perbandingan 3 Model
##
## Call:
## rasch(data = mathg6)
##
## Total Information = 11.75
## Information in (-10, 10) = 11.75 (100%)
## Based on all the items##
## Call:
## ltm(formula = mathg6 ~ z1)
##
## Total Information = 12.56
## Information in (-10, 10) = 12.56 (100%)
## Based on all the items##
## Call:
## tpm(data = mathg6)
##
## Total Information = 16.73
## Information in (-10, 10) = 16.73 (100%)
## Based on all the itemsAnova 3 Model
##
## Likelihood Ratio Table
## AIC BIC log.Lik LRT df p.value
## mathg6.1pl 10434.44 10493.33 -5205.22
## mathg6.2pl 10402.45 10510.42 -5179.22 51.99 10 <0.001##
## Likelihood Ratio Table
## AIC BIC log.Lik LRT df p.value
## mathg6.2pl 10402.45 10510.42 -5179.22
## mathg6.3pl 10423.54 10585.50 -5178.77 0.9 11 1