4 Practical session
4.1 Install packages
install.packages(c("psych", "ltm", "irtoys", "mirt", "latticeExtra"))4.2 Load required libraries
library("psych")
library("ltm")
library("irtoys")
library("mirt")
library("latticeExtra")4.3 Load data
Download data set “mtf.csv”.
Read data set “mtf.csv” into “data.mtf” data frame
data.mtf = read.csv("mtf.csv", header = TRUE) # Includes headers
head(data.mtf) # View first 6 students in the data set## Q1A Q1B Q1C Q1D Q1E Q2A Q2B Q2C Q2D Q2E
## 1 1 0 0 0 0 0 1 1 0 0
## 2 1 0 0 0 1 0 0 1 1 1
## 3 0 1 0 0 1 1 0 1 1 0
## 4 1 1 0 1 1 0 1 0 1 1
## 5 1 1 1 0 1 1 1 1 1 0
## 6 0 1 1 1 1 0 1 1 1 1names(data.mtf) # List down variables in the data set## [1] "Q1A" "Q1B" "Q1C" "Q1D" "Q1E" "Q2A" "Q2B" "Q2C" "Q2D" "Q2E"dim(data.mtf) # Data set consists of 10 variables and 160 students## [1] 160 104.4 Descriptive statistics
Percentages of correct answers (1) by questions
response.frequencies(data.mtf)## 0 1 miss
## Q1A 0.30625 0.69375 0
## Q1B 0.25625 0.74375 0
## Q1C 0.37500 0.62500 0
## Q1D 0.40625 0.59375 0
## Q1E 0.16250 0.83750 0
## Q2A 0.25000 0.75000 0
## Q2B 0.26875 0.73125 0
## Q2C 0.34375 0.65625 0
## Q2D 0.47500 0.52500 0
## Q2E 0.48125 0.51875 04.5 IRT analysis, 2-PL model
Perform analysis by ltm
# Basic statistics using ltm, focus on percentages of correct answers (1) by questions
descript(data.mtf)##
## Descriptive statistics for the 'data.mtf' data-set
##
## Sample:
## 10 items and 160 sample units; 0 missing values
##
## Proportions for each level of response:
## 0 1 logit
## Q1A 0.3062 0.6938 0.8177
## Q1B 0.2562 0.7438 1.0656
## Q1C 0.3750 0.6250 0.5108
## Q1D 0.4062 0.5938 0.3795
## Q1E 0.1625 0.8375 1.6397
## Q2A 0.2500 0.7500 1.0986
## Q2B 0.2688 0.7312 1.0010
## Q2C 0.3438 0.6562 0.6466
## Q2D 0.4750 0.5250 0.1001
## Q2E 0.4812 0.5188 0.0750
##
##
## Frequencies of total scores:
## 0 1 2 3 4 5 6 7 8 9 10
## Freq 2 1 1 7 6 19 38 31 27 16 12
##
##
## Point Biserial correlation with Total Score:
## Included Excluded
## Q1A 0.4259 0.2084
## Q1B 0.3381 0.1236
## Q1C 0.5585 0.3539
## Q1D 0.4177 0.1832
## Q1E 0.3819 0.2068
## Q2A 0.3798 0.1712
## Q2B 0.3497 0.1327
## Q2C 0.4403 0.2175
## Q2D 0.4895 0.2623
## Q2E 0.4619 0.2296
##
##
## Cronbach's alpha:
## value
## All Items 0.5033
## Excluding Q1A 0.4772
## Excluding Q1B 0.5018
## Excluding Q1C 0.4277
## Excluding Q1D 0.4857
## Excluding Q1E 0.4791
## Excluding Q2A 0.4881
## Excluding Q2B 