JMLE: Joint maximum likelihood estimation of item parameters and...
In NPCD: Nonparametric Methods for Cognitive Diagnosis
Description
Usage
Arguments
Value
References
See Also
Examples
Description
This function returns joint maximum likelihood estimates of item parameters and examinee attribute profiles in cognitive diagnostic models. The algorithm starts from the nonparametric estimation of attribute profiles, implemented by the AlphaNP function, and then iteratively estimates item parameters and attribute profiles using conditional maximum likelihood estimation until the algorithm converges. Currently supported models include the DINA model, the DINO model, he NIDA model, the G-NIDA model, and the R-RUM model.
Usage
1
2
3
Arguments
Y
A matrix of binary responses. Rows represent persons and columns represent items. 1=correct, 0=incorrect.
Q
The Q-matrix of the test. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item.
model
Currently support five models: "DINA", "DINO", "NIDA", "GNIDA", and "RRUM". The default is "DINA".
NP.method
The method of the nonparametric estimation in the initial stage. "Hamming": the plain Hamming distance method; "Weighted": the Hamming distance weighted by inversed item variance; "Penalized": the Hamming distance weighted by inversed item variance and specified penalizing weights for guess and slip. The default is "Weighted".
wg
Additional argument for the "penalized" NP.method. wg is the weight assigned to guessing in the DINA or DINO models. A large value of wg results in a stronger impact on Hamming distance (larger loss function values) caused by guessing.
ws
Additional input for the "penalized" NP.method. ws is the weight assigned to slipping in the DINA or DINO models. A large value of ws results in la stronger impact on Hamming distance (larger loss function values) caused by slipping.
conv.crit.par
The critical value for the maximum absolute change in all item parameters values to determine convergence.
conv.crit.att
The critical value for the percentage of examinee attribute profiles that are changed to determine convergence.
max.ite
The maximum number of iterations allowed.
Value
alpha.est
JMLE estimates of examinee attribute profiles. Rows represent persons and columns represent attributes. 1=examinee masters the attribute, 0=examinee does not master the attribute.
par.est
JMLE estimates of item parameters, including par.est$slip, par.est$guess, par.est$se.slip, and par.est$se.guess for the DINA, DINO, NIDA, and GNIDA models, and par.est$pi, par.est$r, par.est$se.pi and par.est$se.r for the R-RUM model. Note that for the G-NIDA model and the R-RUM model, the item parameter estimates and standard errors are not available for the entries where the Q-matrix is 0.
n.tie
Number of ties in the final log-likelihood among the candidate attribute profiles for each person. When we encounter ties, one of the tied attribute profiles is randomly chosen.
undefined.flag
A binary vector indicating whether the parameters of each item are undefined. 1=undefined, 0=defined.
loglike
The final overall log-likelihood value from the estimated item parameters and attribute profiles based on the specified model.
convergence
A message on whether the algorithm converged.
n.ite
Number of iterations performed.
loglike.matrix
The values for the log-likelihood function in the last iteration for each candidate attribute profile by each person. Rows represent candidate attribute profiles in the same order with the pattern matrix; columns represent different examinees.
est.class
The final class number (row index in pattern) for each person's attribute profile. It can also be used for locating the log-likelihood value in loglike.matrix for the estimated attribute profile for each person.
NP.loss.matrix
The values for the loss function of the nonparametric estimation of Alpha. Rows represent candidate attribute profiles in the same order with the pattern matrix; columns represent different examinees.
NP.alpha.est
The estimates of examinee attribute profiles from the initial nonparameteric estimation.
NP.est.class
The class number (row index in pattern) for each person's attribute profile from the initial nonparametric classification. It can also be used for locating the loss function value in NP.loss.matrix for the estimated attribute profile for each person.
pattern
All possible attribute profiles in the search space.
model
The chosen model.
Q
The Q-matrix of the test.
References
Chiu, C. (2011). Flexible approaches to cognitive diagnosis: nonparametric methods and small sample techniques. Invited session of cognitive diagnosis and item response theory at 2011 Joint Statistical Meeting.
Chiu, C. Y., & Douglas, J. A. (2013). A nonparametric approach to cognitive diagnosis by proximity
to ideal response patterns. Journal of Classification 30(2), 225-250.
