Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a three-parameter
logistic item response theory (IRT) model
using priors for the guessing parameters
DATA: FILE = ex5.5part3.dat;
VARIABLE: NAMES = u1-u20;
CATEGORICAL = u1-u20(3pl);
ANALYSIS: ESTIMATOR = MLR;
MODEL: f BY u1-u20*;
f@1;
[u1$2-u20$2] (a1-a20);
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
MODEL PRIORS:
a1-a20~N(1.386,1);
INPUT READING TERMINATED NORMALLY
this is an example of a three-parameter
logistic item response theory (IRT) model
using priors for the guessing parameters
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
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)
ex5.5part3.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.414 2070.000
Category 2 0.586 2930.000
U2
Category 1 0.400 1999.000
Category 2 0.600 3001.000
U3
Category 1 0.397 1986.000
Category 2 0.603 3014.000
U4
Category 1 0.405 2025.000
Category 2 0.595 2975.000
U5
Category 1 0.411 2053.000
Category 2 0.589 2947.000
U6
Category 1 0.404 2019.000
Category 2 0.596 2981.000
U7
Category 1 0.400 2000.000
Category 2 0.600 3000.000
U8
Category 1 0.409 2047.000
Category 2 0.591 2953.000
U9
Category 1 0.393 1966.000
Category 2 0.607 3034.000
U10
Category 1 0.395 1977.000
Category 2 0.605 3023.000
U11
Category 1 0.396 1978.000
Category 2 0.604 3022.000
U12
Category 1 0.404 2019.000
Category 2 0.596 2981.000
U13
Category 1 0.404 2018.000
Category 2 0.596 2982.000
U14
Category 1 0.397 1985.000
Category 2 0.603 3015.000
U15
Category 1 0.398 1991.000
Category 2 0.602 3009.000
U16
Category 1 0.396 1981.000
Category 2 0.604 3019.000
U17
Category 1 0.405 2023.000
Category 2 0.595 2977.000
U18
Category 1 0.408 2039.000
Category 2 0.592 2961.000
U19
Category 1 0.406 2028.000
Category 2 0.594 2972.000
U20
Category 1 0.397 1983.000
Category 2 0.603 3017.000
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 60
Loglikelihood
H0 Value -64414.663
H0 Scaling Correction Factor 0.9470
for MLR
Information Criteria
Akaike (AIC) 128949.326
Bayesian (BIC) 129340.358
Sample-Size Adjusted BIC 129149.698
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.063 0.160 6.626 0.000
U2 1.070 0.138 7.732 0.000
U3 1.194 0.174 6.859 0.000
U4 0.950 0.063 15.048 0.000
U5 1.001 0.156 6.416 0.000
U6 1.065 0.151 7.059 0.000
U7 1.212 0.169 7.185 0.000
U8 1.238 0.164 7.527 0.000
U9 0.929 0.119 7.791 0.000
U10 1.125 0.153 7.355 0.000
U11 1.144 0.170 6.729 0.000
U12 0.937 0.073 12.861 0.000
U13 1.020 0.150 6.812 0.000
U14 0.944 0.135 6.983 0.000
U15 1.090 0.159 6.856 0.000
U16 1.042 0.161 6.457 0.000
U17 1.085 0.163 6.652 0.000
U18 1.079 0.157 6.884 0.000
U19 0.996 0.108 9.221 0.000
U20 0.986 0.101 9.719 0.000
Thresholds
U1$1 0.364 0.255 1.423 0.155
U1$2 0.955 0.298 3.202 0.001
U2$1 0.037 0.220 0.168 0.866
U2$2 1.310 0.406 3.223 0.001
U3$1 0.281 0.250 1.126 0.260
U3$2 0.925 0.288 3.211 0.001
U4$1 -0.212 0.093 -2.277 0.023
U4$2 2.071 0.362 5.718 0.000
U5$1 0.196 0.274 0.717 0.473
U5$2 1.150 0.416 2.761 0.006
U6$1 0.188 0.241 0.779 0.436
U6$2 1.100 0.348 3.163 0.002
U7$1 0.344 0.240 1.430 0.153
U7$2 0.877 0.256 3.421 0.001
U8$1 0.209 0.225 0.927 0.354
U8$2 1.140 0.312 3.649 0.000
U9$1 -0.045 0.225 -0.200 0.842