0.4995
## Excluding Q2C 0.4743
## Excluding Q2D 0.4589
## Excluding Q2E 0.4702
##
##
## Pairwise Associations:
## Item i Item j p.value
## 1 3 5 1.000
## 2 6 8 1.000
## 3 2 10 1.000
## 4 4 5 0.978
## 5 2 3 0.963
## 6 7 10 0.945
## 7 6 7 0.918
## 8 1 4 0.836
## 9 1 5 0.803
## 10 5 8 0.800# Perform the analysis with ltm(), and save the results in "irt.mtf"
irt.mtf = ltm(data.mtf ~ z1, IRT.param = TRUE)
coef(irt.mtf) # Obtain difficulty and discrimination parameter estimates## Dffclt Dscrmn
## Q1A -1.34813444 0.6637809
## Q1B -4.20384339 0.2572201
## Q1C -0.40398852 2.0871272
## Q1D -0.53216018 0.8114138
## Q1E -3.96868564 0.4283655
## Q2A -2.64619595 0.4320399
## Q2B -2.05447180 0.5154989
## Q2C -1.06267344 0.6670853
## Q2D -0.13935513 0.8074819
## Q2E -0.09428061 0.9122159summary(irt.mtf) # Obtain LL, SE & z.vals##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Model Summary:
## log.Lik AIC BIC
## -956.738 1953.476 2014.979
##
## Coefficients:
## value std.err z.vals
## Dffclt.Q1A -1.3481 0.5674 -2.3758
## Dffclt.Q1B -4.2038 4.1223 -1.0198
## Dffclt.Q1C -0.4040 0.1527 -2.6457
## Dffclt.Q1D -0.5322 0.2748 -1.9362
## Dffclt.Q1E -3.9687 2.8787 -1.3786
## Dffclt.Q2A -2.6462 1.6249 -1.6285
## Dffclt.Q2B -2.0545 1.0384 -1.9785
## Dffclt.Q2C -1.0627 0.4600 -2.3101
## Dffclt.Q2D -0.1394 0.2281 -0.6108
## Dffclt.Q2E -0.0943 0.2059 -0.4578
## Dscrmn.Q1A 0.6638 0.2876 2.3077
## Dscrmn.Q1B 0.2572 0.2558 1.0055
## Dscrmn.Q1C 2.0871 0.9927 2.1025
## Dscrmn.Q1D 0.8114 0.3007 2.6980
## Dscrmn.Q1E 0.4284 0.3284 1.3045
## Dscrmn.Q2A 0.4320 0.2762 1.5640
## Dscrmn.Q2B 0.5155 0.2721 1.8949
## Dscrmn.Q2C 0.6671 0.2762 2.4148
## Dscrmn.Q2D 0.8075 0.3078 2.6232
## Dscrmn.Q2E 0.9122 0.3166 2.8810
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): 0.0083
## quasi-Newton: BFGSplot(irt.mtf, type = "ICC", legend = TRUE) # Item Characteristic Curves
plot(irt.mtf, type = "ICC", legend = TRUE, items=3) # Q1c
plot(irt.mtf, type = "IIC", legend = TRUE) # Item Information Curves
# or Item Information Function
plot(irt.mtf, type = "IIC", legend = TRUE, items=3) # Q1c
plot(irt.mtf, items = 0, type = "IIC") # Test Information Function
information(irt.mtf, c(-3,3)) # Test information between -3 to +3 ability range##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Total Information = 7.46
## Information in (-3, 3) = 5.87 (78.7%)
## Based on all the items# "irtoys" package
plot(trf(est(data.mtf, model = "2PL", engine = "ltm"))) #Test Characteristic Curve