See Also
AlphaMLE, AlphaNP, ParMLE, print.JMLE, plot.JMLE
Examples
1
2
3
4
5
6
7
8
9
data("Data.DINA")
JMLE.result <- JMLE(Data.DINA$response, Data.DINA$Q, model="DINA", conv.crit.par=0.001,
conv.crit.att=0.001, max.ite=100)
print(JMLE.result) # Print the estimated item parameters, standard errors,
#and examinee attribute profiles
plot(JMLE.result, nperson=1) # Plot the sorted loss function of different
#attribute profiles for this examinee
ItemFit(JMLE.result)
ModelFit(JMLE.result)
Example output
Loading required package: BB
Loading required package: R.oo
Loading required package: R.methodsS3
R.methodsS3 v1.7.1 (2016-02-15) successfully loaded. See ?R.methodsS3 for help.
R.oo v1.22.0 (2018-04-21) successfully loaded. See ?R.oo for help.
Attaching package: 'R.oo'
The following objects are masked from 'package:methods':
getClasses, getMethods
The following objects are masked from 'package:base':
attach, detach, gc, load, save
Iteration: 1, loglike = -2164.78986, diff.par = 1.00000, diff.att = 1.00000, diff.undefined = 1.00000
Iteration: 2, loglike = -2163.13017, diff.par = 0.00000, diff.att = 0.00000, diff.undefined = 0.00000
Model: DINA
Method: JMLE
Convergence: Convergence criteria met.
Number of iterations: 2
The Estimated Item Parameters
slip SE.slip guess SE.guess
Item 1 0.25000000 0.05103104 0.039473684 0.012895585
Item 2 0.25000000 0.07654655 0.235074627 0.025902699
Item 3 0.19444444 0.04664223 0.271929825 0.029467794
Item 4 0.00000000 0.00000000 0.214765101 0.033642520
Item 5 0.00000000 0.00000000 0.259090909 0.029539097
Item 6 0.03311258 0.01456116 0.154362416 0.029598506
Item 7 0.11038961 0.02525246 0.006849315 0.006825818
Item 8 0.09090909 0.02316578 0.047945205 0.017681827
Item 9 0.27564103 0.03577557 0.194444444 0.032981034
Item 10 0.23076923 0.03373300 0.041666667 0.016652193
Item 11 0.13333333 0.03925227 0.124444444 0.022005860
Item 12 0.22516556 0.03399124 0.013422819 0.009427451
Item 13 0.06944444 0.02995875 0.043859649 0.013562070
Item 14 0.08000000 0.03132624 0.244444444 0.028650488
Item 15 0.25000000 0.03466876 0.131944444 0.028202530
Item 16 0.03246753 0.01428226 0.171232877 0.031176934
Item 17 0.31250000 0.08193819 0.182835821 0.023611192
Item 18 0.00000000 0.00000000 0.089041096 0.023570468
Item 19 0.24000000 0.04931531 0.200000000 0.026666667
Item 20 0.02649007 0.01306842 0.100671141 0.024650097
Model Fit Statistics: AIC = 4420.26, BIC = 4594.34
The Estimated Examinee Attribute Profiles
Attribute 1 Attribute 2 Attribute 3
Examinee 1 1 1 0
Examinee 2 1 1 0
Examinee 3 1 1 0
Examinee 4 1 0 0
Examinee 5 1 0 1
Examinee 6 1 1 0
Examinee 7 1 1 1
Examinee 8 0 1 0
Examinee 9 0 0 1
Examinee 10 0 0 1
Examinee 11 0 1 0
Examinee 12 1 1 1
Examinee 13 1 0 1
Examinee 14 1 0 0
Examinee 15 1 1 0
Examinee 16 1 0 0
Examinee 17 1 1 1
Examinee 18 0 1 1
Examinee 19 1 0 1
Examinee 20 0 0 1
Examinee 21 1 1 1
Examinee 22 0 0 0
Examinee 23 1 0 1
Examinee 24 0 1 1
Examinee 25 1 0 0
Examinee 26 1 0 1
Examinee 27 1 1 1
Examinee 28 0 0 1
Examinee 29 0 0 1
Examinee 30 1 1 1
Examinee 31 0 1 1
Examinee 32 0 0 1
Examinee 33 1 1 1
