Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-parameter logistic
item response theory (IRT) model
DATA: FILE = ex5.5part2.dat;
VARIABLE: NAMES ARE u1-u20;
CATEGORICAL ARE u1-u20;
ANALYSIS: ESTIMATOR = MLR;
MODEL: f BY u1-u20*;
f@1;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of a two-parameter logistic
item response theory (IRT) model
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 20
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
U13 U14 U15 U16 U17 U18
U19 U20
Continuous latent variables
F
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 1
Adaptive quadrature ON
Link LOGIT
Cholesky ON
Input data file(s)
ex5.5part2.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.426 213.000
Category 2 0.574 287.000
U2
Category 1 0.412 206.000
Category 2 0.588 294.000
U3
Category 1 0.432 216.000
Category 2 0.568 284.000
U4
Category 1 0.436 218.000
Category 2 0.564 282.000
U5
Category 1 0.410 205.000
Category 2 0.590 295.000
U6
Category 1 0.400 200.000
Category 2 0.600 300.000
U7
Category 1 0.412 206.000
Category 2 0.588 294.000
U8
Category 1 0.416 208.000
Category 2 0.584 292.000
U9
Category 1 0.412 206.000
Category 2 0.588 294.000
U10
Category 1 0.408 204.000
Category 2 0.592 296.000
U11
Category 1 0.614 307.000
Category 2 0.386 193.000
U12
Category 1 0.614 307.000
Category 2 0.386 193.000
U13
Category 1 0.596 298.000
Category 2 0.404 202.000
U14
Category 1 0.562 281.000
Category 2 0.438 219.000
U15
Category 1 0.562 281.000
Category 2 0.438 219.000
U16
Category 1 0.584 292.000
Category 2 0.416 208.000
U17
Category 1 0.618 309.000
Category 2 0.382 191.000
U18
Category 1 0.592 296.000
Category 2 0.408 204.000
U19
Category 1 0.642 321.000
Category 2 0.358 179.000
U20
Category 1 0.596 298.000
Category 2 0.404 202.000
THE MODEL ESTIMATION TERMINATED NORMALLY
THE CHI-SQUARE TEST CANNOT BE COMPUTED BECAUSE THE FREQUENCY TABLE FOR THE
CATEGORICAL VARIABLES IS TOO LARGE.
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value -6265.315
H0 Scaling Correction Factor 1.0029
for MLR
Information Criteria
Akaike (AIC) 12610.630
Bayesian (BIC) 12779.214
Sample-Size Adjusted BIC 12652.252
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.026 0.152 6.755 0.000
U2 1.062 0.157 6.780 0.000
U3 0.916 0.141 6.482 0.000
U4 1.155 0.161 7.190 0.000
U5 0.980 0.151 6.471 0.000
U6 0.519 0.121 4.298 0.000
U7 1.128 0.159 7.085 0.000
U8 1.043 0.148 7.050 0.000
U9 1.021 0.150 6.827 0.000
U10 0.969 0.141 6.852 0.000
U11 1.235 0.165 7.484 0.000
U12 0.982 0.148 6.651 0.000
U13 1.007 0.146 6.900 0.000
U14 0.760 0.127 5.990 0.000
U15 0.791 0.128 6.203 0.000
U16 0.950 0.141 6.739 0.000
U17 1.144 0.161 7.119 0.000
U18 1.125 0.154 7.323 0.000
U19 0.781 0.131 5.942 0.000
U20 1.094 0.151 7.223 0.000
Thresholds
U1$1 -0.368 0.111 -3.321 0.001
U2$1 -0.443 0.114 -3.901 0.000
U3$1 -0.327 0.107 -3.051 0.002
U4$1 -0.333 0.115 -2.885 0.004
U5$1 -0.441 0.111 -3.976 0.000
U6$1 -0.432 0.098 -4.426 0.000
U7$1 -0.453 0.115 -3.922 0.000
U8$1 -0.420 0.112 -3.767 0.000
U9$1 -0.437 0.112 -3.909 0.000
U10$1 -0.450 0.110 -4.082 0.000
U11$1 0.593 0.122 4.868 0.000
U12$1 0.552 0.112 4.923 0.000
U13$1 0.465 0.111 4.173 0.000
U14$1 0.278 0.102 2.728 0.006
U15$1 0.280 0.103 2.726 0.006
U16$1 0.399 0.109 3.668 0.000
U17$1 0.599 0.119 5.051 0.000
U18$1 0.460 0.116 3.969 0.000
U19$1 0.658 0.108 6.120 0.000
U20$1 0.476 0.115 4.150 0.000
Variances
F 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.125E+00
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
U1
Category 1 0.425
Category 2 0.575
U2
Category 1 0.411
Category 2 0.589
U3
Category 1 0.431
Category 2 0.569
U4
Category 1 0.435
Category 2 0.565
U5
Category 1 0.409
Category 2 0.591
U6
Category 1 0.400
Category 2 0.600
U7
Category 1 0.411
Category 2 0.589
U8
Category 1 0.415
Category 2 0.585
U9
Category 1 0.411
Category 2 0.589
U10
Category 1 0.407
Category 2 0.593
U11
Category 1 0.612
Category 2 0.388
U12
Category 1 0.613
Category 2 0.387
U13
Category 1 0.595
Category 2 0.405
U14
Category 1 0.561
Category 2 0.439
U15
Category 1 0.561
Category 2 0.439
U16
Category 1 0.583
Category 2 0.417
U17
Category 1 0.617
Category 2 0.383
U18
Category 1 0.591
Category 2 0.409
U19
Category 1 0.641
Category 2 0.359
U20
Category 1 0.595
Category 2 0.405
IRT PARAMETERIZATION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Item Discriminations
F BY
U1 1.026 0.152 6.755 0.000
U2 1.062 0.157 6.780 0.000
U3 0.916 0.141 6.482 0.000
U4 1.155 0.161 7.190 0.000
U5 0.980 0.151 6.471 0.000
U6 0.519 0.121 4.298 0.000