# or Test Response Function
# Item fit
item.fit(irt.mtf) # df = 10-2 = 8##
## Item-Fit Statistics and P-values
##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## Q1A 14.3105 0.074
## Q1B 24.0446 0.0023
## Q1C 33.1838 0.0001
## Q1D 14.9949 0.0592
## Q1E 12.8225 0.1181
## Q2A 16.4653 0.0362
## Q2B 19.8424 0.0109
## Q2C 15.9399 0.0432
## Q2D 15.8849 0.0441
## Q2E 15.2307 0.0548# Fit for margins
margins(irt.mtf)##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Fit on the Two-Way Margins
##
## Response: (0,0)
## Item i Item j Obs Exp (O-E)^2/E
## 1 5 6 14 7.24 6.32 ***
## 2 2 5 13 7.11 4.87 ***
## 3 4 7 15 20.18 1.33
##
## Response: (1,0)
## Item i Item j Obs Exp (O-E)^2/E
## 1 2 5 13 18.89 1.84
## 2 5 6 26 32.78 1.40
## 3 4 7 28 22.83 1.17
##
## Response: (0,1)
## Item i Item j Obs Exp (O-E)^2/E
## 1 5 6 12 18.77 2.44
## 2 2 5 28 33.89 1.02
## 3 7 10 23 19.30 0.71
##
## Response: (1,1)
## Item i Item j Obs Exp (O-E)^2/E
## 1 5 6 108 101.22 0.45
## 2 4 7 67 72.09 0.36
## 3 2 5 106 100.10 0.35
##
## '***' denotes a chi-squared residual greater than 3.5table(data.mtf[,5], data.mtf[,6])##
## 0 1
## 0 14 12
## 1 26 108# Personfit
person.fit(irt.mtf)##
## Person-Fit Statistics and P-values
##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Alternative: Inconsistent response pattern under the estimated model
##
## Q1A Q1B Q1C Q1D Q1E Q2A Q2B Q2C Q2D Q2E L0 Lz Pr(<Lz)
## 1 0 0 0 0 0 0 0 0 0 0 -5.3491 0.1492 0.5593
## 2 0 0 0 0 0 0 1 0 0 0 -5.7587 0.0019 0.5008
## 3 0 0 0 0 1 0 0 1 1 0 -7.1412 -0.8338 0.2022
## 4 0 0 0 0 1 1 1 0 0 1 -6.2277 0.0566 0.5226
## 5 0 0 0 1 1 1 0 0 0 0 -6.0112 0.1226 0.5488
## 6 0 0 1 1 0 1 0 0 1 1 -9.3691 -2.7050 0.0034
## 7 0 0 1 1 1 1 0 1 0 1 -7.0497 -0.8796 0.1895
## 8 0 0 1 1 1 1 1 1 0 0 -6.0974 -0.0330 0.4868
## 9 0 0 1 1 1 1 1 1 1 0 -5.8550 -0.1146 0.4544
## 10 0 1 0 0 0 1 1 0 1 0 -6.4326 -0.1797 0.4287
## 11 0 1 0 0 0 1 1 1 0 1 -6.7261 -0.3680 0.3564
## 12 0 1 0 0 1 0 0 0 0 0 -4.4674 1.0838 0.8608
## 13 0 1 0 0 1 0 0 1 1 1 -7.3993 -1.0325 0.1509
## 14 0 1 0 0 1 0 1 0 0 0 -4.5660 1.2017 0.8853
## 15 0 1 0 0 1 1 0 1 0 0 -4.8410 1.1836 0.8817
## 16 0 1 0 0 1 1 0 1 1 0 -5.8466 0.4695 0.6806
## 17 0 1 0 0 1 1 1 0 0 0 -4.2362 1.6547 0.951
## 18 0 1 0 0 1 1 1 1 0 0 -4.5394 1.6404 0.9495
## 19 0 1 0 1 1 0 0 0 0 0 -5.7648 0.2894 0.6139
## 20 0 1 0 1 1 1 0 1 0 0 -5.5319 0.7744 0.7806
## 21 