Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:41 AM

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


IRT PARAMETERIZATION

 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


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.736E-03
       (ratio of smallest to largest eigenvalue)


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:  04:41:53
        Ending Time:  04:41:57
       Elapsed Time:  00:00:04



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