U7 1.128 0.159 7.085 0.000
U8 1.043 0.148 7.050 0.000
U9 1.021 0.150 6.827 0.000
U10 0.969 0.141 6.852 0.000
U11 1.235 0.165 7.484 0.000
U12 0.982 0.148 6.651 0.000
U13 1.007 0.146 6.900 0.000
U14 0.760 0.127 5.990 0.000
U15 0.791 0.128 6.203 0.000
U16 0.950 0.141 6.739 0.000
U17 1.144 0.161 7.119 0.000
U18 1.125 0.154 7.323 0.000
U19 0.781 0.131 5.942 0.000
U20 1.094 0.151 7.223 0.000
Item Difficulties
U1 -0.359 0.113 -3.176 0.001
U2 -0.417 0.112 -3.721 0.000
U3 -0.357 0.122 -2.913 0.004
U4 -0.288 0.101 -2.841 0.004
U5 -0.451 0.120 -3.748 0.000
U6 -0.833 0.253 -3.296 0.001
U7 -0.402 0.107 -3.747 0.000
U8 -0.403 0.114 -3.540 0.000
U9 -0.428 0.116 -3.698 0.000
U10 -0.464 0.122 -3.816 0.000
U11 0.480 0.105 4.555 0.000
U12 0.562 0.129 4.374 0.000
U13 0.462 0.120 3.833 0.000
U14 0.366 0.143 2.560 0.010
U15 0.354 0.138 2.566 0.010
U16 0.420 0.123 3.403 0.001
U17 0.524 0.113 4.626 0.000
U18 0.409 0.109 3.766 0.000
U19 0.843 0.176 4.778 0.000
U20 0.435 0.112 3.882 0.000
Variances
F 1.000 0.000 0.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
21 22 23 24 25
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
26 27 28 29 30
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
31 32 33 34 35
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
36 37 38 39 40
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0 0 0 0 0
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
0 0 0 0 0
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
F
________
U1 1
U2 2
U3 3
U4 4
U5 5
U6 6
U7 7
U8 8
U9 9
U10 10
U11 11
U12 12
U13 13
U14 14
U15 15
U16 16
U17 17
U18 18
U19 19
U20 20
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
U5 0 0 0 0 0
U6 0 0 0 0 0
U7 0 0 0 0 0
U8 0 0 0 0 0
U9 0 0 0 0 0
U10 0 0 0 0 0
U11 0 0 0 0 0
U12 0 0 0 0 0
U13 0 0 0 0 0
U14 0 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 0
U7 0 0
U8 0 0 0
U9 0 0 0 0
U10 0 0 0 0 0
U11 0 0 0 0 0
U12 0 0 0 0 0
U13 0 0 0 0 0
U14 0 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 0
U12 0 0
U13 0 0 0
U14 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 0
U17 0 0
U18 0 0 0
U19 0 0 0 0
U20 0 0 0 0 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
-0.298 -0.356 -0.274 -0.257 -0.364
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
-0.405 -0.356 -0.339 -0.356 -0.372
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
0.464 0.464 0.389 0.249 0.249
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
0.339 0.481 0.372 0.584 0.389
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
U1 1.000
U2 1.000
U3 1.000
U4 1.000
U5 1.000
U6 1.000
U7 1.000
U8 1.000
U9 1.000
U10 1.000
U11 1.000
U12 1.000
U13 1.000
U14 1.000
U15 1.000
U16 1.000
U17 1.000
U18 1.000
U19 1.000
U20 1.000
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
U5 0.000 0.000 0.000 0.000 1.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
U9 0.000 0.000 0.000 0.000 0.000
U10 0.000 0.000 0.000 0.000 0.000
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
U15 0.000 0.000 0.000 0.000 0.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 0.000 1.000
U8 0.000 0.000 1.000
U9 0.000 0.000 0.000 1.000
U10 0.000 0.000 0.000 0.000 1.000
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
U15 0.000 0.000 0.000 0.000 0.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 0.000 1.000
U13 0.000 0.000 1.000
U14 0.000 0.000 0.000 1.000
U15 0.000 0.000 0.000 0.000 1.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 0.000 1.000
U18 0.000 0.000 1.000
U19 0.000 0.000 0.000 1.000
U20 0.000 0.000 0.000 0.000 1.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.62863564D+04 0.0000000 0.0000000 EM
2 -0.62661906D+04 20.1657817 0.0032079 EM
3 -0.62653912D+04 0.7994457 0.0001276 EM
4 -0.62653242D+04 0.0670496 0.0000107 EM
5 -0.62653166D+04 0.0075983 0.0000012 EM
6 -0.62653152D+04 0.0013361 0.0000002 EM
7 -0.62653149D+04 0.0003687 0.0000001 EM
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
F F_SE
________ ________
0.000 0.455
Covariances
F F_SE
________ ________
F 0.791
F_SE 0.001 0.001
Correlations
F F_SE
________ ________
F 1.000
F_SE 0.033 1.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated factor scores, estimated values, residuals)
Scatterplots (sample values, estimated factor scores, estimated values, residuals)
Sample proportions and estimated probabilities
Item characteristic curves
Information curves
Latent variable distribution plots
Beginning Time: 23:11:35
Ending Time: 23:11:36
Elapsed Time: 00:00:01
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