Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:28 AM

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 = ex5.5part2.dat;
  ANALYSIS:	ESTIMATOR = MLR;
  model population:	
    	f by u1-u20*1;
    	f@1;
    	[u1$1-u10$1*-.5 u11$1-u20$1*.5];
  MODEL:	
    	f by u1-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                             -6265.315
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -6265.315      -6265.315
           0.980       0.000        -6265.315      -6265.315
           0.950       0.000        -6265.315      -6265.315
           0.900       0.000        -6265.315      -6265.315
           0.800       0.000        -6265.315      -6265.315
           0.700       0.000        -6265.315      -6265.315
           0.500       0.000        -6265.315      -6265.315
           0.300       0.000        -6265.315      -6265.315
           0.200       0.000        -6265.315      -6265.315
           0.100       0.000        -6265.315      -6265.315
           0.050       0.000        -6265.315      -6265.315
           0.020       0.000        -6265.315      -6265.315
           0.010       0.000        -6265.315      -6265.315

Information Criteria

    Akaike (AIC)

        Mean                             12610.630
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        12610.630      12610.630
           0.980       0.000        12610.630      12610.630
           0.950       0.000        12610.630      12610.630
           0.900       0.000        12610.630      12610.630
           0.800       0.000        12610.630      12610.630
           0.700       0.000        12610.630      12610.630
           0.500       0.000        12610.630      12610.630
           0.300       0.000        12610.630      12610.630
           0.200       0.000        12610.630      12610.630
           0.100       0.000        12610.630      12610.630
           0.050       0.000        12610.630      12610.630
           0.020       0.000        12610.630      12610.630
           0.010       0.000        12610.630      12610.630

    Bayesian (BIC)

        Mean                             12779.214
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        12779.214      12779.214
           0.980       0.000        12779.214      12779.214
           0.950       0.000        12779.214      12779.214
           0.900       0.000        12779.214      12779.214
           0.800       0.000        12779.214      12779.214
           0.700       0.000        12779.214      12779.214
           0.500       0.000        12779.214      12779.214
           0.300       0.000        12779.214      12779.214
           0.200       0.000        12779.214      12779.214
           0.100       0.000        12779.214      12779.214
           0.050       0.000        12779.214      12779.214
           0.020       0.000        12779.214      12779.214
           0.010       0.000        12779.214      12779.214

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                             12652.252
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        12652.252      12652.252
           0.980       0.000        12652.252      12652.252
           0.950       0.000        12652.252      12652.252
           0.900       0.000        12652.252      12652.252
           0.800       0.000        12652.252      12652.252
           0.700       0.000        12652.252      12652.252
           0.500       0.000        12652.252      12652.252
           0.300       0.000        12652.252      12652.252
           0.200       0.000        12652.252      12652.252
           0.100       0.000        12652.252      12652.252
           0.050       0.000        12652.252      12652.252
           0.020       0.000        12652.252      12652.252
           0.010       0.000        12652.252      12652.252



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F        BY
  U1                  1.000     1.0242     0.0000     0.1516     0.0006 1.000 1.000
  U2                  1.000     1.0612     0.0000     0.1565     0.0037 1.000 1.000
  U3                  1.000     0.9146     0.0000     0.1411     0.0073 1.000 1.000
  U4                  1.000     1.1548     0.0000     0.1606     0.0240 1.000 1.000
  U5                  1.000     0.9794     0.0000     0.1513     0.0004 1.000 1.000
  U6                  1.000     0.5184     0.0000     0.1206     0.2319 0.000 1.000
  U7                  1.000     1.1262     0.0000     0.1589     0.0159 1.000 1.000
  U8                  1.000     1.0415     0.0000     0.1477     0.0017 1.000 1.000
  U9                  1.000     1.0202     0.0000     0.1494     0.0004 1.000 1.000
  U10                 1.000     0.9685     0.0000     0.1413     0.0010 1.000 1.000
  U11                 1.000     1.2347     0.0000     0.1650     0.0551 1.000 1.000
  U12                 1.000     0.9808     0.0000     0.1475     0.0004 1.000 1.000
  U13                 1.000     1.0067     0.0000     0.1459     0.0000 1.000 1.000
  U14                 1.000     0.7583     0.0000     0.1266     0.0584 1.000 1.000
  U15                 1.000     0.7912     0.0000     0.1275     0.0436 1.000 1.000
  U16                 1.000     0.9490     0.0000     0.1408     0.0026 1.000 1.000
  U17                 1.000     1.1425     0.0000     0.1604     0.0203 1.000 1.000
  U18                 1.000     1.1241     0.0000     0.1535     0.0154 1.000 1.000
  U19                 1.000     0.7803     0.0000     0.1313     0.0483 1.000 1.000
  U20                 1.000     1.0931     0.0000     0.1513     0.0087 1.000 1.000

 Thresholds
  U1$1               -0.500    -0.3684     0.0000     0.1108     0.0173 1.000 1.000
  U2$1               -0.500    -0.4436     0.0000     0.1136     0.0032 1.000 1.000
  U3$1               -0.500    -0.3266     0.0000     0.1070     0.0301 1.000 1.000
  U4$1               -0.500    -0.3337     0.0000     0.1154     0.0277 1.000 1.000
  U5$1               -0.500    -0.4418     0.0000     0.1110     0.0034 1.000 1.000
  U6$1               -0.500    -0.4319     0.0000     0.0975     0.0046 1.000 1.000
  U7$1               -0.500    -0.4527     0.0000     0.1154     0.0022 1.000 1.000
  U8$1               -0.500    -0.4202     0.0000     0.1115     0.0064 1.000 1.000
  U9$1               -0.500    -0.4380     0.0000     0.1119     0.0038 1.000 1.000
  U10$1              -0.500    -0.4504     0.0000     0.1102     0.0025 1.000 1.000
  U11$1               0.500     0.5931     0.0000     0.1219     0.0087 1.000 1.000
  U12$1               0.500     0.5514     0.0000     0.1121     0.0026 1.000 1.000
  U13$1               0.500     0.4647     0.0000     0.1114     0.0012 1.000 1.000
  U14$1               0.500     0.2780     0.0000     0.1020     0.0493 0.000 1.000
  U15$1               0.500     0.2799     0.0000     0.1029     0.0484 0.000 1.000
  U16$1               0.500     0.3986     0.0000     0.1087     0.0103 1.000 1.000
  U17$1               0.500     0.5988     0.0000     0.1186     0.0098 1.000 1.000
  U18$1               0.500     0.4597     0.0000     0.1159     0.0016 1.000 1.000
  U19$1               0.500     0.6582     0.0000     0.1076     0.0250 1.000 1.000
  U20$1               0.500     0.4760     0.0000     0.1148     0.0006 1.000 1.000

 Variances
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.125E+00
       (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                 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
              ________      ________      ________      ________      ________
               -0.500        -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 -0.62661540D+04   26.6326814    0.0042323  EM
              3 -0.62654614D+04    0.6925835    0.0001105  EM
              4 -0.62653773D+04    0.0840996    0.0000134  EM
              5 -0.62653515D+04    0.0258263    0.0000041  EM
              6 -0.62653377D+04    0.0137288    0.0000022  EM
              7 -0.62653293D+04    0.0084280    0.0000013  EM
              8 -0.62653155D+04    0.0138568    0.0000022  FS
              9 -0.62653149D+04    0.0005872    0.0000001  FS


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
    ex5.5part2.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:28:44
        Ending Time:  03:28:44
       Elapsed Time:  00:00:00



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