U9$2 1.394 0.484 2.880 0.004
U10$1 0.113 0.232 0.490 0.624
U10$2 1.133 0.351 3.223 0.001
U11$1 0.166 0.262 0.633 0.527
U11$2 1.058 0.362 2.922 0.003
U12$1 -0.166 0.120 -1.377 0.168
U12$2 1.879 0.401 4.684 0.000
U13$1 0.078 0.257 0.302 0.763
U13$2 1.277 0.459 2.779 0.005
U14$1 0.003 0.256 0.011 0.991
U14$2 1.342 0.513 2.613 0.009
U15$1 0.192 0.253 0.761 0.447
U15$2 1.041 0.346 3.010 0.003
U16$1 0.052 0.279 0.186 0.852
U16$2 1.241 0.488 2.541 0.011
U17$1 0.227 0.260 0.870 0.384
U17$2 1.054 0.352 2.991 0.003
U18$1 0.129 0.253 0.513 0.608
U18$2 1.236 0.416 2.970 0.003
U19$1 -0.066 0.188 -0.351 0.726
U19$2 1.611 0.475 3.392 0.001
U20$1 -0.120 0.172 -0.694 0.488
U20$2 1.615 0.452 3.574 0.000
Variances
F 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.736E-03
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
U1
Category 1 0.414
Category 2 0.586
U2
Category 1 0.400
Category 2 0.600
U3
Category 1 0.397
Category 2 0.603
U4
Category 1 0.405
Category 2 0.595
U5
Category 1 0.410
Category 2 0.590
U6
Category 1 0.404
Category 2 0.596
U7
Category 1 0.400
Category 2 0.600
U8
Category 1 0.409
Category 2 0.591
U9
Category 1 0.393
Category 2 0.607
U10
Category 1 0.395
Category 2 0.605
U11
Category 1 0.395
Category 2 0.605
U12
Category 1 0.404
Category 2 0.596
U13
Category 1 0.403
Category 2 0.597
U14
Category 1 0.397
Category 2 0.603
U15
Category 1 0.398
Category 2 0.602
U16
Category 1 0.396
Category 2 0.604
U17
Category 1 0.404
Category 2 0.596
U18
Category 1 0.408
Category 2 0.592
U19
Category 1 0.405
Category 2 0.595
U20
Category 1 0.396
Category 2 0.604
IRT PARAMETERIZATION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Item Discriminations
F BY
U1 1.063 0.160 6.626 0.000
U2 1.070 0.138 7.732 0.000
U3 1.194 0.174 6.859 0.000
U4 0.950 0.063 15.048 0.000
U5 1.001 0.156 6.416 0.000
U6 1.065 0.151 7.059 0.000
U7 1.212 0.169 7.185 0.000
U8 1.238 0.164 7.527 0.000
U9 0.929 0.119 7.791 0.000
U10 1.125 0.153 7.355 0.000
U11 1.144 0.170 6.729 0.000
U12 0.937 0.073 12.861 0.000
U13 1.020 0.150 6.812 0.000
U14 0.944 0.135 6.983 0.000
U15 1.090 0.159 6.856 0.000
U16 1.042 0.161 6.457 0.000
U17 1.085 0.163 6.652 0.000
U18 1.079 0.157 6.884 0.000
U19 0.996 0.108 9.221 0.000
U20 0.986 0.101 9.719 0.000
Item Difficulties
U1 0.342 0.195 1.755 0.079
U2 0.035 0.202 0.172 0.864
U3 0.236 0.179 1.317 0.188
U4 -0.223 0.106 -2.102 0.036
U5 0.196 0.246 0.797 0.425
U6 0.176 0.204 0.863 0.388
U7 0.284 0.164 1.730 0.084
U8 0.169 0.162 1.039 0.299
U9 -0.048 0.248 -0.195 0.845
U10 0.101 0.194 0.520 0.603
U11 0.145 0.209 0.691 0.490
U12 -0.177 0.138 -1.285 0.199
U13 0.076 0.242 0.314 0.753
U14 0.003 0.271 0.011 0.991
U15 0.177 0.209 0.844 0.399
U16 0.050 0.261 0.191 0.848
U17 0.209 0.212 0.986 0.324
U18 0.120 0.218 0.550 0.583
U19 -0.066 0.195 -0.340 0.734
U20 -0.121 0.185 -0.655 0.512
Item Guessing
U1 0.278 0.060 4.645 0.000
U2 0.213 0.068 3.126 0.002
U3 0.284 0.059 4.851 0.000
U4 0.112 0.036 3.108 0.002
U5 0.241 0.076 3.161 0.002
U6 0.250 0.065 3.830 0.000
U7 0.294 0.053 5.521 0.000
U8 0.242 0.057 4.223 0.000
U9 0.199 0.077 2.578 0.010
U10 0.244 0.065 3.761 0.000
U11 0.258 0.069 3.719 0.000
U12 0.132 0.046 2.873 0.004