0 1 0 1 1 1 0 1 0 1 -6.2890 0.0724 0.5289
## 22 0 1 0 1 1 1 1 0 0 0 -5.0006 1.2492 0.8942
## 23 0 1 0 1 1 1 1 0 1 0 -5.7161 0.6577 0.7446
## 24 0 1 0 1 1 1 1 0 1 1 -6.1913 0.0810 0.5323
## 25 0 1 0 1 1 1 1 1 0 0 -4.9991 1.3733 0.9152
## 26 0 1 0 1 1 1 1 1 1 0 -5.4548 0.8436 0.8006
## 27 0 1 1 0 0 0 1 0 0 0 -7.8996 -1.5247 0.0637
## 28 0 1 1 0 1 0 1 1 1 1 -6.2894 -0.3985 0.3451
## 29 0 1 1 0 1 1 1 0 0 1 -6.0336 0.1110 0.5442
## 30 0 1 1 0 1 1 1 0 1 0 -5.9842 0.1842 0.5731
## 31 0 1 1 0 1 1 1 1 1 1 -4.9444 0.3598 0.6405
## 32 0 1 1 1 0 1 0 0 1 1 -8.2693 -1.8092 0.0352
## 33 0 1 1 1 0 1 1 1 1 1 -5.9333 -0.4310 0.3332
## 34 0 1 1 1 1 0 1 1 0 1 -5.9688 -0.1709 0.4322
## 35 0 1 1 1 1 0 1 1 1 0 -5.9748 -0.1397 0.4445
## 36 0 1 1 1 1 0 1 1 1 1 -5.3796 -0.0839 0.4666
## 37 0 1 1 1 1 1 0 0 0 0 -6.5403 -0.2283 0.4097
## 38 0 1 1 1 1 1 0 0 0 1 -6.6974 -0.5251 0.2998
## 39 0 1 1 1 1 1 0 1 0 1 -5.9111 -0.1006 0.4599
## 40 0 1 1 1 1 1 1 0 0 0 -5.6659 0.4669 0.6797
## 41 0 1 1 1 1 1 1 1 0 0 -5.0117 0.7396 0.7702
## 42 0 1 1 1 1 1 1 1 1 0 -4.6559 0.6006 0.7259
## 43 0 1 1 1 1 1 1 1 1 1 -3.7934 0.6764 0.7506
## 44 1 0 0 0 0 0 1 1 0 0 -6.9109 -0.6356 0.2625
## 45 1 0 0 0 1 0 0 1 1 1 -7.9170 -1.5621 0.0591
## 46 1 0 0 0 1 1 0 1 1 1 -7.0419 -0.7051 0.2404
## 47 1 0 0 0 1 1 1 0 0 1 -6.0914 0.2702 0.6065
## 48 1 0 0 0 1 1 1 0 1 1 -6.6073 -0.2652 0.3954
## 49 1 0 0 0 1 1 1 1 0 0 -5.2154 1.1030 0.865
## 50 1 0 0 1 0 1 1 1 1 1 -7.5369 -1.2126 0.1126
## 51 1 0 0 1 1 0 1 0 1 0 -7.0246 -0.6586 0.2551
## 52 1 0 0 1 1 1 0 1 1 0 -6.6411 -0.3033 0.3808
## 53 1 0 0 1 1 1 1 1 0 0 -5.5093 0.8545 0.8036
## 54 1 0 1 0 0 1 0 1 1 0 -8.2484 -1.8260 0.0339
## 55 1 0 1 0 0 1 1 0 1 0 -7.8653 -1.4952 0.0674
## 56 1 0 1 0 1 0 1 0 1 0 -7.3076 -0.9952 0.1598
## 57 1 0 1 0 1 0 1 1 1 0 -6.6629 -0.5472 0.2921
## 58 1 0 1 0 1 1 1 0 0 1 -6.2595 -0.1931 0.4234
## 59 1 0 1 0 1 1 1 0 1 1 -5.9749 -0.2324 0.4081
## 60 1 0 1 0 1 1 1 1 0 1 -5.4343 0.1994 0.579
## 61 1 0 1 1 0 0 1 1 0 0 -8.0274 -1.6300 0.0516
## 62 1 0 1 1 0 0 1 1 0 1 -7.8626 -1.5206 0.0642
## 63 1 0 1 1 0 1 0 0 1 1 -8.3552 -1.8750 0.0304
## 64 1 0 1 1 1 1 0 0 0 1 -6.8642 -0.7376 0.2304
## 65 1 0 1 1 1 1 0 1 1 0 -5.9563 -0.2370 0.4063
## 66 1 0 1 1 1 1 1 0 0 1 -5.6539 -0.0117 0.4953
## 67 1 0 1 1 1 1 1 0 1 1 -4.9732 0.0941 0.5375
## 68 1 0 1 1 1 1 1 1 0 0 -5.1215 0.4673 0.6798
## 69 1 0 1 1 1 1 1 1 1 1 -3.4214 0.6813 0.7522
## 70 1 1 0 0 1 0 0 0 0 0 -5.0246 0.8719 