Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:11 PM

INPUT INSTRUCTIONS

  TITLE:          this is an example of a two-parameter logistic
                  item response theory (IRT) model
  DATA:           FILE = ex5.5part2.dat;
  VARIABLE:       NAMES ARE u1-u20;
                  CATEGORICAL ARE u1-u20;
  ANALYSIS:       ESTIMATOR = MLR;
  MODEL:          f BY u1-u20*;
                  f@1;
  OUTPUT:	        TECH1 TECH8;
  PLOT:           TYPE = PLOT3;



INPUT READING TERMINATED NORMALLY



this is an example of a two-parameter logistic
item response theory (IRT) model

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of dependent variables                                   20
Number of independent variables                                  0
Number of continuous latent variables                            1

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4          U5          U6
   U7          U8          U9          U10         U11         U12
   U13         U14         U15         U16         U17         U18
   U19         U20

Continuous latent variables
   F


Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
  Maximum number of iterations                                 100
  Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
  Maximum number of iterations                                 500
  Convergence criteria
    Loglikelihood change                                 0.100D-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
  Maximum value for logit thresholds                            15
  Minimum value for logit thresholds                           -15
  Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            1
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON

Input data file(s)
  ex5.5part2.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.426          213.000
      Category 2    0.574          287.000
    U2
      Category 1    0.412          206.000
      Category 2    0.588          294.000
    U3
      Category 1    0.432          216.000
      Category 2    0.568          284.000
    U4
      Category 1    0.436          218.000
      Category 2    0.564          282.000
    U5
      Category 1    0.410          205.000
      Category 2    0.590          295.000
    U6
      Category 1    0.400          200.000
      Category 2    0.600          300.000
    U7
      Category 1    0.412          206.000
      Category 2    0.588          294.000
    U8
      Category 1    0.416          208.000
      Category 2    0.584          292.000
    U9
      Category 1    0.412          206.000
      Category 2    0.588          294.000
    U10
      Category 1    0.408          204.000
      Category 2    0.592          296.000
    U11
      Category 1    0.614          307.000
      Category 2    0.386          193.000
    U12
      Category 1    0.614          307.000
      Category 2    0.386          193.000
    U13
      Category 1    0.596          298.000
      Category 2    0.404          202.000
    U14
      Category 1    0.562          281.000
      Category 2    0.438          219.000
    U15
      Category 1    0.562          281.000
      Category 2    0.438          219.000
    U16
      Category 1    0.584          292.000
      Category 2    0.416          208.000
    U17
      Category 1    0.618          309.000
      Category 2    0.382          191.000
    U18
      Category 1    0.592          296.000
      Category 2    0.408          204.000
    U19
      Category 1    0.642          321.000
      Category 2    0.358          179.000
    U20
      Category 1    0.596          298.000
      Category 2    0.404          202.000



THE MODEL ESTIMATION TERMINATED NORMALLY

     THE CHI-SQUARE TEST CANNOT BE COMPUTED BECAUSE THE FREQUENCY TABLE FOR THE
     CATEGORICAL VARIABLES IS TOO LARGE.




MODEL FIT INFORMATION

Number of Free Parameters                       40

Loglikelihood

          H0 Value                       -6265.315
          H0 Scaling Correction Factor      1.0029
            for MLR

Information Criteria

          Akaike (AIC)                   12610.630
          Bayesian (BIC)                 12779.214
          Sample-Size Adjusted BIC       12652.252
            (n* = (n + 2) / 24)



MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

 F        BY
    U1                 1.026      0.152      6.755      0.000
    U2                 1.062      0.157      6.780      0.000
    U3                 0.916      0.141      6.482      0.000
    U4                 1.155      0.161      7.190      0.000
    U5                 0.980      0.151      6.471      0.000
    U6                 0.519      0.121      4.298      0.000
    U7                 1.128      0.159      7.085      0.000
    U8                 1.043      0.148      7.050      0.000
    U9                 1.021      0.150      6.827      0.000
    U10                0.969      0.141      6.852      0.000
    U11                1.235      0.165      7.484      0.000
    U12                0.982      0.148      6.651      0.000
    U13                1.007      0.146      6.900      0.000
    U14                0.760      0.127      5.990      0.000
    U15                0.791      0.128      6.203      0.000
    U16                0.950      0.141      6.739      0.000
    U17                1.144      0.161      7.119      0.000
    U18                1.125      0.154      7.323      0.000
    U19                0.781      0.131      5.942      0.000
    U20                1.094      0.151      7.223      0.000

