Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-parameter
logistic item response theory (IRT) model
montecarlo:
names = u1-u20;
generate = u1-u20(1);
categorical = u1-u20;
nobs = 500;
nreps = 1;
save = ex5.5.dat;
ANALYSIS: ESTIMATOR = MLR;
model population:
f by u1@1 u2-u20*1;
f*1;
[u1$1-u10$1*-.5 u11$1-u20$1*.5];
MODEL:
f by u1@1 u2-u20*1;
f*1;
[u1$1-u10$1*-.5 u11$1-u20$1*.5];
OUTPUT: TECH8 tech9;
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 replications
Requested 1
Completed 1
Value of seed 0
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
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value
Mean -6265.316
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6265.316 -6265.316
0.980 0.000 -6265.316 -6265.316
0.950 0.000 -6265.316 -6265.316
0.900 0.000 -6265.316 -6265.316
0.800 0.000 -6265.316 -6265.316
0.700 0.000 -6265.316 -6265.316
0.500 0.000 -6265.316 -6265.316
0.300 0.000 -6265.316 -6265.316
0.200 0.000 -6265.316 -6265.316
0.100 0.000 -6265.316 -6265.316
0.050 0.000 -6265.316 -6265.316
0.020 0.000 -6265.316 -6265.316
0.010 0.000 -6265.316 -6265.316
Information Criteria
Akaike (AIC)
Mean 12610.632
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12610.632 12610.632
0.980 0.000 12610.632 12610.632
0.950 0.000 12610.632 12610.632
0.900 0.000 12610.632 12610.632
0.800 0.000 12610.632 12610.632
0.700 0.000 12610.632 12610.632
0.500 0.000 12610.632 12610.632
0.300 0.000 12610.632 12610.632
0.200 0.000 12610.632 12610.632
0.100 0.000 12610.632 12610.632
0.050 0.000 12610.632 12610.632
0.020 0.000 12610.632 12610.632
0.010 0.000 12610.632 12610.632
Bayesian (BIC)
Mean 12779.216
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12779.216 12779.216
0.980 0.000 12779.216 12779.216
0.950 0.000 12779.216 12779.216
0.900 0.000 12779.216 12779.216
0.800 0.000 12779.216 12779.216
0.700 0.000 12779.216 12779.216
0.500 0.000 12779.216 12779.216
0.300 0.000 12779.216 12779.216
0.200 0.000 12779.216 12779.216
0.100 0.000 12779.216 12779.216
0.050 0.000 12779.216 12779.216
0.020 0.000 12779.216 12779.216
0.010 0.000 12779.216 12779.216
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 12652.254
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12652.254 12652.254
0.980 0.000 12652.254 12652.254
0.950 0.000 12652.254 12652.254
0.900 0.000 12652.254 12652.254
0.800 0.000 12652.254 12652.254
0.700 0.000 12652.254 12652.254
0.500 0.000 12652.254 12652.254
0.300 0.000 12652.254 12652.254
0.200 0.000 12652.254 12652.254
0.100 0.000 12652.254 12652.254
0.050 0.000 12652.254 12652.254
0.020 0.000 12652.254 12652.254
0.010 0.000 12652.254 12652.254
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0354 0.0000 0.2043 0.0013 1.000 1.000
U3 1.000 0.8932 0.0000 0.1738 0.0114 1.000 1.000
U4 1.000 1.1266 0.0000 0.2343 0.0160 1.000 1.000
U5 1.000 0.9553 0.0000 0.2059 0.0020 1.000 1.000
U6 1.000 0.5056 0.0000 0.1419 0.2444 0.000 1.000
U7 1.000 1.0996 0.0000 0.2242 0.0099 1.000 1.000
U8 1.000 1.0174 0.0000 0.2142 0.0003 1.000 1.000
U9 1.000 0.9952 0.0000 0.2095 0.0000 1.000 1.000
U10 1.000 0.9447 0.0000 0.1948 0.0031 1.000 1.000
U11 1.000 1.2047 0.0000 0.2285 0.0419 1.000 1.000
U12 1.000 0.9571 0.0000 0.1882 0.0018 1.000 1.000
U13 1.000 0.9815 0.0000 0.2038 0.0003 1.000 1.000
U14 1.000 0.7405 0.0000 0.1691 0.0673 1.000 1.000
U15 1.000 0.7715 0.0000 0.1568 0.0522 1.000 1.000
U16 1.000 0.9262 0.0000 0.1962 0.0054 1.000 1.000
U17 1.000 1.1159 0.0000 0.2297 0.0134 1.000 1.000
U18 1.000 1.0971 0.0000 0.2128 0.0094 1.000 1.000