Examinee 34 0 1 1
Examinee 35 1 1 1
Examinee 36 1 1 1
Examinee 37 1 0 1
Examinee 38 1 0 1
Examinee 39 1 1 1
Examinee 40 0 0 0
Examinee 41 0 1 0
Examinee 42 0 0 0
Examinee 43 1 1 0
Examinee 44 1 1 0
Examinee 45 0 1 1
Examinee 46 1 1 1
Examinee 47 0 0 0
Examinee 48 0 1 0
Examinee 49 1 0 1
Examinee 50 0 1 0
Examinee 51 1 1 1
Examinee 52 1 1 0
Examinee 53 1 0 1
Examinee 54 0 0 1
Examinee 55 1 0 1
Examinee 56 0 1 0
Examinee 57 0 1 1
Examinee 58 1 0 1
Examinee 59 0 1 0
Examinee 60 0 1 1
Examinee 61 0 0 1
Examinee 62 0 1 1
Examinee 63 1 0 0
Examinee 64 0 1 0
Examinee 65 0 0 0
Examinee 66 0 1 0
Examinee 67 1 1 0
Examinee 68 0 1 1
Examinee 69 1 0 0
Examinee 70 0 0 0
Examinee 71 0 1 1
Examinee 72 1 0 0
Examinee 73 1 0 1
Examinee 74 0 0 0
Examinee 75 1 1 1
Examinee 76 0 1 0
Examinee 77 0 1 0
Examinee 78 1 0 0
Examinee 79 0 1 0
Examinee 80 1 1 0
Examinee 81 1 1 0
Examinee 82 0 1 1
Examinee 83 0 1 1
Examinee 84 1 0 1
Examinee 85 1 1 1
Examinee 86 1 0 0
Examinee 87 0 1 1
Examinee 88 0 1 1
Examinee 89 0 1 1
Examinee 90 1 1 0
Examinee 91 1 0 0
Examinee 92 1 1 1
Examinee 93 1 1 1
Examinee 94 0 0 0
Examinee 95 1 0 0
Examinee 96 0 1 0
Examinee 97 0 1 1
Examinee 98 0 1 1
Examinee 99 0 1 0
Examinee 100 0 1 1
Examinee 101 0 0 0
Examinee 102 1 0 0
Examinee 103 1 0 0
Examinee 104 0 1 0
Examinee 105 1 1 0
Examinee 106 1 0 1
Examinee 107 1 0 1
Examinee 108 0 1 1
Examinee 109 1 1 0
Examinee 110 0 0 0
Examinee 111 1 1 0
Examinee 112 0 1 1
Examinee 113 1 1 1
Examinee 114 0 1 1
Examinee 115 1 0 0
Examinee 116 1 0 1
Examinee 117 0 1 1
Examinee 118 0 0 1
Examinee 119 1 0 1
Examinee 120 0 1 0
Examinee 121 0 1 1
Examinee 122 1 0 0
Examinee 123 0 1 0
Examinee 124 0 1 0
Examinee 125 0 0 0
Examinee 126 1 1 0
Examinee 127 0 1 1
Examinee 128 0 0 0
Examinee 129 1 1 1
Examinee 130 0 0 1
Examinee 131 1 0 1
Examinee 132 1 0 0
Examinee 133 0 1 1
Examinee 134 0 1 1
Examinee 135 1 0 0
Examinee 136 1 0 1
Examinee 137 0 0 1
Examinee 138 1 1 1
Examinee 139 0 1 0
Examinee 140 0 1 0
Examinee 141 0 1 0
Examinee 142 0 0 0
Examinee 143 1 0 1
Examinee 144 0 1 1
Examinee 145 0 0 1
Examinee 146 0 0 0
Examinee 147 0 0 1
Examinee 148 1 1 0
Examinee 149 1 0 0
Examinee 150 1 0 0
Examinee 151 1 0 0
Examinee 152 1 0 1
Examinee 153 0 1 1
Examinee 154 0 1 1
Examinee 155 0 0 0
Examinee 156 0 1 0
Examinee 157 0 1 0
Examinee 158 0 0 1
Examinee 159 1 0 0
Examinee 160 0 1 0
Examinee 161 1 1 0
Examinee 162 0 0 1
Examinee 163 1 1 0
Examinee 164 0 1 1
Examinee 165 1 1 0
Examinee 166 1 0 1
Examinee 167 0 1 1
Examinee 168 0 0 1
Examinee 169 0 1 1
Examinee 170 1 0 0
Examinee 171 1 0 0
Examinee 172 1 1 0
Examinee 173 0 1 0
Examinee 174 1 0 1
Examinee 175 0 0 1
Examinee 176 1 1 0
Examinee 177 0 0 0
Examinee 178 1 1 1
Examinee 179 0 1 1
Examinee 180 1 0 1
Examinee 181 1 0 1
Examinee 182 0 1 0
Examinee 183 0 0 1
Examinee 184 1 0 1
Examinee 185 1 1 0
Examinee 186 0 0 0
Examinee 187 1 0 0
Examinee 188 1 1 0
Examinee 189 0 0 1
Examinee 190 1 1 0
Examinee 191 0 1 0
Examinee 192 1 1 1
Examinee 193 1 1 0
Examinee 194 0 1 0
Examinee 195 0 0 0
Examinee 196 0 0 0
Examinee 197 1 0 1
Examinee 198 1 0 1