U13 0.218 0.078 2.783 0.005
U14 0.207 0.084 2.457 0.014
U15 0.261 0.067 3.912 0.000
U16 0.224 0.085 2.640 0.008
U17 0.259 0.068 3.829 0.000
U18 0.225 0.073 3.102 0.002
U19 0.167 0.066 2.527 0.012
U20 0.166 0.063 2.653 0.008
Variances
F 1.000 0.000 0.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
21 22 23 24 25
TAU
U3$2 U4$1 U4$2 U5$1 U5$2
________ ________ ________ ________ ________
26 27 28 29 30
TAU
U6$1 U6$2 U7$1 U7$2 U8$1
________ ________ ________ ________ ________
31 32 33 34 35
TAU
U8$2 U9$1 U9$2 U10$1 U10$2
________ ________ ________ ________ ________
36 37 38 39 40
TAU
U11$1 U11$2 U12$1 U12$2 U13$1
________ ________ ________ ________ ________
41 42 43 44 45
TAU
U13$2 U14$1 U14$2 U15$1 U15$2
________ ________ ________ ________ ________
46 47 48 49 50
TAU
U16$1 U16$2 U17$1 U17$2 U18$1
________ ________ ________ ________ ________
51 52 53 54 55
TAU
U18$2 U19$1 U19$2 U20$1 U20$2
________ ________ ________ ________ ________
56 57 58 59 60
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 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
-0.348 2.000 -0.407 2.000 -0.417
TAU
U3$2 U4$1 U4$2 U5$1 U5$2
________ ________ ________ ________ ________
2.000 -0.385 2.000 -0.362 2.000
TAU
U6$1 U6$2 U7$1 U7$2 U8$1
________ ________ ________ ________ ________
-0.390 2.000 -0.406 2.000 -0.367
TAU
U8$2 U9$1 U9$2 U10$1 U10$2
________ ________ ________ ________ ________
2.000 -0.434 2.000 -0.425 2.000
TAU
U11$1 U11$2 U12$1 U12$2 U13$1
________ ________ ________ ________ ________
-0.424 2.000 -0.390 2.000 -0.391
TAU
U13$2 U14$1 U14$2 U15$1 U15$2
________ ________ ________ ________ ________
2.000 -0.418 2.000 -0.413 2.000
TAU
U16$1 U16$2 U17$1 U17$2 U18$1
________ ________ ________ ________ ________
-0.422 2.000 -0.387 2.000 -0.373
TAU
U18$2 U19$1 U19$2 U20$1 U20$2
________ ________ ________ ________ ________
2.000 -0.383 2.000 -0.420 2.000
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 -0.64540859D+05 0.0000000 0.0000000 EM
2 -0.64483240D+05 57.6191217 0.0008928 EM
3 -0.64454540D+05 28.7000844 0.0004451 EM
4 -0.64438261D+05 16.2792257 0.0002526 EM
5 -0.64428520D+05 9.7409144 0.0001512 EM
6 -0.64423460D+05 5.0597548 0.0000785 FS
7 -0.64417792D+05 5.6681655 0.0000880 FS
8 -0.64416033D+05 1.7585274 0.0000273 EM
9 -0.64415043D+05 0.9903042 0.0000154 EM
10 -0.64414796D+05 0.2467509 0.0000038 EM
11 -0.64414707D+05 0.0886650 0.0000014 EM
12 -0.64414680D+05 0.0271963 0.0000004 EM
13 -0.64414670D+05 0.0100292 0.0000002 EM
14 -0.64414666D+05 0.0042308 0.0000001 EM
15 -0.64414664D+05 0.0019833 0.0000000 EM
16 -0.64414663D+05 0.0009892 0.0000000 EM
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
F F_SE
________ ________
0.000 0.532
Covariances
F F_SE
________ ________
F 0.715
F_SE -0.017 0.002
Correlations
F F_SE
________ ________
F 1.000
F_SE -0.504 1.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated factor scores)
Scatterplots (sample values, estimated factor scores)
Sample proportions and estimated probabilities
Item characteristic curves
Information curves
Latent variable distribution plots
Beginning Time: 23:11:36
Ending Time: 23:11:39
Elapsed Time: 00:00:03
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