U19 1.000 0.7613 0.0000 0.1660 0.0570 1.000 1.000
U20 1.000 1.0669 0.0000 0.2124 0.0045 1.000 1.000
Thresholds
U1$1 -0.500 -0.3708 0.0000 0.1109 0.0167 1.000 1.000
U2$1 -0.500 -0.4458 0.0000 0.1137 0.0029 1.000 1.000
U3$1 -0.500 -0.3290 0.0000 0.1071 0.0293 1.000 1.000
U4$1 -0.500 -0.3359 0.0000 0.1155 0.0269 1.000 1.000
U5$1 -0.500 -0.4439 0.0000 0.1111 0.0032 1.000 1.000
U6$1 -0.500 -0.4330 0.0000 0.0976 0.0045 1.000 1.000
U7$1 -0.500 -0.4556 0.0000 0.1155 0.0020 1.000 1.000
U8$1 -0.500 -0.4230 0.0000 0.1117 0.0059 1.000 1.000
U9$1 -0.500 -0.4398 0.0000 0.1119 0.0036 1.000 1.000
U10$1 -0.500 -0.4522 0.0000 0.1102 0.0023 1.000 1.000
U11$1 0.500 0.5904 0.0000 0.1218 0.0082 1.000 1.000
U12$1 0.500 0.5495 0.0000 0.1120 0.0025 1.000 1.000
U13$1 0.500 0.4624 0.0000 0.1113 0.0014 1.000 1.000
U14$1 0.500 0.2764 0.0000 0.1020 0.0500 0.000 1.000
U15$1 0.500 0.2784 0.0000 0.1029 0.0491 0.000 1.000
U16$1 0.500 0.3964 0.0000 0.1087 0.0107 1.000 1.000
U17$1 0.500 0.5964 0.0000 0.1185 0.0093 1.000 1.000
U18$1 0.500 0.4570 0.0000 0.1158 0.0018 1.000 1.000
U19$1 0.500 0.6565 0.0000 0.1075 0.0245 1.000 1.000
U20$1 0.500 0.4737 0.0000 0.1147 0.0007 1.000 1.000
Variances
F 1.000 1.0500 0.0000 0.3111 0.0025 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.431E-02
(ratio of smallest to largest eigenvalue)
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 0
U2 1
U3 2
U4 3
U5 4
U6 5
U7 6
U8 7
U9 8
U10 9
U11 10
U12 11
U13 12
U14 13
U15 14
U16 15
U17 16
U18 17
U19 18
U20 19
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 20
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500 -0.500
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500 -0.500
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
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
POPULATION VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500 -0.500
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500 -0.500
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
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 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.000 0.000
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 0.000
U7 0.000 0.000
U8 0.000 0.000 0.000
U9 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
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 0.000
U12 0.000 0.000
U13 0.000 0.000 0.000
U14 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
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 0.000
U17 0.000 0.000
U18 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.62927867D+04 0.0000000 0.0000000 EM
2 -0.62666050D+04 26.1816930 0.0041606 EM
3 -0.62654629D+04 1.1420797 0.0001822 EM
4 -0.62653728D+04 0.0900950 0.0000144 EM
5 -0.62653479D+04 0.0249093 0.0000040 EM
6 -0.62653355D+04 0.0124155 0.0000020 EM
7 -0.62653279D+04 0.0075665 0.0000012 EM
8 -0.62653231D+04 0.0047955 0.0000008 EM
9 -0.62653201D+04 0.0030605 0.0000005 EM
10 -0.62653181D+04 0.0019558 0.0000003 EM
11 -0.62653168D+04 0.0012502 0.0000002 EM
12 -0.62653160D+04 0.0007992 0.0000001 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
THE CHI-SQUARE TEST CANNOT BE COMPUTED BECAUSE THE FREQUENCY TABLE FOR THE
CATEGORICAL VARIABLES IS TOO LARGE.
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
U5
U6
U7
U8
U9
U10
U11
U12
U13
U14
U15
U16
U17
U18
U19
U20
Save file
ex5.5.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:40
Ending Time: 22:23:41
Elapsed Time: 00:00:01
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