Examinee 199 0 0 1
Examinee 200 1 0 0
Examinee 201 0 0 1
Examinee 202 0 0 0
Examinee 203 1 1 1
Examinee 204 1 1 0
Examinee 205 1 0 0
Examinee 206 1 0 1
Examinee 207 1 1 0
Examinee 208 0 0 0
Examinee 209 0 1 1
Examinee 210 1 0 1
Examinee 211 1 0 1
Examinee 212 1 0 0
Examinee 213 0 1 1
Examinee 214 0 0 1
Examinee 215 1 1 0
Examinee 216 1 0 1
Examinee 217 1 0 1
Examinee 218 0 1 1
Examinee 219 1 1 1
Examinee 220 0 0 0
Examinee 221 0 1 1
Examinee 222 1 1 0
Examinee 223 1 1 1
Examinee 224 0 1 1
Examinee 225 1 0 1
Examinee 226 1 0 1
Examinee 227 1 1 1
Examinee 228 0 0 0
Examinee 229 1 0 1
Examinee 230 1 1 0
Examinee 231 0 0 1
Examinee 232 0 0 1
Examinee 233 0 0 0
Examinee 234 0 1 0
Examinee 235 1 0 0
Examinee 236 1 1 1
Examinee 237 1 1 1
Examinee 238 0 0 1
Examinee 239 0 1 1
Examinee 240 1 0 1
Examinee 241 0 0 1
Examinee 242 0 0 1
Examinee 243 1 0 0
Examinee 244 0 0 0
Examinee 245 0 0 0
Examinee 246 0 0 0
Examinee 247 1 1 1
Examinee 248 0 1 1
Examinee 249 1 1 0
Examinee 250 0 1 0
Examinee 251 0 0 0
Examinee 252 0 0 1
Examinee 253 0 0 0
Examinee 254 0 1 1
Examinee 255 1 0 0
Examinee 256 0 0 0
Examinee 257 1 1 1
Examinee 258 0 0 1
Examinee 259 1 0 1
Examinee 260 0 0 1
Examinee 261 0 1 1
Examinee 262 1 1 1
Examinee 263 0 1 1
Examinee 264 0 1 0
Examinee 265 1 0 1
Examinee 266 1 0 1
Examinee 267 1 1 0
Examinee 268 0 1 1
Examinee 269 0 0 1
Examinee 270 0 1 1
Examinee 271 0 0 0
Examinee 272 0 1 0
Examinee 273 0 1 1
Examinee 274 1 0 0
Examinee 275 1 0 0
Examinee 276 1 0 0
Examinee 277 0 0 0
Examinee 278 1 0 0
Examinee 279 1 0 1
Examinee 280 1 1 1
Examinee 281 1 0 1
Examinee 282 1 0 0
Examinee 283 0 0 0
Examinee 284 1 1 0
Examinee 285 1 1 0
Examinee 286 0 0 1
Examinee 287 1 1 0
Examinee 288 1 1 0
Examinee 289 0 1 0
Examinee 290 1 1 1
Examinee 291 1 1 0
Examinee 292 1 1 0
Examinee 293 0 0 1
Examinee 294 0 0 0
Examinee 295 1 0 0
Examinee 296 0 1 1
Examinee 297 0 1 1
Examinee 298 1 0 1
Examinee 299 0 1 0
Examinee 300 1 1 0
RMSEA Chisq Chisq p-value Chisq df
Item 1 0.03883294 7.197522 0.30296624 6
Item 2 0.06072963 6.153152 0.40625455 6
Item 3 0.07173369 7.909216 0.24483011 6
Item 4 0.04574086 3.872171 0.69397015 6
Item 5 0.07143841 8.055343 0.23407673 6
Item 6 0.05857104 14.065573 0.02891219 6
Item 7 0.01117358 2.626200 0.85408509 6
Item 8 0.03741441 6.070887 0.41529634 6
Item 9 0.06681806 8.207048 0.22332355 6
Item 10 0.05337763 7.152564 0.30696845 6
Item 11 0.04602093 5.829368 0.44257344 6
Item 12 0.03210471 4.003819 0.67615952 6
Item 13 0.03218800 5.923558 0.43180754 6
Item 14 0.03659569 2.261616 0.89413470 6
Item 15 0.03618671 2.823820 0.83061222 6
Item 16 0.05570668 8.532586 0.20162122 6
Item 17 0.07232093 10.502161 0.10503625 6
Item 18 0.02485390 2.436912 0.87546033 6
Item 19 0.06827556 8.721065 0.18988353 6
Item 20 0.04488968 7.927114 0.24349192 6
$AIC
[1] 4420.26
$BIC
[1] 4594.338
NPCD documentation built on Nov. 16, 2019, 1:08 a.m.
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Description Usage Arguments Value References See Also Examples
Description