0.8084
## 71 1 1 0 0 1 0 1 1 0 0 -5.0779 1.1979 0.8845
## 72 1 1 0 0 1 0 1 1 0 1 -5.8639 0.5036 0.6927
## 73 1 1 0 0 1 0 1 1 1 0 -5.7578 0.6147 0.7306
## 74 1 1 0 0 1 1 0 0 0 0 -4.6496 1.3514 0.9117
## 75 1 1 0 0 1 1 0 1 0 1 -5.7167 0.6555 0.7439
## 76 1 1 0 0 1 1 1 0 0 0 -4.3491 1.8175 0.9654
## 77 1 1 0 0 1 1 1 0 1 0 -5.1259 1.2456 0.8935
## 78 1 1 0 0 1 1 1 1 0 0 -4.3989 1.9559 0.9748
## 79 1 1 0 0 1 1 1 1 0 1 -4.9956 1.3034 0.9038
## 80 1 1 0 0 1 1 1 1 1 1 -5.1697 0.8453 0.801
## 81 1 1 0 1 0 1 0 1 0 0 -6.5941 -0.2354 0.407
## 82 1 1 0 1 0 1 0 1 1 0 -7.1560 -0.8032 0.2109
## 83 1 1 0 1 0 1 1 1 0 0 -6.0012 0.3694 0.6441
## 84 1 1 0 1 1 0 1 0 1 1 -6.5220 -0.2712 0.3931
## 85 1 1 0 1 1 0 1 1 0 1 -5.8787 0.3542 0.6384
## 86 1 1 0 1 1 1 0 0 1 1 -6.4110 -0.1536 0.439
## 87 1 1 0 1 1 1 0 1 0 1 -5.7623 0.4852 0.6862
## 88 1 1 0 1 1 1 0 1 1 1 -5.8264 0.1775 0.5704
## 89 1 1 0 1 1 1 1 0 0 0 -4.8102 1.5624 0.9409
## 90 1 1 0 1 1 1 1 0 0 1 -5.3456 0.9240 0.8222
## 91 1 1 0 1 1 1 1 1 1 0 -4.8045 1.2109 0.887
## 92 1 1 1 0 0 0 1 1 1 1 -6.9988 -0.9553 0.1697
## 93 1 1 1 0 1 1 0 0 0 1 -6.2213 -0.0917 0.4635
## 94 1 1 1 0 1 1 0 1 0 0 -5.5539 0.5654 0.7141
## 95 1 1 1 0 1 1 1 0 1 0 -5.1456 0.6381 0.7383
## 96 1 1 1 0 1 1 1 0 1 1 -4.7604 0.4832 0.6855
## 97 1 1 1 0 1 1 1 1 0 0 -4.5552 1.1784 0.8807
## 98 1 1 1 0 1 1 1 1 0 1 -4.2418 0.9028 0.8167
## 99 1 1 1 0 1 1 1 1 1 0 -4.2654 0.9445 0.8275
## 100 1 1 1 0 1 1 1 1 1 1 -3.4982 0.9309 0.8241
## 101 1 1 1 1 0 0 0 0 0 0 -8.3867 -2.0246 0.0215
## 102 1 1 1 1 0 0 1 1 0 0 -6.9665 -0.7589 0.224
## 103 1 1 1 1 0 0 1 1 0 1 -6.6777 -0.7364 0.2307
## 104 1 1 1 1 1 0 0 1 0 1 -6.0762 -0.2961 0.3836
## 105 1 1 1 1 1 0 1 0 1 0 -5.7898 -0.0038 0.4985
## 106 1 1 1 1 1 0 1 0 1 1 -5.1965 0.0318 0.5127
## 107 1 1 1 1 1 0 1 1 1 0 -4.7628 0.4177 0.6619
## 108 1 1 1 1 1 0 1 1 1 1 -3.7415 0.5882 0.7218
## 109 1 1 1 1 1 1 0 0 1 1 -5.1815 0.0768 0.5306
## 110 1 1 1 1 1 1 0 1 0 1 -4.6903 0.4544 0.6752
## 111 1 1 1 1 1 1 0 1 1 0 -4.7336 0.4765 0.6831
## 112 1 1 1 1 1 1 0 1 1 1 -3.7708 0.6136 0.7303
## 113 1 1 1 1 1 1 1 0 0 0 -4.8260 0.8868 0.8124
## 114 1 1 1 1 1 1 1 0 0 1 -4.4388 0.6942 0.7562
## 115 1 1 1 1 1 1 1 0 1 1 -3.6114 0.7856 0.7839
## 116 1 1 1 1 1 1 1 1 0 0 -3.9443 1.1638 0.8777
## 117 1 1 1 1 1 1 1 1 0 1 -3.1747 1.1231 0.8693
## 118 1 1 1 1 1 1 1 1 1 0 -3.2570 1.1337 0.8715
## 119 1 1 1 1 1 1 1 1 1 1 -1.9076 1.3843 0.9169# Unidimensional test
unidimTest(irt.mtf) # This takes a long time to run##