 Thresholds
    U1$1              -0.368      0.111     -3.321      0.001
    U2$1              -0.443      0.114     -3.901      0.000
    U3$1              -0.327      0.107     -3.051      0.002
    U4$1              -0.333      0.115     -2.885      0.004
    U5$1              -0.441      0.111     -3.976      0.000
    U6$1              -0.432      0.098     -4.426      0.000
    U7$1              -0.453      0.115     -3.922      0.000
    U8$1              -0.420      0.112     -3.767      0.000
    U9$1              -0.437      0.112     -3.909      0.000
    U10$1             -0.450      0.110     -4.082      0.000
    U11$1              0.593      0.122      4.868      0.000
    U12$1              0.552      0.112      4.923      0.000
    U13$1              0.465      0.111      4.173      0.000
    U14$1              0.278      0.102      2.728      0.006
    U15$1              0.280      0.103      2.726      0.006
    U16$1              0.399      0.109      3.668      0.000
    U17$1              0.599      0.119      5.051      0.000
    U18$1              0.460      0.116      3.969      0.000
    U19$1              0.658      0.108      6.120      0.000
    U20$1              0.476      0.115      4.150      0.000

 Variances
    F                  1.000      0.000    999.000    999.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.125E+00
       (ratio of smallest to largest eigenvalue)


RESULTS IN PROBABILITY SCALE

                    Estimate

 U1
    Category 1         0.425
    Category 2         0.575
 U2
    Category 1         0.411
    Category 2         0.589
 U3
    Category 1         0.431
    Category 2         0.569
 U4
    Category 1         0.435
    Category 2         0.565
 U5
    Category 1         0.409
    Category 2         0.591
 U6
    Category 1         0.400
    Category 2         0.600
 U7
    Category 1         0.411
    Category 2         0.589
 U8
    Category 1         0.415
    Category 2         0.585
 U9
    Category 1         0.411
    Category 2         0.589
 U10
    Category 1         0.407
    Category 2         0.593
 U11
    Category 1         0.612
    Category 2         0.388
 U12
    Category 1         0.613
    Category 2         0.387
 U13
    Category 1         0.595
    Category 2         0.405
 U14
    Category 1         0.561
    Category 2         0.439
 U15
    Category 1         0.561
    Category 2         0.439
 U16
    Category 1         0.583
    Category 2         0.417
 U17
    Category 1         0.617
    Category 2         0.383
 U18
    Category 1         0.591
    Category 2         0.409
 U19
    Category 1         0.641
    Category 2         0.359
 U20
    Category 1         0.595
    Category 2         0.405


IRT PARAMETERIZATION

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

 Item Discriminations

 F        BY
    U1                 1.026      0.152      6.755      0.000
    U2                 1.062      0.157      6.780      0.000
    U3                 0.916      0.141      6.482      0.000
    U4                 1.155      0.161      7.190      0.000
    U5                 0.980      0.151      6.471      0.000
    U6                 0.519      0.121      4.298      0.000
    U7                 1.128      0.159      7.085      0.000
    U8                 1.043      0.148      7.050      0.000
    U9                 1.021      0.150      6.827      0.000
    U10                0.969      0.141      6.852      0.000
    U11                1.235      0.165      7.484      0.000
    U12                0.982      0.148      6.651      0.000
    U13                1.007      0.146      6.900      0.000
    U14                0.760      0.127      5.990      0.000
    U15                0.791      0.128      6.203      0.000
    U16                0.950      0.141      6.739      0.000
    U17                1.144      0.161      7.119      0.000
    U18                1.125      0.154      7.323      0.000
    U19                0.781      0.131      5.942      0.000
    U20                1.094      0.151      7.223      0.000

 Item Difficulties
    U1                -0.359      0.113     -3.176      0.001
    U2                -0.417      0.112     -3.721      0.000
    U3                -0.357      0.122     -2.913      0.004
    U4                -0.288      0.101     -2.841      0.004
    U5                -0.451      0.120     -3.748      0.000
    U6                -0.833      0.253     -3.296      0.001
    U7                -0.402      0.107     -3.747      0.000
    U8                -0.403      0.114     -3.540      0.000
    U9                -0.428      0.116     -3.698      0.000
    U10               -0.464      0.122     -3.816      0.000
    U11                0.480      0.105      4.555      0.000
    U12                0.562      0.129      4.374      0.000
    U13                0.462      0.120      3.833      0.000
    U14                0.366      0.143      2.560      0.010
    U15                0.354      0.138      2.566      0.010
    U16                0.420      0.123      3.403      0.001
    U17                0.524      0.113      4.626      0.000
    U18                0.409      0.109      3.766      0.000
    U19                0.843      0.176      4.778      0.000
    U20                0.435      0.112      3.882      0.000

 Variances
    F                  1.000      0.000      0.000      1.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                   21            22            23            24            25


           TAU
              U6$1          U7$1          U8$1          U9$1          U10$1
              ________      ________      ________      ________      ________
                   26            27            28            29            30


           TAU
              U11$1         U12$1         U13$1         U14$1         U15$1
              ________      ________      ________      ________      ________
                   31            32            33            34            35


           TAU
              U16$1         U17$1         U18$1         U19$1         U20$1
              ________      ________      ________      ________      ________
                   36            37            38            39            40