This function returns joint maximum likelihood estimates of item parameters and examinee attribute profiles in cognitive diagnostic models. The algorithm starts from the nonparametric estimation of attribute profiles, implemented by the AlphaNP function, and then iteratively estimates item parameters and attribute profiles using conditional maximum likelihood estimation until the algorithm converges. Currently supported models include the DINA model, the DINO model, he NIDA model, the G-NIDA model, and the R-RUM model.
Usage
1 2 3 |
Arguments
Y |
A matrix of binary responses. Rows represent persons and columns represent items. 1=correct, 0=incorrect. |
Q |
The Q-matrix of the test. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item. |
model |
Currently support five models: |
NP.method |
The method of the nonparametric estimation in the initial stage. |
wg |
Additional argument for the "penalized" NP.method. |
ws |
Additional input for the "penalized" NP.method. |
conv.crit.par |
The critical value for the maximum absolute change in all item parameters values to determine convergence. |
conv.crit.att |
The critical value for the percentage of examinee attribute profiles that are changed to determine convergence. |
max.ite |
The maximum number of iterations allowed. |
Value
alpha.est |
JMLE estimates of examinee attribute profiles. Rows represent persons and columns represent attributes. 1=examinee masters the attribute, 0=examinee does not master the attribute. |
par.est |
JMLE estimates of item parameters, including |
n.tie |
Number of ties in the final log-likelihood among the candidate attribute profiles for each person. When we encounter ties, one of the tied attribute profiles is randomly chosen. |
undefined.flag |
A binary vector indicating whether the parameters of each item are undefined. 1=undefined, 0=defined. |
loglike |
The final overall log-likelihood value from the estimated item parameters and attribute profiles based on the specified model. |
convergence |
A message on whether the algorithm converged. |
n.ite |
Number of iterations performed. |
loglike.matrix |
The values for the log-likelihood function in the last iteration for each candidate attribute profile by each person. Rows represent candidate attribute profiles in the same order with the pattern matrix; columns represent different examinees. |
est.class |
The final class number (row index in |
NP.loss.matrix |
The values for the loss function of the nonparametric estimation of Alpha. Rows represent candidate attribute profiles in the same order with the pattern matrix; columns represent different examinees. |
NP.alpha.est |
The estimates of examinee attribute profiles from the initial nonparameteric estimation. |
NP.est.class |
The class number (row index in |
pattern |
All possible attribute profiles in the search space. |
model |
The chosen model. |
Q |
The Q-matrix of the test. |
References
Chiu, C. (2011). Flexible approaches to cognitive diagnosis: nonparametric methods and small sample techniques. Invited session of cognitive diagnosis and item response theory at 2011 Joint Statistical Meeting.