## Unidimensionality Check using Modified Parallel Analysis
##
## Call:
## ltm(formula = data.mtf ~ z1, IRT.param = TRUE)
##
## Matrix of tertachoric correlations
## Q1A Q1B Q1C Q1D Q1E Q2A Q2B Q2C Q2D
## Q1A 1.0000 -0.0873 0.2124 0.0501 0.0738 0.0964 0.2495 0.2419 0.2960
## Q1B -0.0873 1.0000 0.0319 0.0669 0.4343 0.1619 0.1139 0.1501 0.0742
## Q1C 0.2124 0.0319 1.0000 0.4312 0.0167 0.1025 0.3287 0.2354 0.3051
## Q1D 0.0501 0.0669 0.4312 1.0000 -0.0370 0.0881 -0.1215 0.2428 0.0858
## Q1E 0.0738 0.4343 0.0167 -0.0370 1.0000 0.5049 0.1484 0.0724 0.2314
## Q2A 0.0964 0.1619 0.1025 0.0881 0.5049 1.0000 -0.0451 0.0134 0.1961
## Q2B 0.2495 0.1139 0.3287 -0.1215 0.1484 -0.0451 1.0000 0.1125 0.1690
## Q2C 0.2419 0.1501 0.2354 0.2428 0.0724 0.0134 0.1125 1.0000 0.1643
## Q2D 0.2960 0.0742 0.3051 0.0858 0.2314 0.1961 0.1690 0.1643 1.0000
## Q2E 0.1961 0.0131 0.4066 0.2681 0.0947 0.1352 -0.0330 0.1498 0.1734
## Q2E
## Q1A 0.1961
## Q1B 0.0131
## Q1C 0.4066
## Q1D 0.2681
## Q1E 0.0947
## Q2A 0.1352
## Q2B -0.0330
## Q2C 0.1498
## Q2D 0.1734
## Q2E 1.0000
##
## Alternative hypothesis: the second eigenvalue of the observed data is substantially larger
## than the second eigenvalue of data under the assumed IRT model
##
## Second eigenvalue in the observed data: 1.1476
## Average of second eigenvalues in Monte Carlo samples: 0.9433
## Monte Carlo samples: 100
## p-value: 0.0891Repeat analysis with mirt
# "mirt" package
# simple way to fit the model
mirt.mtf = mirt(data.mtf, 1, itemtype = "2PL")coef(mirt.mtf, IRTpars = T, simplify = T)## $items
## a b g u
## Q1A 0.663 -1.349 0 1
## Q1B 0.257 -4.207 0 1
## Q1C 2.093 -0.404 0 1
## Q1D 0.811 -0.532 0 1
## Q1E 0.428 -3.973 0 1
## Q2A 0.432 -2.648 0 1
## Q2B 0.516 -2.053 0 1
## Q2C 0.667 -1.063 0 1
## Q2D 0.807 -0.140 0 1
## Q2E 0.912 -0.094 0 1
##
## $means
## F1
## 0
##
## $cov
## F1
## F1 1# test info
areainfo(mirt.mtf, c(-3,3))## LowerBound UpperBound Info TotalInfo Proportion nitems
## -3 3 5.877779 7.467052 0.787162 10# plots
plot(mirt.mtf, type = "trace")
plot(mirt.mtf, type = "infotrace")
plot(mirt.mtf, type = "info")
plot(mirt.mtf, type = "infoSE")
plot(mirt.mtf)
# model fit
M2(mirt.mtf) # M2 nsig.## Warning in (1 - accel) * longpars: Recycling array of length 1 in array-vector arithmetic is deprecated.