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           NU
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           NU
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           NU
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           LAMBDA
              F
              ________
 U1                 1
 U2                 2
 U3                 3
 U4                 4
 U5                 5
 U6                 6
 U7                 7
 U8                 8
 U9                 9
 U10               10
 U11               11
 U12               12
 U13               13
 U14               14
 U15               15
 U16               16
 U17               17
 U18               18
 U19               19
 U20               20


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0
 U5                 0             0             0             0             0
 U6                 0             0             0             0             0
 U7                 0             0             0             0             0
 U8                 0             0             0             0             0
 U9                 0             0             0             0             0
 U10                0             0             0             0             0
 U11                0             0             0             0             0
 U12                0             0             0             0             0
 U13                0             0             0             0             0
 U14                0             0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 U6                 0
 U7                 0             0
 U8                 0             0             0
 U9                 0             0             0             0
 U10                0             0             0             0             0
 U11                0             0             0             0             0
 U12                0             0             0             0             0
 U13                0             0             0             0             0
 U14                0             0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 U11                0
 U12                0             0
 U13                0             0             0
 U14                0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 U16                0
 U17                0             0
 U18                0             0             0
 U19                0             0             0             0
 U20                0             0             0             0             0


           ALPHA
              F
              ________
                    0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     STARTING VALUES


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -0.298        -0.356        -0.274        -0.257        -0.364


           TAU
              U6$1          U7$1          U8$1          U9$1          U10$1
              ________      ________      ________      ________      ________
               -0.405        -0.356        -0.339        -0.356        -0.372


           TAU
              U11$1         U12$1         U13$1         U14$1         U15$1
              ________      ________      ________      ________      ________
                0.464         0.464         0.389         0.249         0.249


           TAU
              U16$1         U17$1         U18$1         U19$1         U20$1
              ________      ________      ________      ________      ________
                0.339         0.481         0.372         0.584         0.389


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             1.000
 U2             1.000
 U3             1.000
 U4             1.000
 U5             1.000
 U6             1.000
 U7             1.000
 U8             1.000
 U9             1.000
 U10            1.000
 U11            1.000
 U12            1.000
 U13            1.000
 U14            1.000
 U15            1.000
 U16            1.000
 U17            1.000
 U18            1.000
 U19            1.000
 U20            1.000


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000
 U5             0.000         0.000         0.000         0.000         1.000
 U6             0.000         0.000         0.000         0.000         0.000
 U7             0.000         0.000         0.000         0.000         0.000
 U8             0.000         0.000         0.000         0.000         0.000
 U9             0.000         0.000         0.000         0.000         0.000
 U10            0.000         0.000         0.000         0.000         0.000
 U11            0.000         0.000         0.000         0.000         0.000
 U12            0.000         0.000         0.000         0.000         0.000
 U13            0.000         0.000         0.000         0.000         0.000
 U14            0.000         0.000         0.000         0.000         0.000
 U15            0.000         0.000         0.000         0.000         0.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 U6             1.000
 U7             0.000         1.000
 U8             0.000         0.000         1.000
 U9             0.000         0.000         0.000         1.000
 U10            0.000         0.000         0.000         0.000         1.000
 U11            0.000         0.000         0.000         0.000         0.000
 U12            0.000         0.000         0.000         0.000         0.000
 U13            0.000         0.000         0.000         0.000         0.000
 U14            0.000         0.000         0.000         0.000         0.000
 U15            0.000         0.000         0.000         0.000         0.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 U11            1.000
 U12            0.000         1.000
 U13            0.000         0.000         1.000
 U14            0.000         0.000         0.000         1.000
 U15            0.000         0.000         0.000         0.000         1.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 U16            1.000
 U17            0.000         1.000
 U18            0.000         0.000         1.000
 U19            0.000         0.000         0.000         1.000
 U20            0.000         0.000         0.000         0.000         1.000


           ALPHA
              F
              ________
                0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.62863564D+04    0.0000000    0.0000000  EM
              2 -0.62661906D+04   20.1657817    0.0032079  EM
              3 -0.62653912D+04    0.7994457    0.0001276  EM
              4 -0.62653242D+04    0.0670496    0.0000107  EM
              5 -0.62653166D+04    0.0075983    0.0000012  EM
              6 -0.62653152D+04    0.0013361    0.0000002  EM
              7 -0.62653149D+04    0.0003687    0.0000001  EM


SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES


     SAMPLE STATISTICS


           Means
              F             F_SE
              ________      ________
                0.000         0.455


           Covariances
              F             F_SE
              ________      ________
 F              0.791
 F_SE           0.001         0.001


           Correlations
              F             F_SE
              ________      ________
 F              1.000
 F_SE           0.033         1.000


PLOT INFORMATION

The following plots are available:

  Histograms (sample values, estimated factor scores, estimated values, residuals)
  Scatterplots (sample values, estimated factor scores, estimated values, residuals)
  Sample proportions and estimated probabilities
  Item characteristic curves
  Information curves
  Latent variable distribution plots

     Beginning Time:  23:11:35
        Ending Time:  23:11:36
       Elapsed Time:  00:00:01



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