Chiu, C. Y., & Douglas, J. A. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification 30(2), 225-250.
See Also
AlphaMLE, AlphaNP, ParMLE, print.JMLE, plot.JMLE
Examples
1 2 3 4 5 6 7 8 9 | data("Data.DINA")
JMLE.result <- JMLE(Data.DINA$response, Data.DINA$Q, model="DINA", conv.crit.par=0.001,
conv.crit.att=0.001, max.ite=100)
print(JMLE.result) # Print the estimated item parameters, standard errors,
#and examinee attribute profiles
plot(JMLE.result, nperson=1) # Plot the sorted loss function of different
#attribute profiles for this examinee
ItemFit(JMLE.result)
ModelFit(JMLE.result)
|
Example output
Loading required package: BB
Loading required package: R.oo
Loading required package: R.methodsS3
R.methodsS3 v1.7.1 (2016-02-15) successfully loaded. See ?R.methodsS3 for help.
R.oo v1.22.0 (2018-04-21) successfully loaded. See ?R.oo for help.
Attaching package: 'R.oo'
The following objects are masked from 'package:methods':
getClasses, getMethods
The following objects are masked from 'package:base':
attach, detach, gc, load, save
Iteration: 1, loglike = -2164.78986, diff.par = 1.00000, diff.att = 1.00000, diff.undefined = 1.00000
Iteration: 2, loglike = -2163.13017, diff.par = 0.00000, diff.att = 0.00000, diff.undefined = 0.00000
Model: DINA
Method: JMLE
Convergence: Convergence criteria met.
Number of iterations: 2
The Estimated Item Parameters
slip SE.slip guess SE.guess
Item 1 0.25000000 0.05103104 0.039473684 0.012895585
Item 2 0.25000000 0.07654655 0.235074627 0.025902699
Item 3 0.19444444 0.04664223 0.271929825 0.029467794
Item 4 0.00000000 0.00000000 0.214765101 0.033642520
Item 5 0.00000000 0.00000000 0.259090909 0.029539097
Item 6 0.03311258 0.01456116 0.154362416 0.029598506
Item 7 0.11038961 0.02525246 0.006849315 0.006825818
Item 8 0.09090909 0.02316578 0.047945205 0.017681827
Item 9 0.27564103 0.03577557 0.194444444 0.032981034
Item 10 0.23076923 0.03373300 0.041666667 0.016652193
Item 11 0.13333333 0.03925227 0.124444444 0.022005860
Item 12 0.22516556 0.03399124 0.013422819 0.009427451
Item 13 0.06944444 0.02995875 0.043859649 0.013562070
Item 14 0.08000000 0.03132624 0.244444444 0.028650488
Item 15 0.25000000 0.03466876 0.131944444 0.028202530
Item 16 0.03246753 0.01428226 0.171232877 0.031176934
Item 17 0.31250000 0.08193819 0.182835821 0.023611192
Item 18 0.00000000 0.00000000 0.089041096 0.023570468
Item 19 0.24000000 0.04931531 0.200000000 0.026666667
Item 20 0.02649007 0.01306842 0.100671141 0.024650097
Model Fit Statistics: AIC = 4420.26, BIC = 4594.34
The Estimated Examinee Attribute Profiles
Attribute 1 Attribute 2 Attribute 3
Examinee 1 1 1 0
Examinee 2 1 1 0
Examinee 3 1 1 0
Examinee 4 1 0 0
Examinee 5 1 0 1
Examinee 6 1 1 0