## Use c() or as.vector() instead.## Warning in accel * preMstep.longpars: Recycling array of length 1 in array-vector arithmetic is deprecated.
## Use c() or as.vector() instead.## M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR
## stats 45.27155 35 0.1145428 0.04296208 0 0.07530942 0.07488569
## TLI CFI
## stats 0.7982402 0.8430757itemfit(mirt.mtf)## item S_X2 df.S_X2 p.S_X2
## 1 Q1A 1.353 5 0.929
## 2 Q1B 9.367 5 0.095
## 3 Q1C 0.132 3 0.988
## 4 Q1D 9.299 5 0.098
## 5 Q1E 3.241 4 0.518
## 6 Q2A 10.220 5 0.069
## 7 Q2B 1.231 5 0.942
## 8 Q2C 2.134 5 0.830
## 9 Q2D 6.402 5 0.269
## 10 Q2E 4.570 4 0.334personfit(mirt.mtf)## Zh
## 1 -0.59920953
## 2 -1.55278581
## 3 0.48361416
## 4 -0.28806330
## 5 0.86186607
## 6 -0.12945241
## 7 0.43249649
## 8 -0.21983954
## 9 -0.28447053
## 10 1.16550221
## 11 0.41626410
## 12 0.35450391
## 13 1.07463370
## 14 0.41054254
## 15 1.63477195
## 16 1.35254110
## 17 1.20135830
## 18 0.07666715
## 19 -0.15323259
## 20 0.06945484
## 21 1.06490231
## 22 0.05086960
## 23 0.64776424
## 24 -0.76909670
## 25 -0.23601304
## 26 -2.02591373
## 27 -0.34175787
## 28 0.14815545
## 29 -0.15091822
## 30 0.20695314
## 31 1.25676002
## 32 1.80902937
## 33 0.53015360
## 34 1.10417602
## 35 0.81470044
## 36 0.04837985
## 37 1.35254110
## 38 -0.28002229
## 39 0.39074013
## 40 1.25676002
## 41 -0.78175354
## 42 0.13335641
## 43 1.06490231
## 44 1.35254110
## 45 1.22027754
## 46 0.15455766
## 47 1.96074685
## 48 0.57072655
## 49 -0.07278620
## 50 -0.76577439
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## 54 -1.52812052
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## 56 1.35445353
## 57 -0.01659993
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## 59 0.29636756
## 60 0.87044347
## 61 0.64776424
## 62 0.78414741
## 63 1.35254110
## 64 -1.49875377
## 65 -0.34604077
## 66 1.05858201
## 67 1.10994010
## 68 1.96074685
## 69 -0.15091822
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## 71 0.86424000
## 72 -0.07278620
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## 74 -0.79381635
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## 76 1.35254110
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## 87 0.62716282
## 88 0.64776424
## 89 -1.87225814
## 90 -0.21983954
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## 92 1.35254110