Examinee 7 1 1 1
Examinee 8 0 1 0
Examinee 9 0 0 1
Examinee 10 0 0 1
Examinee 11 0 1 0
Examinee 12 1 1 1
Examinee 13 1 0 1
Examinee 14 1 0 0
Examinee 15 1 1 0
Examinee 16 1 0 0
Examinee 17 1 1 1
Examinee 18 0 1 1
Examinee 19 1 0 1
Examinee 20 0 0 1
Examinee 21 1 1 1
Examinee 22 0 0 0
Examinee 23 1 0 1
Examinee 24 0 1 1
Examinee 25 1 0 0
Examinee 26 1 0 1
Examinee 27 1 1 1
Examinee 28 0 0 1
Examinee 29 0 0 1
Examinee 30 1 1 1
Examinee 31 0 1 1
Examinee 32 0 0 1
Examinee 33 1 1 1
Examinee 34 0 1 1
Examinee 35 1 1 1
Examinee 36 1 1 1
Examinee 37 1 0 1
Examinee 38 1 0 1
Examinee 39 1 1 1
Examinee 40 0 0 0
Examinee 41 0 1 0
Examinee 42 0 0 0
Examinee 43 1 1 0
Examinee 44 1 1 0
Examinee 45 0 1 1
Examinee 46 1 1 1
Examinee 47 0 0 0
Examinee 48 0 1 0
Examinee 49 1 0 1
Examinee 50 0 1 0
Examinee 51 1 1 1
Examinee 52 1 1 0
Examinee 53 1 0 1
Examinee 54 0 0 1
Examinee 55 1 0 1
Examinee 56 0 1 0
Examinee 57 0 1 1
Examinee 58 1 0 1
Examinee 59 0 1 0
Examinee 60 0 1 1
Examinee 61 0 0 1
Examinee 62 0 1 1
Examinee 63 1 0 0
Examinee 64 0 1 0
Examinee 65 0 0 0
Examinee 66 0 1 0
Examinee 67 1 1 0
Examinee 68 0 1 1
Examinee 69 1 0 0
Examinee 70 0 0 0
Examinee 71 0 1 1
Examinee 72 1 0 0
Examinee 73 1 0 1
Examinee 74 0 0 0
Examinee 75 1 1 1
Examinee 76 0 1 0
Examinee 77 0 1 0
Examinee 78 1 0 0
Examinee 79 0 1 0
Examinee 80 1 1 0
Examinee 81 1 1 0
Examinee 82 0 1 1
Examinee 83 0 1 1
Examinee 84 1 0 1
Examinee 85 1 1 1
Examinee 86 1 0 0
Examinee 87 0 1 1
Examinee 88 0 1 1
Examinee 89 0 1 1
Examinee 90 1 1 0
Examinee 91 1 0 0
Examinee 92 1 1 1
Examinee 93 1 1 1
Examinee 94 0 0 0
Examinee 95 1 0 0
Examinee 96 0 1 0
Examinee 97 0 1 1
Examinee 98 0 1 1
Examinee 99 0 1 0
Examinee 100 0 1 1
Examinee 101 0 0 0
Examinee 102 1 0 0
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RMSEA Chisq Chisq p-value Chisq df
Item 1 0.03883294 7.197522 0.30296624 6
Item 2 0.06072963 6.153152 0.40625455 6
Item 3 0.07173369 7.909216 0.24483011 6
Item 4 0.04574086 3.872171 0.69397015 6
Item 5 0.07143841 8.055343 0.23407673 6
Item 6 0.05857104 14.065573 0.02891219 6
Item 7 0.01117358 2.626200 0.85408509 6
Item 8 0.03741441 6.070887 0.41529634 6
Item 9 0.06681806 8.207048 0.22332355 6
Item 10 0.05337763 7.152564 0.30696845 6
Item 11 0.04602093 5.829368 0.44257344 6
Item 12 0.03210471 4.003819 0.67615952 6
Item 13 0.03218800 5.923558 0.43180754 6
Item 14 0.03659569 2.261616 0.89413470 6
Item 15 0.03618671 2.823820 0.83061222 6
Item 16 0.05570668 8.532586 0.20162122 6
Item 17 0.07232093 10.502161 0.10503625 6
Item 18 0.02485390 2.436912 0.87546033 6
Item 19 0.06827556 8.721065 0.18988353 6
Item 20 0.04488968 7.927114 0.24349192 6
$AIC
[1] 4420.26
$BIC
[1] 4594.338
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