## 93 0.20695314
## 94 -1.63070670
## 95 1.35254110
## 96 0.73355830
## 97 1.25676002
## 98 0.51453078
## 99 0.89232188
## 100 0.39954995
## 101 1.35254110
## 102 -1.50017716
## 103 0.38152393
## 104 0.54912052
## 105 -0.30169107
## 106 -0.57831523
## 107 0.47169486
## 108 0.41626410
## 109 0.82230273
## 110 -0.55239952
## 111 0.07850495
## 112 1.57198816
## 113 0.35450391
## 114 -0.16844663
## 115 1.06490231
## 116 -0.18877086
## 117 1.18950617
## 118 0.86186607
## 119 0.86186607
## 120 1.05858201
## 121 0.52909299
## 122 0.80017804
## 123 -0.64344399
## 124 0.29636756
## 125 -0.70571658
## 126 1.35254110
## 127 0.91572740
## 128 -0.26241847
## 129 -1.00637158
## 130 0.31503532
## 131 -0.79758405
## 132 0.33709094
## 133 0.13929727
## 134 -1.52812052
## 135 0.57072655
## 136 -1.52812052
## 137 0.86186607
## 138 -0.98137057
## 139 1.30235700
## 140 -0.06599807
## 141 -0.90361524
## 142 -2.67731095
## 143 0.28574583
## 144 0.02564499
## 145 1.35254110
## 146 0.62129773
## 147 -0.46778735
## 148 0.66826134
## 149 -1.01123703
## 150 0.07850495
## 151 0.82230273
## 152 -0.16561168
## 153 -0.23118694
## 154 1.35254110
## 155 1.96074685
## 156 -0.44042666
## 157 0.08194588
## 158 -1.80566517
## 159 1.65468756
## 160 1.11965959# reliabilities: marginal & empirical
marginal_rxx(mirt.mtf) # 0.5574205## [1] 0.5574205theta_se = fscores(mirt.mtf, full.scores.SE = T)
empirical_rxx(theta_se) # 0.5681729## F1
## 0.5681729Refer to Brown (2014) for explanations abour marginal and empirical reliabilities.
4.6 References
- Arifin, W. N., Yusoff, M. S. B. (in press). Item Response Theory for Medical Educationists. Education in Medicine Journal.
- Baker, F. B. (2001). The basics of item response theory (2nd ed). USA: ERIC Clearinghouse on Assessment and Evaluation. Retrieved from: http://echo.edres.org:8080/irt/baker/final.pdf
- Brown, A. (2014). Item Response Theory approaches to test scoring and evaluating the score accuracy. In Irwing, P., Booth, T. & Hughes, D. (Eds.), The Wiley Handbook of Psychometric Testing. London: John Wiley & Sons. Retrieved from: https://kar.kent.ac.uk/44777/1/Brown%20-%20IRT%20Test%20Scoring%20-%202nd%20revision%20-%20Accepted.pdf
- de Ayala, R. J. (2009). The theory and practice of item response theory. New York: The Guilford Press.
- Edelen, M. O., & Reeve, B. B. (2007). Applying item response theory (IRT) modeling to questionnaire development, evaluation, and refinement. Quality of Life Research, 16(1), 5-18.
- Hambleton, R.K. and Swaminathan, H. and Rogers, H.J. (1991). Fundamentals of Item Response Theory. California, USA: Sage Publications.